|Publication number||US20040115586 A1|
|Application number||US 10/635,152|
|Publication date||17 Jun 2004|
|Filing date||6 Aug 2003|
|Priority date||19 Jan 1990|
|Also published as||DE69327661D1, DE69327661T2, EP0667753A1, EP0667753B1, US5683243, US6015289, US6244861, US6616444, US20020006597, WO1994010935A1|
|Publication number||10635152, 635152, US 2004/0115586 A1, US 2004/115586 A1, US 20040115586 A1, US 20040115586A1, US 2004115586 A1, US 2004115586A1, US-A1-20040115586, US-A1-2004115586, US2004/0115586A1, US2004/115586A1, US20040115586 A1, US20040115586A1, US2004115586 A1, US2004115586A1|
|Inventors||Craig Andreiko, Mark Payne|
|Original Assignee||Ormco Corporation|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (35), Referenced by (69), Classifications (28)|
|External Links: USPTO, USPTO Assignment, Espacenet|
 This application is a continuation of copending and commonly assigned U.S. patent application Ser. No. 09/431,466, filed Nov. 1, 1999, which is a continuation of U.S. patent application Ser. No. 08/960,908, filed Oct. 30, 1997, now U.S. Pat. No. 6,015,289,
 which is a continuation of U.S. patent application Ser. No. 08/456,666, filed Jun. 2, 1995, now U.S. Pat. No. 5,683,243,
 which is a divisional of the following U.S. Patent Applications, each filed Nov. 9, 1992, each by the inventors of the present application, each commonly assigned to the assignee of the present application, and each containing a specific reference to the other such applications:
 Ser. No. 07/973,973 entitled Method of Forming Custom Orthodontic Appliance, now U.S. Pat. No. 5,431,562,
 Ser. No. 07/973,965 entitled Custom Orthodontic Brackets and Bracket forming Method and Apparatus, now U.S. Pat. No. 5,454,717,
 Ser. No. 07/973,947 entitled Custom Orthodontic Archwire forming Method and Apparatus, now U.S. Pat. No. 5,447,432, and
 Ser. No. 07/973,844 entitled Method and Apparatus for Forming Jigs for Custom Placement of Orthodontic Appliances on Teeth and Jigs formed Therewith, now U.S. Pat. No. 5,368,478,
 all of which are hereby expressly incorporated by reference herein.
 The present invention relates to the orthodontic treatment of patients, particularly to the providing of orthodontic appliances in the treatment of such patients. The invention more particularly relates to the design, manufacture and/or use of orthodontic appliances for the straightening of teeth, and more particularly, to the automated design, manufacture and use of orthodontic appliances, especially custom orthodontic appliances based on individual patient anatomy.
 The orthodontic treatment of patients has as its fundamental objective the repositioning or realignment of the teeth of a patient in the patient's mouth to positions where they function optimally together and occupy relative locations and orientations that define a pair of opposed and cooperating planar, or nearly planar, smooth arches. The teeth of the two arches, the maxillary arch of the teeth of the upper jaw and the mandibular arch of the teeth of the lower jaw, when in an optimal or ideal position, contact the teeth of the opposite arch along a surface that is usually flat or slightly upwardly concave and commonly referred to as the plane of occlusion.
 The treatment applied to patients who have been diagnosed as having teeth insufficiently close to the ideal positions to require orthodontic correction includes an initial or rough procedure to overcome the more serious defects of tooth positioning followed by a finish treatment designed to bring the teeth as closely as possible or practical to their ideal positions. The rough treatment usually involves the movement of certain teeth through the use of any of a number of recognized techniques performed by an orthodontist, and sometimes procedures such as the extraction of certain teeth or surgery on the patient's jaw performed by an oral surgeon.
 In the finish treatment, the orthodontist applies an appliance, or set of braces, to the teeth of the patient to exert continual forces on the teeth of the patient to gradually urge them toward their ideal positions. The application of the appliance usually involves the attachment of brackets to the teeth, either with the application of adhesive to the teeth or the securing of bands around the teeth. The brackets are usually each provided with a slot through which an archwire is extended. One archwire is provided for the upper teeth and one for the lower teeth. Typically, the slots in the brackets are of rectangular cross-section and the archwire is of rectangular cross-section. The archwire installed in the slots of the brackets interconnects the teeth, through the brackets, and exerts forces on the teeth to translate or rotate them toward a finish position envisioned by the orthodontist.
 It has been recognized in the design and application of orthodontic appliances that an ideally designed and installed orthodontic appliance will present the slots of the brackets in a position to initially receive a pre-shaped archwire that will elastically deform to exert corrective forces on the teeth to urge them toward their finish positions. When in their finish positions, the archwire of the ideally designed appliance will no longer be elastically deformed, and will no longer exert forces upon the teeth. Achieving this objective has been inhibited by certain problems in the prior art.
 One problem presented by the prior art is that current orthodontic products are designed and manufactured to average anatomy. As a result, orthodontists are faced with the need to select what they perceive to be the brackets and archwires of the closest design to those required by a particular patient, and to modify the designs for treatment of the patient. Some of this modification may be performed when the appliance is initially installed, but almost inevitably modification is required during the course of treatment of the patient. This modification may take the form of the replacement of brackets, but most commonly requires a periodic bending and reshaping of the archwire as the treatment progresses. Thus, the treatment of the patient has become a manual feedback system in which the orthodontist monitors the progress of the patient's treatment and then readjusts the appliance, usually by bending the archwires, to correct the forces being applied to the teeth to bring the teeth to their ultimate positions, which are less than ideal. As a result, the patient may be subjected to treatment over a period that is longer than would be necessary if the appliance were initially made to the optimum design. In addition, the time required of the orthodontist for implementation of the treatment may be several times greater than it would be if modification of the appliance were unnecessary. Thus, the orthodontist is able to treat fewer patients and the cost of the treatment to the patient or to the orthodontist is increased.
 Location of the connection points for the appliance to the teeth also presents a problem in the prior art. Typically, brackets are bonded to the teeth and then interconnected by the installation of the archwires. This is done when the teeth are in their maloccluded positions, with the orthodontist having only a mental vision of where the finish positions of the teeth will be and where the brackets are to be placed to move the teeth to those finish positions. For more effective use of the appliance and to promote ease in cleaning the teeth, the orthodontist prefers to locate the brackets and archwires away from the gums. If they are placed too close to the tips of the teeth, however, they may interfere with the teeth of the opposite arch as the teeth approach their finish positions.
 Another problem of the prior art that has inhibited the selection or design of an ideal orthodontic appliance for the patient is the difficulty in arriving at an expression of the ideal finish position of the teeth. Orthodontists typically make models of the patient's mouth and, with the models and the aid of x-rays, determine a treatment to move the teeth to finish tooth positions. This process is time consuming and presents a source of error and inaccuracy. From the measurements and based on the judgment of the orthodontist, appliance components are selected to implement the prescribed treatment. In reality, the treatment of patients is in many cases more of an art than a science, with results ranging from poor to excellent, and generally variable.
 The need for custom manufactured orthodontic appliances and the use of automatic design techniques has been recognized by some, while others have advocated adherence to standard components and manual techniques in view of a perceived lack of practical custom appliance manufacturing and automated appliance design systems of the art.
 The development of automated custom appliance design systems has encountered several difficulties. These difficulties have included the task of developing an automated system that includes reliable and efficient decision making algorithms and techniques for automatically determining an ideal finish position of the teeth. Further, these difficulties have included arriving at an expression of appliance geometry in terms that can be efficiently produced by automated appliance manufacturing equipment. Furthermore, the prior art has not provided a way to accurately manufacture an appliance on an individualized basis in accordance with the appliance design. An additional problem in the automated design and manufacture of orthodontic appliances lies in the difficulty in designing the custom design system to take into account the professionally recognized parameters and criteria, derived over many years from the knowledge and experience of the practicing and clinical orthodontist, upon which diagnosis and treatment is based.
 Accordingly, there is a great need in orthodontics for a practical, reliable and efficient custom appliance automated design and manufacturing system, and method of providing custom appliances and treating patients therewith.
 A primary objective of the present invention is to provide a practical, reliable and efficient custom appliance automated design and manufacturing system and methods of automatically designing custom orthodontic appliances and treating patients therewith.
 It is a particular objective of the present invention to provide an automated custom orthodontic appliance design and manufacturing system that can be easily and reliably used by practicing orthodontists and that will make best use of the skills, knowledge and experience that the orthodontist possesses. It is a further objective of the present invention to increase the accuracy of the orthodontist's treatment, to render the use of the orthodontist's time more efficient, to eliminate sources of error and guesswork from the orthodontist's treatment of patients, and to efficiently, repeatedly and reliably perform automatically many of the routine steps in the diagnosis, prescription and implementation of orthodontic treatment and in the design and manufacture of orthodontic appliances.
 It is a further objective of the present invention to improve the practice of orthodontics by aiding the practitioner in achieving optimal finish treatment of patients and in more accurately determining and precisely achieving the finish placement of a patient's teeth. An additional objective of the present invention is to provide for the accumulation of data from individual patients for the analysis of the data to advance the orthodontic art.
 It is still another objective of the present invention to apportion the tasks involved in the design and manufacture of custom appliances most efficiently between orthodontist and appliance manufacturing facility in accordance with the scale and other particulars of the individual practitioner operation.
 According to the principles of the present invention, a system and method are provided which depart from traditional design and manufacture by designing orthodontic appliances around the anatomy of the individual patient. Further, unlike current orthodontic products that are designed and manufactured to average anatomy, the orthodontic products of the present invention and the methods of manufacturing and using them are tailored to the individual anatomy of the patient.
 In accordance with the preferred embodiment of the present invention, there is provided a computerized system and method with which finish positions of the teeth of a patient are derived from digitized information of anatomical shapes of the patient's mouth, an orthodontic appliance is automatically designed from the digitized shape information and the derived tooth finish positions, machine code is generated for production of the orthodontic appliance and communicated to NC machines, and the appliance is automatically fabricated with the machines in response to the machine code.
 In accordance with the preferred and illustrated embodiment of the invention, the digitized information is generated from measurements from the mouth of the patient, either taken directly or from a model thereof, and preferably includes information of the shapes of the individual teeth of the patient and of the patient's lower jaw.
 In the preferred embodiment, the finish tooth position derivation includes the derivation of one or more archforms, preferably conforming to a skeletal archform defined by the shape of the lower jaw. The appliance is also configured in accordance with the shape of the derived archform, preferably with a mandibular skeletal archform having size and shape conforming to that of the trough of the lower jaw. In the preferred embodiments, additional archforms are constructed using information of the shapes of the individual teeth and the lower jaw skeletal archform to define the positions of the buccal cusps and incisal tips of the mandibular teeth, the marginal ridges of the upper posterior teeth, and the lingual points of occlusion of the upper anterior teeth to position the teeth according to a preferred treatment plan.
 In certain preferred embodiments of the invention, the digitized data is taken by measurements of the patient's individual teeth and the data is reduced to certain landmark data that becomes key to effective and efficient arrival at highly preferred finish tooth positions. The individual teeth are arranged on the various derived archforms with mesial and distal contact points of adjacent teeth in contact. The spacing between the opposite contact points of each tooth are preferably extracted from a computerized image formed in horizontal plan views of the patient's teeth. Furthermore, relative locations of the incisal tips, marginal ridges, gingival contact points and the external surfaces of the teeth to which the appliance connects, for example, by the mounting of brackets, and which occlude with teeth of the opposite jaw, are determined by digitizing vertical profiles of the surfaces of the crowns of the teeth. This data is reduced to define contact points of the mandibular teeth with the lower jaw, such as the gingival center points, to define crown axes of the teeth, and other parameters that are amenable to manipulation with a simple and reliable algorithm in calculating the finish positions of the teeth. The landmarks also include inter-cusp and inter-ridge spacing measurements that provide a basis for prescribing arch expansion treatment with exactness based on the computer aided calculation of precise finish tooth positions. Further, the tooth position calculations provided improve upon prior orthodontic practice by preserving crown long axis inclination angles and setting the teeth to preferred crown long axis inclination angles for population groups according to seed values that are statistically improved upon by the present invention.
 In certain embodiments of the invention, images are digitized to produce the tooth and jaw shape data. Preferably, the images include a scanner which, in one form, generates a video image from which selected points are digitized to produce data from which finish tooth positioning and appliance design is carried out. Alternatively, three dimensional imaging of the teeth and jaw of the patient is carried out with laser or other scanner to form full three dimensional images of the teeth and jaw of the patient. The images may be formed from the patient's teeth and jaw or from a model thereof. Additional data is digitized by taking vertical profiles of the patient's teeth, either by tracing with a computer the three dimensional images generated with other scanners, or by scanning with a mechanical contact probe or with a non-contact probe the individual teeth of the patient, or model thereof. The data may be taken directly from the patient using CAT scans, MRI, positron emission tomography or other technique.
 Also in accordance with certain embodiments of the invention, the finish tooth positioning includes the establishment of cuspid rise criteria by rigorous calculations made from measured and statistical anatomical data so that the height of the cuspids and other teeth can be adjusted relative to each other so that the teeth can be positioned to guide the jaws into proper occlusion. With the present invention, numerical relationships are provided for cuspid rise that are an improvement of the prior art.
 In accordance with certain preferred embodiments of the invention, an archwire forming machine that is responsive to NC code is driven by signals generated by a computer that reads input data of anatomical shapes of the patient's mouth, is provided to automatically form an arcuate appliance that interconnects the teeth to move them toward their finish positions by rotational and translational forces applied in three dimensions each by the arcuate appliance. Generally, the arcuate appliance is an archwire, and the machine for forming the appliance includes an archwire forming machine that is responsive to NC code, is driven by signals generated by a computer that reads input data of anatomical shape of the patient's mouth, preferably of the patient's jaw and teeth, derives the tooth finish positions and archwire and bracket designs that will move the teeth to the calculated finish positions, and generates the machine code to produce the archwire in accordance with the design. Preferably, the archwires have shapes that conform to archforms related to the finish tooth positions, particularly to the shape of the patient's lower jaw, and is represented as a series of segments of a continuous archwire that each have a constant radius of curvature over the length of the segment, and that preferably join adjacent segments in a smooth transition, with the segments tangent where they join.
 Further in accordance with certain preferred embodiments of the invention, a bracket fabrication machine, also responsive to NC code, is driven by similar signals from a computer responsive to computer generated finish tooth position calculations and digitized tooth shape data. Preferably, the brackets have bases that mount on computer determined positions on the teeth and have slots to receive archwires that are inclined at computer determined angles. The fabrication of the brackets may include the formation of a slope and/or curvature to the mounting surfaces of the bases of the brackets, or, as with the illustrated embodiment, by cutting custom slots in the brackets. In the preferred embodiment, the design and manufacture of the archwires and brackets are interrelated so that the curve of the archwire is optimized to minimize curvature changes and the brackets are optimize to minimize their profiles, or the distances from the bases to the archwire slots. The calculations provide a basis for the selection of appropriate bracket blanks for the optimized appliance design.
 Additionally, in accordance with other aspects of the invention, one or more placement fixtures are manufactured from the input data and the calculated tooth positions for locating points on the teeth, preferably determined by the computer, for the connection of the appliance to the teeth, such as for the mounting of the brackets to the teeth. The fixtures preferably include a set of bracket placement jigs, one for each bracket that is to be mounted on a tooth, to position and hold the bracket to the tooth so that it can be secured thereto in a precise mounting location. The jigs of the preferred embodiment include a tooth profile or three dimensional surface that fits against the tooth to precisely locate the jig on the tooth and hold a bracket at a precise position and inclination thereon so that it can be secured to the tooth with adhesive.
 With the present invention, a custom orthodontic appliance is fabricated under the control of a computer directly from data taken from the teeth and/or jaw of a patient or a model thereof. The appliance so formed, when connected to the teeth of the patient, moves the teeth of the patient to precise calculated finish positions without the need for the orthodontist to bend archwires over the course of the treatment. As a result, the orthodontist's time is conserved, the treatment of the patient is achieved in a shorter amount of time and the finish positions of the teeth are more nearly ideal, and consistently so, than those achieved with the procedures of the prior art. Furthermore, the appliance fabricating processes result in the generation of data useful in establishing treatment techniques and criteria that will improve the practice of orthodontics.
 Further, movement of the teeth to the finish positions calculated in accordance with the present invention results in far more stable placement of the teeth than with other methods of the prior art which often experience movement of the teeth to inferior positions after the orthodontic treatment is terminated.
 These and other objectives and advantages of the present invention will be more readily apparent from the following detailed description of the drawings in which:
 FIGS. 1-1F are diagrams illustrating the preferred embodiments of the system of the present invention, of which:
FIG. 1 is a block diagram illustrating one preferred embodiment of an automated system for the design and manufacture of custom orthodontic appliances for the treatment of patients therewith according to the principles of the present invention.
FIG. 1A is an elevational diagram of a video graphics image forming embodiment of the data input portion of one embodiment of the scanner of the system of FIG. 1.
FIG. 1B is an elevational diagram of a laser scanner version of a three dimensional graphics imaging embodiment of a scanner of the system of FIG. 1.
FIG. 1C is an elevational diagram of a mechanical tooth profile probe scanner version of a two dimensional imaging portion of one embodiment of the scanner of the system of FIG. 1.
FIG. 1D is an isometric diagram of one embodiment of a bracket cutting device of the system of FIG. 1.
FIG. 1E is an isometric diagram of one embodiment of a wire forming device of the system of FIG. 1.
FIG. 1F is an isometric diagram of a bracket placement jig forming device of the system of FIG. 1.
 FIGS. 2-2Z are flow chart diagrams of the preferred methods of carrying out the present invention, of which:
FIG. 2 is a flow chart of one preferred embodiment of the process of the present invention performed with the system of FIG. 1.
FIG. 2A is a more specific flow chart illustrating the steps of the input procedure of automated tooth positioning and appliance design and manufacturing operation of the process of FIG. 2.
FIG. 2B is a more specific flow chart illustrating the steps of the analysis and tooth finish position calculating procedure of the automated tooth positioning and appliance design and manufacturing operation of the process of FIG. 2.
FIG. 2C is a more specific flow chart illustrating the steps of the custom appliance design procedure of the automated appliance design and manufacturing operation of the process of FIG. 2.
FIG. 2D is a more specific flow chart illustrating the steps of the custom appliance manufacturing procedure of the automated tooth positioning and appliance design and manufacturing operation of the process of FIG. 2.
FIG. 2E is a detailed flow chart illustrating the substeps of the identification data input step of the input procedure of FIG. 2A.
FIG. 2F is a detailed flow chart illustrating the substeps of the patient history and treatment data input step of the input procedure of FIG. 2A.
FIG. 2G is a detailed flow chart illustrating the substeps of the mandibular bone and horizontal tooth dimension data input step of the input procedure of FIG. 2A.
FIG. 2H is a detailed flow chart illustrating the substeps of the maxillary horizontal tooth dimension data input step of the input procedure of FIG. 2A.
FIG. 2I is a detailed flow chart illustrating the substeps of the individual tooth vertical profile data input step of the input procedure of FIG. 2A.
FIG. 2J is a detailed flow chart illustrating the substeps of the individual tooth profile analysis and landmark identification step of the analysis procedure of FIG. 2B.
FIG. 2K is a detailed flow chart illustrating the substeps of the cuspid rise calculation step of the analysis procedure of FIG. 2B.
FIG. 2L is a detailed flow chart illustrating the substeps of the mandibular preliminary horizontal tooth finish position calculation step of the analysis procedure of FIG. 2B.
FIG. 2M is a detailed flow chart illustrating the substeps of the best fit mandibular cusp arch equation calculation step of the analysis procedure of FIG. 2B.
FIG. 2N is a detailed flow chart illustrating the substeps of the calculation step of the mandibular tooth finish position on the best fit mandibular cusp arch equation of the analysis procedure of FIG. 2B.
FIG. 2O is a detailed flow chart illustrating the substeps of the maxillary horizontal tooth finish position calculation step of the analysis procedure of FIG. 2B.
FIG. 2P is a detailed flow chart illustrating the substeps of the mandibular archwire plane calculation step of the appliance design procedure of FIG. 2C.
FIG. 2Q is a detailed flow chart illustrating the substeps of the mandibular bracket slot inclination calculation step of the appliance design procedure of FIG. 2C.
FIG. 2R is a detailed flow chart illustrating the substeps of the maxillary archwire plane calculation step of the appliance design procedure of FIG. 2C.
FIG. 2S is a detailed flow chart illustrating the substeps of the maxillary bracket slot inclination calculation step of the appliance design procedure of FIG. 2C.
FIG. 2T is a detailed flow chart illustrating the substeps of the mandibular archwire and bracket slot in-out dimension calculation step of the appliance design procedure of FIG. 2C.
FIG. 2U is a detailed flow chart illustrating the substeps of the maxillary archwire and bracket slot in-out dimension calculation step of the appliance design procedure of FIG. 2C.
FIG. 2V is a detailed flow chart summarizing the substeps of the bracket placement jig shape calculation step of the appliance design procedure of FIG. 2C that is illustrated in more detail in the flowchart of the jig modification step of FIG. 2Z described below.
FIG. 2W is a detailed flow chart illustrating the substeps of the cubic spline curve fitting, spline to circle conversion and tooth placement calculation subroutines employed in placing teeth on calculated archforms in certain steps of the tooth positioning and appliance design and manufacturing operation of FIG. 2C.
FIG. 2X is a detailed flow chart illustrating the NC code generation and slot cutting substeps of the bracket manufacturing step of the procedure of FIG. 2D, and FIGS. 2X-1 through 2X-4 are more detailed flowcharts illustrating substeps of FIG. 2X.
FIG. 2Y is a detailed flow chart of the substeps of the wire bending code generation and wire manufacturing step of the appliance manufacturing procedure of FIG. 2D.
FIG. 2Z is a detailed flow chart illustrating the substeps of the jig manufacturing step of the appliance manufacturing procedure of FIG. 2D. FIGS. 2Z-1 through 2Z-6 are more detailed flowcharts illustrating details of substeps of FIG. 2Z.
 FIGS. 3-3C are illustrations of graphics computer images produced in the input procedure, in which:
FIG. 3 is an example of a computer display of a video image generated by the scanner of the system of FIG. 1 illustrating in a top plan view a mandibular model produced by the scanner of the type shown in FIG. 1A.
FIG. 3A is an example of a portion of a three dimensional digital image, illustrated in perspective, and produced by the scanner of the type shown in FIG. 1B.
FIG. 3B is an illustration similar to FIG. 3A of another portion of a three dimensional digital image produced by the scanner of FIG. 1B.
FIG. 3C is an example of a set of vertical tooth profile images produced by the scanner of FIG. 1C.
 FIGS. 4-4E are plan views of the teeth of the patient on tooth placement archforms at various stages of the tooth position calculation procedure of FIG. 2B, of which:
FIG. 4 is a geometric diagram illustrating a horizontal plan view data input screen showing diagrammatically the video image of FIG. 3 used as a template, with variables relevant to the digitization of data from the mandibular video image marked thereon.
FIG. 4A is a geometric diagram similar to FIG. 4 for the maxillary teeth.
FIG. 4B is a geometric diagram plotting horizontal mandibular archforms calculated through the analysis procedure of FIG. 2B.
FIG. 4C is a geometric diagram plotting horizontal maxillary archforms calculated through the analysis procedure of FIG. 2B.
FIG. 4D is a horizontal plan diagram showing the maxillary teeth in their finish positions.
FIG. 4E is a horizontal plan diagram showing the mandibular teeth in their finish positions and with the custom appliance in place.
 FIGS. 5-5P are mathematical calculation diagrams for reference in connection with spline to circle conversion and tooth placement routines of FIG. 2W, in which:
FIG. 5 is a horizontal plan diagram illustrating the placement of a tooth on an archform equation described in circle segment form.
 FIGS. 5A-5J are detailed diagrams of the spline to circle conversion and tooth placement subroutines.
 FIGS. 5K-5P are detailed diagrams of the tooth placement subroutine.
 FIGS. 6-6I are diagrams of tooth profiles illustrating landmark determination, tooth inclination and vertical positioning, in which:
FIG. 6 is an isometric image of a three-dimensional computerized representation, similar to FIG. 2B, of a molar showing the locations of alternative vertical labial-lingual profile planes and tooth profiles.
FIG. 6A is a mathematical tooth profile plot as illustrated on the computer screen of the system of FIG. 1 of a mandibular molar showing selected landmark parameters.
FIG. 6B is a mathematical tooth profile plot, similar to FIG. 6A, of a mandibular cuspid or incisor showing selected landmark parameters.
FIG. 6C is a mathematical tooth profile plot, similar to FIG. 6A, of a maxillary molar or bicuspid showing selected landmark parameters.
FIG. 6D is a mathematical tooth profile plot, similar to FIG. 6A, of a maxillary cuspid or incisor showing selected landmark parameters relevant thereto.
FIG. 6E is representation of a display, similar to FIG. 3C, of an array of mathematical tooth profile plots of all of the teeth, angularly oriented, with landmark parameters marked thereon.
FIG. 6F is representation of a display of an array of mathematical tooth profile plots, similar to a portion of FIG. 6E, of the mandibular teeth with working horizontal placement planes marked thereon.
FIG. 6G is mathematical tooth profile plot, similar to FIG. 6A, of a mandibular posterior tooth with relevant dimensional variables for placement of the tooth marked thereon.
FIG. 6H is mathematical tooth profile plot, similar to FIG. 6B, of a mandibular anterior tooth with relevant dimensional variables for the placement of the tooth marked thereon.
FIG. 6I is mathematical tooth profile plot, similar to FIG. 6H, of the tallest mandibular tooth.
 FIGS. 7-7D are diagrams for reference in connection with the finish tooth position calculation, of which:
FIG. 7 is an elevational diagram of the relationship of the jaws of a patient for illustration of cuspid rise occlusion calculation.
FIG. 7A is an enlarged view of a portion of FIG. 7.
FIG. 7B is a plan mathematical diagram illustrating certain of the mathematics of tooth placement on the mandibular offset arch.
FIG. 7C is a perspective diagram illustrating the relationship of the vertical tooth profile planes and relevant horizontal arch planes in the course of tooth finish position calculation.
FIG. 7D is a set of related elevational profiles of mandibular and maxillary teeth showing occlusal and overlap relationships in the course of tooth finish position calculations.
 FIGS. 8-8H are diagrams for reference in connection with the steps of the custom appliance design procedure, of which:
FIG. 8 is a diagram similar to FIG. 7D illustrating archwire plane and bracket slot design on positioned teeth.
FIG. 8A is an elevational diagram illustrating a bracket and slot configuration in connection with the diagram of FIG. 8.
FIG. 8B is a top view illustrating the relation of a tooth to an archform by placement routine of FIG. 2W.
FIG. 8C is a tooth profile diagram illustrating the slot in-out dimension calculation.
FIG. 8D is a perspective diagram illustrating the placement of a custom bracket onto a tooth with the use of a custom placement jig.
FIG. 8E is a plan diagram of a custom archwire for the appliance required to move the mandibular teeth to the finish positions illustrated in FIG. 4E.
FIG. 8F is a plan diagram illustrating the labial installed appliance on the teeth of the patient in their initial positions.
FIG. 8G is a plan diagram, similar to FIG. 8F, illustrating a lingual appliance installed on the teeth of the patient.
FIG. 8H is an elevational diagram illustrating an orthodontic lingual bracket of the appliance of FIG. 8G.
FIG. 8I is a top view of a bracket having a base slot curvature conforming to that of an archwire supported therein.
 FIGS. 9-9W are diagrams relating to appliance manufacturing steps, of which:
 FIGS. 9-9H relate to substeps of the bracket slot cutting code generation and bracket manufacturing step.
 FIGS. 9I-9W relate to the substeps of the bracket placement jig manufacturing step.
 The preferred embodiment of the invention provides a system and method for designing and manufacturing orthodontic appliances and for employing the appliances to orthodontically treat patients for the straightening of teeth. Unlike traditional orthodontic products, however, the appliances resulting from the practice of the present invention are designed around the anatomy of the individual patients. It further incorporates in its design criteria the parameters and professional treatment approaches of the treating orthodontists, and applies automated decision making processes in the appliance design that take into account the professionally recognized characteristics and anatomical landmarks of the patients.
 The overall configuration of the system 10 is illustrated diagrammatically in FIG. 1. The overall operations of the preferred method of the invention are illustrated in the flowchart of FIG. 2.
 In accordance with the preferred embodiment of the invention as illustrated in FIGS. 1 and 2, examination of a patient is performed by an orthodontist at the orthodontist's office for the purpose of assembling the information necessary to determine the patient's condition, prescribe the appropriate treatment, and specify the type of orthodontic appliance to implement the treatment. The information is then communicated to a remotely located appliance design and manufacturing facility where the design of a custom appliance for use in administering the treatment is carried out with the use of computer analysis. The appliance design, together with the information necessary for the orthodontist to install the appliance on the patient is then transmitted back to the orthodontist, who installs the appliance and administers the treatment in accordance with the appliance manufacturer's instructions and his own professional expertise.
 In accordance with alternative embodiments of the invention, digitization of anatomical information for computer input is performed either at the appliance design and manufacturing facility, by the orthodontist at his office, or preferably divided between the two. Similarly, the present invention contemplates the manufacture of the appliance to be performed at either the appliance manufacturing facility, at the orthodontist's office, or preferably divided between the two locations and in accordance with the analysis and design provided by the system of the present invention.
 The practice of the present invention involves the use of certain system hardware, tangible records of information, and communications paths described below in connection with FIG. 1 and related illustrations, and the performance of operations, procedures and steps described in connection with the flowchart of FIG. 2 and related diagrams, all as set forth in detail below.
 Throughout the description, references are made to tangible elements illustrated in the drawings and to actions performed by hand and by computer. In the description, numbers used to refer to structure or other tangible items illustrated in the drawings of the preferred embodiment appear in conventional form in the text, while numbers that refer to method steps in the illustrated flowchart are enclosed in parentheses in the following description. Letter symbols are used to refer to geometric or mathematical representations of variables, parameters, dimensions and values, input into or calculated by a computer, tie into equations and diagrams illustrated in the drawings, or correspond to computer codes or conceptual items set forth in the disclosure.
 Throughout this description, the various teeth of the patient, up to thirty-two in number, may be identified as TJSI, or T(J,S,I), where J designates the jaw (upper: J=U; lower: J=B), where S designates the side (patient's right: S=R; patient's left: S=L), and I designates the tooth by position relative to the jaw centerline as follows:
I = 1: Central Incisor I = 2: Lateral Incisor I = 3: Cuspid I = 4: First Bicuspid I = 5: Second Bicuspid I = 6: First (6 year) Molar I = 7: Second (12 year) Molar I = 8: Third (Wisdom Tooth) Molar
 The wisdom teeth are, however, customarily not involved in orthodontic procedure and usually are not yet present in the mouth of patients of treatment age. Furthermore, the second molars are often not involved in orthodontic treatment. To simplify the description and drawings, however, these designations are eliminated except where they are necessary to avoid ambiguity. Instead, the description below states verbally when it relates to, for example, the lower jaw (thus making use of the J subscript unnecessary) or where it relates to data or calculations relevant to a particular or either side of a jaw (thus making use of the S subscript unnecessary).
 Further, many values are calculated or measured for each tooth I, or for each of a limited group of teeth, as, for example, the mesio-distal width MDW or the mesial and distal extremities MX,Y and DX,Y as in the description of step (300) below. Wherever possible, the I designation is also eliminated and the description instead describes how the variables relate to the various teeth. In addition, where some values such as MDW discussed above relate to a tooth dimension or the distance between two points on a tooth (and may be represented by a scalar value in a computer), other values such as the points MX,Y and DX,Y relate to points M and D, respectively (and may be represented by a pair of X and Y coordinates in a computer). Usually, the subscripts designating the two coordinates are omitted, and where helpful to clarify the description, a single one of the subscripts X or Y may be used, such as with DX or DY, to designate that only the X or Y coordinate is employed, for example, in a calculation.
 Referring to the system diagram of FIG. 1, an orthodontic appliance manufacturing and patient treatment system 10 is illustrated. The system components are distributed between two locations, a doctor's office 11, and an appliance design and manufacturing facility 13. At the doctor's office 11, a patient 12, who requires orthodontic treatment, is examined by an orthodontist 14, who makes a diagnosis 15 of the condition of the patient and of the treatment, if any, needed. The examination involves the traditional application of the skill, knowledge and expertise of the orthodontist 14, and results in the preparation of detailed records 16 of the anatomy and condition of the mouth 18 of the patient, of the treatment proposed, and of other information necessary to the preparation of an orthodontic appliance.
 The records 16 prepared by the orthodontist include a physical model 20 from a mold of the patient's mouth 18, which includes a mandibular model 21 of the patient's lower jaw or mandible 22 and a maxillary model 23 of the patient's upper jaw or maxilla 24. The records 16 also include prescription 27 wherein the orthodontist sets forth a treatment to be applied to the patient and a result to be achieved by the treatment. The prescription 27 may also include a specification of techniques that are to be included in the treatment and a designation of an orthodontic appliance to be employed. The records 16 will further include identification information 17 and patient history information 19.
 In the illustrated embodiment of the invention, the records 16 are transmitted to the appliance manufacturing facility 13, at which the finish position of the teeth are calculated and a custom appliance 25 is designed and manufactured. The facility 13 is provided with one or more trained operators 28. In some embodiments, the physical model 20 itself is transmitted in the information 16 to the facility 13. In such cases, one of the primary functions of the operators 28 is to input digital information 26 from the records 16 into a computer 30 a. Another function is to operate the same or another computer 30 b to design the custom appliance 25, and to operate NC equipment 38 controlled by one of the same or another computer 30 c to manufacture the appliance 25. Where the inputting, design and manufacture are performed at the appliance facility 13, the computers 30 a, 30 b and 30 c may be the same computer 30.
 In other embodiments of the invention, the orthodontist 14 digitizes data from the model 20, in which case the inputting computer 30 is located at the orthodontist's office 11. In these embodiments, the digitized information 26, rather than the physical model 20, is transmitted to the appliance facility 13. The analyzing and appliance design computer is nonetheless preferably at the appliance facility 13.
 The entry of the information into the input computer 30 involves a digitizing of the information 16 to produce the digitized anatomical information 26 in machine readable form for analysis by the analyzing computer 30 b. The input computer 30 connected thereto by a scanner 33, which, in the alternative embodiments of the invention, includes equipment that employs one or more video cameras, mechanical probes, laser scanners, ultrasonic scanners, moire image scanners or other forms of imaging or measurement hardware that alone, or in combination with other such components, produce anatomical geometric information that describes the patient's teeth and jaw. The images may be three-dimensional or be made along a plurality of planes or other surfaces that can ultimately be combined to provide information in three dimensions.
 The combined information from the scanner 33 of the illustrated embodiment provides a basis for three dimensional analysis of the patient's teeth and from which calculations of finish tooth positions can be made. From the final positional calculations and tooth anatomy data, automatic design and manufacture of the custom orthodontic appliance 25 is carried out. In the illustrated embodiment, the data is imaged in a plurality of differently oriented two dimensional planes in the computer 30, then mathematically manipulated and combined in the computer 30 b to construct a three dimensional solution to the tooth positioning and appliance design problems.
 In a configuration in which the scanner 33 is connected to a separate dedicated inputting computer 30 is herein described, the functional equivalent of the inputting computer 30 may be included in circuitry within the scanner 33 itself.
 Preferably, the digital input process utilizes interactive methods by which an operator 28 uses a pointing device and digitizer to select particularly useful orthodontic parameters from graphics images produced by the scanner 33 on a screen 35 of a display connected to the inputting computer 30.
 In embodiments where some or all of the extraction of the digitized anatomical information 26 from the model 20, which may also be derived directly from the mouth 18 of the patient 12, is accomplished by the orthodontist 14 at the orthodontist's office 11, the information 26 is digitized by the orthodontist 14 then transmitted as part of the information 16 to the appliance design center 13. The transmitted information 16 is preferably transmitted from the orthodontist's office 11 to the appliance facility 13 by modem, but may be transmitted in any other available manner.
 An analysis and design computer 30 b, preferably at the appliance design facility 13, produces an archive diskette 34 that is formatted and written with all of the relevant information of the analysis and the history and prescribed treatment of the patient 14.
 The computer 30 b at the appliance facility 13 calculates, based on the digitized information 26, the final position of the patient's teeth, and the configuration of the appliance 25 required to move the patient's teeth to this final or finish position. As a result, calculated information for the patient is stored in a patient data file 36. From the calculations the computer 30 c produces CNC machine readable code 42 for operating NC manufacturing equipment 38 to produce the appliance 25. An instruction document or file 37 is also produced, either by the computer 30 b or the computer 30 c, of information to aid the orthodontist 14 in treating the patient 14 with the custom appliance 25.
 The manufacturing equipment 38 includes an appliance bracket cutting or forming machine 39 which produces custom brackets for the appliance 25 by cutting slots calculated angles and to calculated depths in slotless generic brackets. The machine 39 may also or alternatively shape the surfaces of the bracket bases. This provides the bracket design option of torquing the teeth by either the bracket slot or base, as may be best for various bracket materials.
 The equipment 38 also includes an appliance archwire bending or forming machine 40 which produces custom shaped archwires for the appliance 25 by feeding and bending wire of any one of several available materials and stiffnesses into the custom archwire shape. The equipment 38 may also include a machine for forming patient treatment components and hardware to aid in the manufacture or installation of the appliance 25. In the illustrated embodiment, this includes a machine 41 for the making of bracket placement jigs, which cuts each tooth crown portion of the tooth profile into a plastic form, along with a superimposed cutout of the positioned bracket, for use in accurately installing the custom brackets in their calculated positions on the teeth.
 The appliance manufacturing machines 38 may be connected directly to the analyzing computer 30 b or one or more may be connected to a separate manufacturing equipment controlling computer or machine controller 30 c. The computer 30 c may be located at the appliance facility 13 or, together with one or more of the appliance manufacturing machines 38, 40 or 41, be located at the orthodontist's office 11. In one preferred embodiment of the invention, one manufacturing computer 30 c and the bracket cutting machine 40 are located at the orthodontist's office, along with the scanner 33 and input computer 30, which may be the same computer as the manufacturing computer 30 c, while another manufacturing central computer 30 c, which may be the analyzing computer 30 b, the wire bending machine 40 and the jig forming machine 41 are located at the appliance facility 13. The optimum distribution of the computers 30, 30 b and 30 c and the scanner 33 and appliance manufacturing machines 38, 40 and 41 will be determined by the scale of the orthodontist's practice and the orthodontist's preferences. In the illustrated embodiment, the computers 30-30 c are IBM PC clones, with Intel 80386 or 80486 microprocessors and equipped with 80387 or 80487 math coprocessors, respectively.
 Certain components of the system 10 of FIG. 1 are described below in further detail.
 Three steps in the information input procedure (82), described below, involve the inputting into the computer 30, for analysis in digital form, of data concerning the shape of the mouth 18 of the patient 12 and of the shapes of the individual teeth therein. In these steps, digitized images and measurement data of the mouth 18 of the patient 12, preferably taken indirectly from the model 20, and digitized to form a three dimensional mathematical model of the patient's mouth 18. The mathematical model includes, in the preferred embodiment of the invention, the definition of certain parameters of the patient's lower jaw and individual teeth, and may include some information of the initial position and orientation of the teeth in the mouth 18 of the patient 12 for evaluating the magnitude of the treatment.
 The input information 26 is, in some embodiments of the invention, input as a full three dimensional image, and then simplified by reducing it to a plurality of curves in a plurality of differently oriented planes or fairly flat curved surfaces, each defined in the independent X-Y coordinate system of the respective surface or plane. In subsequent analysis, these planes are oriented, translated and rescaled with respect to each other in arriving at a derivation of the ideal finish positions of the teeth and the design of the custom appliance 25. In accordance with the preferred embodiment of the invention, curves and points on the contours of the jaw and teeth of the patient 12 are expressed in terms of accepted or generally applicable orthodontic parameters so that manual and automated decision making can combine and coordinate the best of orthodontic knowledge and experience with the efficiency and precision of computer analysis to minimize the use of the orthodontist's time, shorten the patient's treatment period and optimize the final treatment result.
 The various types of and components of the scanner 33 of various embodiments of the invention are described below.
 Video Scanning Data Input Assembly 43:
 One preferred form or component of the scanner 33 includes a video imaging assembly 43 as illustrated in FIG. 1A. The video imaging assembly 43 includes one or more video cameras 44 which each produce two dimensional images of the patient's mouth 18, preferably by forming an image of the model 20. When two or more are used together, the video assembly 43 produces stereo images capable of being resolved in three dimensions. In the illustrated embodiment of the invention, a single video camera 44 is employed to produce two dimensional video images of a plan view of the patient's lower or upper jaws 22 and 24, from the models 21 or 23, respectively, in generally horizontal X-Y planes. In accordance with this embodiment, other forms or components of the scanner 33 are preferably employed to produce information in a third dimension as described below.
 Referring to FIG. 1A, the video imaging assembly 43 is shown diagrammatically in side elevation at the appliance manufacturer's facility 13. The video imaging assembly 43, in its preferred form, is an operator-computer graphical interface that includes the video camera 44 connected to a video interface board 44 a in the input computer 30. The camera 44 is mounted on a stand 45 to face downwardly to form a top plan view of one of the halves 21 or 23 of the model 20, shown as the mandibular portion 21 in FIG. 3, on a horizontal support 46 attached to a base 45 a of the stand 45. The model half 21 or 23 is positioned on the support 46 such that the teeth face upwardly toward the camera 44 and so that the tips thereof lie generally in a horizontal plane that is maintained at a known fixed distance from the camera 44, so that the scale of the image formed by the camera 44 is known. This may be accomplished by mounting the support 46 on springs 46 a to urge the model half 21 or 23 upwardly against a transparent horizontal plate 45 b.
 The input computer 30 has connected thereto a pointing device which may be a mouse 47 a or, as shown, a mouse equipped digitizer board 47. The camera 44 produces a graphics image display 48 on the screen 35 of the computer 30, which an operator 28 may align with the assistance of a positioning grid G (FIG. 4A). With the digitizer 47, the operator selects points by positioning a curser 48 a on the screen 35 with the mouse 47 a. The selection results in the storage of X,Y coordinate data for each of the points selected. The points selected, in the description of the preferred process below, correspond to preselected boundary points of the teeth and, from the mandibular model 21, the lower jaw. From these top view boundary points, tooth and mandibular jaw dimensions are calculated. The calculated dimensions are used in analysis steps to calculate equations for the mandibular bone structure or mandibular trough MT and to calculate from the trough equation and the calculated horizontal dimensions and relative positions of features on individual teeth the finish positions of the teeth.
 In the alternative to selecting points from the video image display 48, the same points may be selected in the same manner from a plan view video image of a digitized three-dimensional computerized image of the teeth and jaws, such as an image formed by a laser scanner, moire interference pattern scanner, ultrasonic scanner, stereo video cameras, or other three-dimensional imaging apparatus. Sectional displays 55 a and 55 b of such a three-dimensional computerized image made with a laser scanner are shown in perspective in FIGS. 3A and 3B, respectively. Such a laser scanner is described in connection with FIG. 1B below.
 Laser Three-dimensional Image Input Assembly 51:
 One preferred form or component of the scanner 33 is the laser generated three-dimensional image forming assembly 50 illustrated in FIG. 1B. Referring to FIG. 1B, one of the halves 21 and 23 of the model 20 is mounted on a support 51 while laser 52 directs a laser beam 52 a onto the model 21 or 22. The laser beam 52 a is reflected and the reflected beam is detected by a sensor 53 composed of a photoelectric pixel array which uses a triangulation method to convert a change in position on the sensor into a change in distance between the assembly 50 and the model 21 or 23 mounted to translate parallel to the model 21 or 23 on a support 54 so as to scan the model with the laser beam. Equipment for producing images using laser technology in this manner is commercially available for forming computerized representations in three dimensions of manufactured and other objects. An example of equipment suitable for this purpose are the Cyber Scan™ Measurement System manufactured by Cyber Optics Corporation of Minneapolis, Minn. The images formed by such equipment would preferably include full detailed three-dimensional image data of the patient's lower and upper jaws 22 and 24, taken from the model 20, with the teeth in their original positions. The data is written in standard ASCII files by the equipment described and is readable by the input computer 30 a into the digitized information files 26.
 Illustrated in FIGS. 3A and 3B are two sections of the mandibular digitized model, and include a section 55 a showing the front mandibular incisors TBR1 and TBL1 of the patient 12, and a section 55 b showing the right mandibular second bicuspid TBR5 and first molar TBR6 of the patient 12. When such images are rotated to a horizontal plan view, a derivation of the same information that is available from the video imager 43 of FIG. 1A may be derived, and points may be selected therefrom for digitization automatically with software, or through an operator/computer interactive process as with the video scanner 43. The three-dimensional image 55 may be rotated into other orientations for the derivation of other information in various planes such as vertical tooth profile information that is derived with the mechanical scanner 57 described below. Additionally, other computerized procedures may be used to automatically derive information from the three dimensional image 55 with or without intervention or interaction by an operator.
 The scanner may also include, alternatively or in combination with other scanning equipment such as the video scanner assembly 43 of FIG. 1A or the laser scanning assembly of FIG. 1B above, a mechanical probe assembly 57 as illustrated in FIG. 1C. This entire assembly 57 is used in the illustrated embodiment of the invention in combination with the video scanner 43 to derive labial-lingual vertical profiles of the individual teeth of the patient from the model 20 to supplement jaw and horizontal tooth dimensional and shape information derived from a video image produced by the video scanner 43 from the model 20. Alternatively, portions of this assembly can be used to produce the same information from a three dimensional image 55 produced by equipment such as the laser scanning assembly 50.
 Referring to FIG. 1C, the probe assembly 57 includes a measurement probe 60 which is moveable over the individual teeth of the model 21 to produce an electrical signal that is digitized for computer input of point locations or profiles of the surfaces of the teeth in separate X-Y for each tooth. In the illustrated embodiment of the process of the invention, the information 26 preferably derived from the model 21 includes the tooth profiles curves PF1 in a labial-lingual plane viewed in a mesial-to-distal direction.
 The probe assembly 57 further includes a magnetic base 59 upon which is mounted the model 20, and from which extends an upstanding vertical support 58 on which the probe 60 is mounted. The probe tip 60 a is freely rotatable about a vertical axis on which its tip lies, while the probe itself is hooked to allow the tip to track recesses in the surfaces of the teeth of the model 21. The probe 60 is mounted on the support 58 to move in X and Y directions in a vertical plane preferably that extends through the support 58 and the probe 60. In this manner, the probe tip 60 a is positioned to scan the surface of a tooth of the model 21 along this plane. The probe 60 is linked to the support 58 through a pair of orthogonal measurement position transducers 61, which respectively generate electrical analog measurements of the positions of the tip of the probe 60 along respective ones of the X-Y orthogonal coordinates. The outputs of the transducers 61 are connected to circuitry that generates a sequence of periodic readings of the transducer measurements of the probe tip positions which are then digitized. These outputs are sent in along lines 61 a connected to input computer 30, preferably to a serial port thereof.
 In use, a half of the model 20, for example, the mandibular model 21, is mounted upon the magnetic base 59 on a steel surveyor's mount 62 which slides on the base 59 when lightly urged, but which otherwise holds its place thereon for precise positioning. The mount can be raised, lowered or tilted for leveling. In operation, the probe 60 is manually moved by an operator 28 or automatically to scan the surface of each selected tooth of the model 21 to produce profile curves PF of a section of each tooth as illustrated in FIG. 3C. The profile PF may be generated by any one of a number of commercially available off-the-shelf CAD/CAM or illustration software packages, such as VERSACAD™ available from Prime Computers, Inc. of Bedford, Mass. The computer programs described in the flowcharts herein is written for use with VERSACAD™ in CPL™, the programming language of therefor. The video images 63 of the profiles PF are displayed on the screen 35 and the digitized profiles are stored as part of the input information 26 in non-volatile memory of the computer 30.
 With the curves such as the profile PF so formed, an operator can, with the use of the pointing device 47, select, by positioning the cursor on the formed profile on the screen 35, point parameters of the tooth, the coordinates of which can be thereby input digitally into the computer 30.
 The manufacturing equipment 38 of the preferred embodiment of the invention includes: an appliance bracket cutting or forming machine 39 that custom forms the bracket bases to mount to the teeth and cuts archwire slots in the brackets at precise calculated positions and angles; an appliance archwire bending or forming machine 40 that precisely bends archwires to a shape that will cooperate with the custom brackets to apply corrective forces to the teeth until they are in their calculated finish positions; and a bracket placement jig forming machine 41 that manufactures bracket placement jigs that conform to the contours of the patient's teeth, as recorded in the profiles PF. These jigs are used by the orthodontist to precisely place the custom brackets at calculated positions on the teeth.
 The manufacturing equipment 38 is controlled by NC computer generated programs based on the data from the digitized input information files 26 and the calculated patient data files 36.
 Bracket Cutting Machine 39:
 Referring to FIG. 1D, a bracket slot cutting machine 39 is illustrated. The machine 39 includes a stationary base 72 on which is fixed a pair of upwardly extending workpiece support brackets 72 a to the top of which is pivotally mounted a workpiece or bracket support 73. On the support, a full set 80 a of brackets 80 for the custom appliance 25 is mounted, prearranged in an assembly or cartridge of twenty or twenty-four brackets. The support 73 pivots about an axis 73 a extending between the brackets 72 a. Connected to the axis 73 a is an angular positioning motor 74 which positions the support 73, and the brackets 80 mounted thereto, to any angular orientation with respect to the horizontal. The motor 74 has an input connected to the computer 30 c to set the inclination to the slot inclination angle of the bracket design in response to NC command codes.
 Also fixed to the base 72 and extending upwardly therefrom is a saw support bracket 72 b. To the top of the support bracket 72 b is a saw drive motor 75 and a set of three saw blade positioning linear drive actuator 76, including an X-drive actuator 76 x, a Y drive actuator 76 y, and a Z drive actuator 76 z through which a saw support arm 77 is supported to move respectively in the X, Y and Z directions, that is, in an X direction horizontally perpendicular to the axis of rotation 73 a of the bracket holder 73, in a Y direction horizontally parallel to the axis of rotation 73 a of the workpiece holder 73, and in a vertical Z direction. The actuators 76 have inputs connected to the computer 30 c to receive positioning signals from the computer 30 c to cut arcuate slots in the X-Y plane of the machine 39 in response to NC commands generated in accordance with a custom appliance design.
 At the remote end of the moveable arm 77 is a slot cutter assembly 77 a, driveably linked to the motor 75. The assembly 77 a has extending downwardly therefrom a rotatable cutter blade drive shaft 77 b, which has fixed to the lower end thereof a circular slot cutter blade 77 c. The blade 77 c lies in the horizontal X-Y plane and is of the thickness of the slot needed for the thickness of archwire selected. The archwires are typically rectangular in cross-section so that they are able to exert torque on the bracket, which accordingly will be provided by the saw blade 77 c with a slot of rectangular cross-section. The base of the slot will be cut, in accordance with the command signals from the computer 30 c, at an angle in the X-Y plane of the machine 39 that is tangent to the final curve of the archwire that it will receive. The base of the slot will be convex to accommodate the curve of the wire in the horizontal plane. The inclination of the bracket slot is achieved by the angle of the support 73 in response to control signals from the computer 30 c. The computer 30 c is programmed to account for changes in elevation of the bracket 80 due to the offset of the brackets from the support axis of rotation 73 a.
 Wire Bending Machine 40:
 The wire bending apparatus 40 is illustrated diagrammatically in FIG. 1E. Primary control of the apparatus 40 is preferably by an IBM PC clone, preferably with an 80386 or 80486 microprocessor with a math coprocessor, and with motion controller board 65 installed. The controller board 65 is, for example, an MC300 Motion controller 3-axis card manufactured by Motion Engineering, Inc. The MC300 is a dedicated motion control card which sends and receives signals to and from MC-OLS stepper interfaces 66 a and 66 b. MC-OLS stepper motor interfaces 66 a and 66 b send control signal commands to the stepper motor power supplies 67 a and 67 b, such as Compumotor S-Drive stepper power supplies #88-011483D, regarding rate and direction of motion of the motors.
 The power supply 67 a has an output connected to wire feed rollers 68, positioned on opposite sides of a wire guide 68 a, which guides archwire 69 to feed it from a continuous coil supply. The power supply 67 b has an output connected to a wire bending roller assembly or wire anvil 70.
 The controller 66 b additionally is adapted to receive feedback signals regarding position from a disc encoder 70 a, such as a Dynapar/Veeder Root #E1000A76500, which monitors the position of wire forming roller 70 b, providing closed loop control of a wire bending roller 70 b. The roller is driven by a wire anvil motor 70 c, such as a Compumotor #S/SX 57-102, through a drive screw 70 d, such as an Industrial Devices Corp. Electric cylinder #X995A-2-M56-MT1-200-PS. The screw 70 d converts the angular position of the motor 70 c into linear motion of the roller 70 b to deflect and bend the wire 69 as it is fed through the guide 68 a by the rollers 68.
 By coordinating the anvil 70 and the wire feed 68, formed archwires 64 of any planar shape are fabricated. The rollers 68 pinch the wire, forcing it to advance into the anvil 70. The roller 70 b of the anvil 70 moves up and down varying the radius and thus controlling the radius to which the wire is permanently deformed. In the formation of archwires with inflection points, that is that have bends in opposite directions, a second anvil would be provided opposite the wire 69 from the anvil 70 and controlled in synchronism therewith.
 A wire position sensor 71 is provided that inspects the finished archwire by comparing the width of the formed wire 64 to the desired width. The sensor 71 is mounted with respect to the anvil 70 and feed rollers 68 to detect the position of the formed archwire 64 when it is at the end of its forming cycle. This measurement provides a feedback signal that provides compensation for material property variations that effect the formed shape and the amount of over-bending required. The sensor 71 sends information back to the computer 30 c as to whether the wire 64 is acceptable or over-bent or under-bent. If the wire is either over or under-bent, the computer 30 c calculates the correction required and incrementally modifies the signals through the interfaces 66 a and 66 b to provide compensation to progressively correct successive archwires 64 until the result of the signal from the sensor 71 is deemed acceptable by the computer 30 c.
 Bracket Placement Jig Forming Machine 41:
 The bracket jig forming equipment 41 is preferably a standard NC mill configured as illustrated in FIG. 1F. The machine 41 includes the standard mill 81, having a downwardly projecting rotary tool head 81 a on which is mounted an endmill tool 81 b of, for example, 0.020 inches in diameter, where 0.022 inch archwire is used, and, for example 0.016 inches in diameter where 0.018 inch archwire is used.
 The mill 81 is either connected to a controller which will have been loaded with CNC program code 42 prepared by the computer 30 c or will be directly connected to the computer 30 c. The mill 81 is provided with a tool support 81 c to which a set of circular ABS plastic jig blanks 83, usually twenty or twenty-four in number, are fed by a feeding mechanism 81 d, equipped with a magazine 81 e of the sets 83 a of jig blanks 83. The tool head 81 a is moveable vertically to bring the tool 81 b into contact with the blanks 83 and horizontally in the X-Y directions in accordance with the tool path instructions from the code 42.
 In the preferred and illustrated embodiment of the invention, the overall configuration of which is illustrated diagrammatically in FIG. 1, the full custom system 10 is operated to produce the orthodontic appliance 25 based on the individual anatomy of the patient 12. One preferred method of the invention is represented by the operations and procedures illustrated in the flowchart of FIG. 2.
 The method of the present invention, in its preferred embodiment, includes three general operations. The first operation, is (85) a patient evaluation operation performed by the orthodontist 14 at the doctor's office 11 on the patient 12. This operation includes the traditional professional diagnosis and general prescription of treatment. According to the present invention, the evaluation operation (85) is followed by (87) a computer aided analysis and appliance design and manufacturing operation performed, preferably at least in part, at the appliance facility 13 to produce the custom appliance 25, and in turn followed by a patient treatment operation (89), which includes treatment of the patient 12 by the orthodontist 14 at the doctor's office 11, with the installation and use of the appliance 25.
 Referring to the system diagram of FIG. 1 and the flow chart of FIG. 2, the orthodontic evaluation operation (85) is performed at a doctor's office 11. The operation (85) includes the procedures (90) of the examination of a patient 12, (91) the preparation of the model 20 of the patient's mouth and teeth, (92) the prescription by the orthodontist 14 of treatment, (93) and communication with the appliance facility 13.
 During the examination procedure (90) the patient 12, who requires orthodontic treatment, is examined by an orthodontist 14, who makes a diagnosis of the condition of the patient and of the treatment, if any, needed. Based on the diagnosis 15, the orthodontist or doctor 14 assembles the information 16 that is necessary to implement the prescribed treatment.
 In assembling the information 16, the orthodontist 14 (91) prepares a model of the patient's mouth 18, usually a physical model 20 from a mold of the patient's mouth, in its initial condition at the time of the diagnosis 15. The model 20 includes the mandibular model 21 of the patient's lower jaw or mandible 22 and the maxillary model 23 of the patient's upper jaw or maxilla 24.
 Then, further based on the diagnosis 15, the orthodontist 14 (92) prescribes a particular treatment and generates a prescription 27 in a tangible record form.
 The orthodontist 14 then (93) communicates the information 16, for example, by transmitting the model 20, the prescription for treatment 27, a record of information 17 identifying the doctor 14 and the patient 12, together with information 19 containing statistical and historic data of the patient 12, to an appliance design facility 13, at some remote location. At the appliance design facility 13, the information 16 is digitized and input into the computer 30 for analysis.
 Alternatively, the orthodontist 14 may convert the information 16 to digital computer readable form and transmit the digitized information to the appliance design facility 13. In this alternative, the system 10 would be configured with the input computer 30 located at the orthodontist's office 11, and the orthodontist 14 or assisting personnel would perform portions of a data input procedure (94) described below.
 When the information 16, which includes, for example, the model 20, the prescription 27 and the information 17 and 19, are received either at the appliance system manufacturer 13 or is ready to be digitized at the orthodontist's office 11, (87) an analysis, finish tooth position calculation, and orthodontic appliance design and manufacturing operation is begun. In the operation (87), the information 16 is processed and the custom appliance 25 for moving the patient's teeth to an optimum final or finish position in accordance with treatment prescribed by the orthodontist 14 is produced.
 The operation (87) includes the procedures of (94) inputting into a computer the information 16 from the orthodontist 14, in digital form, (95) analyzing with the aid of computer 30 b the input digitized information to arrive at the finish position of the teeth, (96) designing with a computer a custom orthodontic appliance in accordance with the computer analysis, (97) manufacturing the custom appliance 25 in accordance with the computer assisted design with the aid of computer controlled machinery, and (98) communicating the custom appliance 25 and accompanying instructions to the orthodontist 14.
 In accordance with certain embodiments of the present invention, some or all of the appliance manufacturing step (97) can be performed at the facilities 11 of the orthodontist 14, in which case the communicating step (98) would involve the communication of machine readable code, in lieu of some or all of the completed custom appliance 25, from the design facility 13 to the orthodontist 14.
 (94) Input Procedure:
 In the input procedure (90) as illustrated in the flowchart of FIG. 2A. In the procedure (94), the received information 16 is input, in the illustrated embodiment by operator 28 at the design facility 13, into a computer 30 in digital form. Even where the inputting is performed by operator at the design facility 13, some information 16, such as the information 17 and 19, may be supplied by the orthodontist 14 in machine readable form and input directly into the computer 30. The input procedure (94) includes five steps (100)-(500), the substeps of which are described in detail in connection with the flowchart details of FIGS. 2E-2I below. The steps of the input procedure (90), in the illustrated embodiment, also include certain substeps that are part of the function of the analysis step (92) but are more conveniently performed at the time the information is entered into the computer.
 The input steps (100) and (200) involve the entry of background information assembled by the orthodontist 14. In the input steps (300), (400) and (500), tooth and jaw positions and profiles are defined in terms of orthodontic parameters and landmarks that can be later analyzed by computer to best implement the orthodontic knowledge, skill and experience embodied in the prescription 27 and of the orthodontic profession while efficiently automatically producing a optimum result. These steps of the input procedure (90) include:
 (100) The inputting of the doctor-patient identification information 17 in digital form into the computer 30 a:
 This information is used to identify the records of the patient and the products produced.
 (200) The inputting of patient background information 19 in digital form into the computer 30 a:
 This information is used in part in calculating the finish position of the patient's teeth in accordance with genetic characteristics. Sex and race, for example, are used to assign certain seed values such as the inclination of the axes of the individual teeth of the patient 12 to an arch plane in step (625), which is used to determine an offset for tips of the teeth from the jaw bone or gum line.
 This information also includes diagnostic determinations and treatment option decisions made by the orthodontist 14, such as determinations to extract teeth, or employ optional treatment norms.
 (300) The inputting into the computer 30, from a top view image of the patient's mandibular model 21, the mandibular jaw shape and tooth dimensional information:
 In implementing a treatment to correct the tooth alignment of the patient 12, the mandible 22 is the logical starting point because it is a solid bone and has relatively little pliancy. By contrast, the maxilla or upper jaw 24 is composed of segments held together by sutures which do not fuse until mid or late teens.
 Furthermore, these sutures can be separated by the orthodontist even after the point of initial fusion by simple and commonly known clinical techniques. These anatomical factors require that the orthodontist 14 make relatively small changes in the mandibular bone 22 and the preponderance of skeletal changes in the maxilla 24. For this reason, the position of the mandibular trough MT therefore taken as a constraint on the positions of the roots of the lower teeth.
 In step (300) information is input for use, in part, to define from the patient's lower jaw bone the shape of the mandibular trough MT, which serves as the first constraint in arriving at the finish position of the teeth. In one embodiment, this is accomplished by superimposing a predefined grid G on a video or graphics image of the mandibular trough (from FIG. 3) in the manner illustrated in FIG. 4. In addition, the distances between the mesio-distal extremities, or mesio-distal widths MDW, that is, their contact points with adjacent teeth, in a horizontal plane, are input. These determine the total length of the dental arch and the relative center-to-center spacings of the teeth along the arch.
 A mandibular trough equation MTE is derived, and may be converted to a symmetrical equation SMT As a starting point toward calculating finish tooth position, the mesio-distal widths of the mandibular teeth are mathematically placed on the trough equation. This is explained more fully below in connection with FIG. 4.
 In the above and in many archform calculations below, a cubic spline equation form is used initially in fitting a curve to data points, then converted to a circle segment equation that provides advantages in the analysis and design process and in the final calculations needed to operate NC manufacturing equipment. This is explained below in connection with FIG. 5 et seq.
 Measured initial contra-lateral cusp spacing data are generated for use by the orthodontist 14 in evaluating the custom design and treatment parameters resulting from the final calculations below.
 In some embodiments, horizontal profile data of the lower jaw may be input in this step, additional landmarks in the horizontal plane may be identified, or full three-dimensional images of the teeth and lower jaw may be made, for example, as discussed in the descriptions of FIGS. 1A-1C above.
 (400) The inputting into the computer 30, from a bottom view image of the patient's maxillary model 23, maxillary tooth dimensional information:
 The shape of the maxilla, which is made of a segmented bone, is a variable capable of being altered orthodontically in response to final tooth position calculations as set forth below. Therefore, its initial shape and initial maxillary tooth position is relevant only in evaluating the feasibility of the amount of alteration required and the type of treatment to be used.
 In step (400), information is input into the computer 30 c of maxillary jaw shape and tooth dimensional information from the maxillary model 23. This information is used in part to determine the mesiodistal widths MDW of each upper tooth, in a horizontal plane, and to determine the total length of the dental arch and the relative center to center spacings of the teeth along the arch.
 Measured initial contra-lateral cusp and central groove/fossa spacing data are generated for use by the orthodontist 14 in evaluating the custom design and treatment parameters resulting from the final calculations below.
 As with step (300) above, in some embodiments, horizontal profile data of the upper jaw may be input in this step, additional landmarks in the horizontal plane may be identified, or full three-dimensional images of the teeth and lower jaw may be made, for example, as discussed in the descriptions of FIGS. 1A-1C above. In these embodiments, techniques such as those described in step (500) may be employed in the horizontal plane in steps (300) and (400).
 (500) The inputting of individual tooth elevational profile information from the two halves of the model 20:
 The tooth profile information can be generated using computer analysis or interactive computer imaging from three-dimensional images, if employed, as illustrated in FIG. 3A formed with scanners such as illustrated in FIG. 1B, or with the use of the probe assembly 57 of FIG. 1C from the physical model 20 of the jaw. Use of the probe assembly 57 is herein described.
 Rapid reduction of tooth shape information to important dimensions and landmark data for efficient and realizable calculations of finish tooth position is achieved by imaging carefully selected profiles of the teeth. Profiles are produced by outlining the tooth crown surfaces along a vertical plane or other similarly oriented surface that extends in a labial-lingual direction generally perpendicular to the arch of the teeth in the respective jaw. For the single cusp anterior teeth, this surface is generally a surface bisecting the tooth and through the crown long axis CLA of the tooth. For multiple cusp teeth, the same generally applies except modification or displacement of the surface is intelligently made on some teeth to pick up the highest cusp or a marginal ridge that is relevant to development of the proper occlusion.
 For most calculations, as set forth in the detailed explanation below, the tooth features profile can be assumed to be on a plane through the tooth centerline, even when they are not. With the features selected herein, such assumptions result in errors that are still much smaller than those accepted in conventional methods. In other calculations, the precise position of a feature must be considered, and provision for such considerations are made in the certain embodiments of the invention.
 For each tooth, profile data is taken in separate X-Y coordinates that relate only to the selected surface or plane. In the course of the analysis and calculation of finish tooth position, these planes are separately translated and reoriented with respect to those of the other teeth and those of the trough and archforms, in several steps, until the ultimate interplane relationships are established.
 (95) Analysis and Tooth Positioning Procedure:
 The computer analysis procedure is illustrated in the flowchart of FIG. 2B. In the computer analysis procedure (95), the digitized information input by the input procedure (94) is analyzed to calculate the finish position of the teeth, so that the custom appliance 25 can be designed in computerized design procedure (96) and manufactured in computer controlled manufacturing procedure (97). The analysis procedure (95) includes six steps and subroutines (600)-(1100), the substeps of which are described in detail in connection with the flowchart details of FIGS. 2J-2O below. These steps include the following:
 (600) The dental analysis step in which the orthodontic landmarks of the teeth are identified:
 A minimum number of points on the tooth profiles are selected that are sufficient for determining the contact points between teeth that are relevant to finish tooth position calculation and appliance design. These points are selected such that the calculations made from them are relatively insensitive to measurement errors in the input of the data in step (500). From the selected points, for each tooth, other parameters are derived, including an incisal center point ICP, a gingival center point GCP and the crown long axis CLA through the ICP and GCP, as explained below in connection with step (600) and FIG. 6 et seq.
 In order to determine the relationship between the crown long axes and archwire planes, twenty-four of each crown type were removed from a set of orthodontic casts and sectioned along the mid-sagittal plane. These crowns were then mounted and projected at twenty times magnification on an optical comparator. Tracings were then made of these profiles. As a result, a procedure was determined for use to establishing the crown long axis inclination angles to produce the desired occlusion, and seed values were tabulated and correlated with data such as the sex and race of the patient as entered in step (200). As a result of this analysis, preferred crown long axis inclination angles are produced with the present invention that are an improvement over the facial inclination angles employed in the prior art.
 From the tabulated data, angles of inclination LAIs of the crown long axes CLAs of each of the teeth of each jaw are set relative to the plane that contains the mandibular trough equation MTE. This plane is parallel to a facial axis plane FAP used in clinical studies through a clinically defined facial axis FA of a tooth. These LAIs are later used to determine the horizontal offsets from the MTE of the tips of the lower teeth in step (1000) below, as well as the maxillary tooth placement in step (1100). The rotation of the inclination angle places new Y coordinates of each of the tooth profile planes established in step (500) parallel, and the X axes of these planes parallel to the same plane but with their relative horizontal orientations and relative vertical positions yet to be determined. Once the teeth are rotated to their finish inclinations, precise crown heights, incisal and cusp tip locations, and other points and contours of the tooth surface are precisely defined for intertooth contact and appliance design and positioning calculations.
 As an example, for the maxillary bicuspids and molars, a marginal ridge elevation MRE is determined for later use in calculations relative finish positions of the upper and lower teeth.
 (700) The cuspid rise determination step in which the occlusion of the upper and lower teeth is defined:
 The orthodontist 14 will have selected the technique to be used to guide the teeth of the patient into occlusion as the jaws come together. Depending on the selected occlusion technique, either all or part of the occlusion is brought by a rise of the cuspids above that of the other teeth, to thereby initiate contact between the upper and lower teeth which aligns the two arches as the jaw closes. Most orthodontists prefer to accomplish this with the rise of the cuspids.
 From anatomical studies, data is employed and the amount of cuspid rise, or other cusp rise if selected, that is necessary to clear the buccal cusp height BHC of the teeth, which is determined from the landmark data of step (600).
 (800) The mandibular tooth placement step in which the plane of the mandibular teeth is defined and the teeth are positioned with respect to the mandibular trough:
 The step (800) accomplishes the preliminary mathematical construction of the mandibular occlusion. This step first calculates the positions of the mandibular teeth to place their tips in an occlusal plane pending final refinement of the placement.
 The starting point for the mandibular tooth placement is to assume tooth positions that place the teeth with their crown long axes CLAs intersecting the plane of the mandibular trough on the mandibular trough equation MTE. This satisfies the condition that the mandibular teeth are set in the bone of the lower jaw. The CLAs of the teeth are also inclined at the seed value angles LAIs established in step (600).
 Next, the positions of the teeth are adjusted vertically to place the tips of all of the mandibular teeth, except the cuspids, in the same plane. The tips of the mandibular cuspids are set to extend above the plane of the tips of the other mandibular teeth by a distance according to the cuspid rise criteria selected, preferably by setting the distance equal to one third of the total cuspid rise, as calculated in step (700).
 Then, a horizontal OFFSET from the MTE, generally in the labial direction, is calculated trigonometrically for each mandibular tooth from its crown height above the mandibular trough and its long axis inclination angle LAI. This calculation results in a mandibular trough offset equation MO, which is an outward radial expansion of the MTE. The MTE was defined in the form of a series of circle segments in step (300). The expanded MO equation is a discontinuous arch constructed by adding the respective OFFSET of each tooth to the radius of the circle segment of the MTE with which the midpoint of the width of the tooth is associated.
 The teeth are then placed on the offset equation MO beginning with the placement of the central with its mesial contact point on the mandible centerline and the tooth midpoints on the MO. Then moving distally, the remaining teeth on the same side of the mandible are placed on the MO with their mesial contact points MCP in contact with the distal contact point DCP of the previous tooth. The same procedure is employed for the teeth on the other side of the mandibular arch.
 An alternative further refinement would consider the vertical position on the teeth of their widest points and, considering also the inclinations of the teeth, make a trigonometric adjustment so that the tooth contact points are spaced by the tooth widths MDW at the height of their actual widest points, rather than assuming the teeth contact in the plane of their tips.
 (900) The best fit cusp step in which the best fit equation is derived for mandibular arch:
 In this step, a continuous curve is derived using statistical methods to produce a best fit buccal cusp equation BFBCE from the disconnected line segments of the MO. This is also illustrated in FIG. 4A. In the embodiment described below, a Bezier equation is used. A cubic equation is then generated from resulting data points that define the best fit equation. The cubic equation of the BFBCE is then converted to circle segment form as with the MTE above.
 (1000) The mandibular teeth placement step in which the positions of the mandibular teeth are calculated for placement on the best fit arch equation:
 The positions of the lower teeth are then recalculated to move the teeth horizontally, parallel to the MOC, such that the incisal center points ICP lie on the BFBCE. For incisors and cuspids, the ICPs are the tips of the teeth in the profile planes of steps (500) and (600). For the bicuspids and molars, the ICPs are the buccal cusp tips of the teeth. For purposes of placement of the teeth on the BFBCEor other archform, the ICPs are assumed to lie midway between the mesial and distal contact points of the respective teeth. Accordingly, tooth placement is achieved by moving the teeth normal to the circle segment associated with these ICPS. This recalculation of position has the effect of moving the roots of the teeth normal to the arch associated with their ICPs, either labially or lingually, such that their ICPs fall on BFBCE, when viewed from above.
 This placement is the finish position of the mandibular teeth.
 (1100) The maxillary placement step in which the maxillary arch is derived for occlusion with the placed mandibular teeth:
 This step fits the positions of the maxillary teeth to the already positioned mandibular teeth. The maxillary teeth have not yet been positioned with respect to any equation, but the inclination angles of their dimensions and crown long axes CLAs have been determined in step (600). This positioning involves setting the tips of the maxillary teeth on the BFBCE, with certain modifications to the equation and the placement criteria to account for the way the different types of teeth occlude.
 In adjusting maxillary tooth positions, the cuspids, the anterior teeth and the posterior teeth are treated separately to bring their relevant contact surfaces into three different respective arches that are then aligned relative to each other.
 Since the anterior teeth do not occlude incisal edge to incisal edge, the BFBCE is modified to take into account the distance from the BFBCE to the labial contact points of the mandibular incisors and laterals, plus a horizontal or labial clearance, with the maxillary teeth. This defines the points of occlusion with the maxillary anteriors, at the intersection of their lingual surfaces with the plane of occlusion MOC. These points lie in a maxillary anterior contact arch form MAAF. This equation is calculated by expanding the BFBCE, by enlarging the radii of the circle segments of which it is made up, to account for these tooth dimensions and the clearances.
 The vertical positioning of the maxillary anteriors and cuspids is then performed based on the vertical occlusion methods that have been prescribed, establishing an overlap for the incisors and cuspid rise as determined in step (700). This defines the vertical position of the maxillary cuspids and anteriors with respect to the MOC, and thereby defines the incisal overlap or overbite.
 Placement of the maxillary posterior teeth places the intersections of the marginal ridges and the central grooves from steps (400) to (600) the cusps of the mandibular teeth with which they will occlude. The maxillary tooth movements needed to achieve this occlusion are applied to calculate a central groove marginal ridge arch form CGMRAF by modifying the BFBCE. The cusp tips of the maxillary cuspids are placed between the archforms of the incisors and of the posteriors, for example, by averaging the distance from the BFBCE to the MAAF and to the buccal cusp of the first maxillary bicuspid, by placing the cuspid mesial and distal contact points in contact with the adjacent teeth, by calculating a clearance as was done for the incisors or by some other criteria. The archforms for the maxillary tooth placement are illustrated in FIG. 4B.
 The vertical positioning of the remaining teeth takes into account the occlusion and other prescription information input in step (200). The remaining calculations are set forth in detail below.
 (96) Appliance Design Procedure:
 The appliance design procedure (96), as illustrated in the flowchart of FIG. 2C, calculates the dimensions of the appliance components in a form capable of being translated into NC codes for operating NC machinery for production of the appliance components, such as the brackets and archwires and also placement jigs for installing the brackets in the proper positions on the teeth of the patient. The appliance design procedure (96) includes the following steps (1200) through (1800), which are further illustrated in the detailed flowcharts of FIGS. 2P-2V:
 (1200) The mandibular archwire plane step in which the plane of the archwire for the mandibular teeth is defined in relation to the teeth of the mandible:
 Where labial brackets are to be applied, as illustrated in FIG. 8, a plane is selected for the mandibular archwire that avoids interference with the mandibular archwire and brackets with the maxillary teeth, which overlap on the labial side of the mandibular teeth. Where lingual brackets are to be applied, this step is performed to define a maxillary archwire plane to avoid interference between the lingually mounted maxillary archwires and brackets with the mandibular teeth that overlap on the lingual side of the maxillary teeth.
 This step involves the selection of the archwire plane and defines it in mathematical relation to the MOC. Once defined, the bracket positions on the teeth are determined such that the archwire slots will lie within the dimensional limits of the bracket. Where possible, it is preferable that the archwire lie in a literally flat plane and be symmetrical about the midline of the arch. As such, the archwire will be properly shaped for installation with either side facing upward.
 (1300) The mandibular slot inclination step in which the angles of the slots of the mandibular tooth brackets of the appliance are calculated:
 The slot inclination angle for the mandibular brackets is calculated from the angle between the mandibular archwire plane and the angle of the mandibular tooth surface to which the base of the bracket is to be mounted. The slot inclination angle may be achieved by cutting the full angle into the slot, by inclining the bracket base, or by both of these methods.
 (1400) The maxillary archwire plane step in which the plane of the archwire for the maxillary teeth is defined in relation to the teeth of the maxilla:
 The maxillary archwire plane in the case of labial appliances, and the mandibular archwire plane in the case of lingual appliances, has few constraints on its position and may be selected based on cosmetic considerations. It is usually selected as a plane midway on the crown of the maxillary teeth. It is therefore normally not parallel to the mandibular archwire plane. Once defined, the bracket positions on the teeth are determined such that the archwire slots will lie within the dimensional limits of the bracket.
 (1500) The maxillary slot inclination step in which the angles of the slots of the maxillary tooth brackets of the appliance are calculated:
 The slot inclination angle for the maxillary brackets is calculated from the angle between the maxillary archwire plane and the angle of the maxillary tooth surface to which the base of the bracket is to be mounted. The slot inclination angle may be achieved by cutting the full angle into the slot, by inclining the bracket base, or by both of these methods.
 (1600) The mandibular archwire and bracket in-out dimension calculation step in which the slot depth and bracket geometry is calculated for the mandibular tooth brackets:
 For each bracket, the deepest and shallowest slot depths is determined to develop a window into which the archwire must pass, as illustrated in FIG. 8A. Then the smoothest archwire curve that will pass between the depth limits is determined. The smoothest curve is considered to be one with the least variation in radius changes along the curve, and preferably with no inflection points. A cubic spline equation is used to fit the points and the equation is then converted to one of circle segment form.
 (1700) The maxillary archwire and bracket in-out dimension calculation step in which the slot depth and bracket geometry is calculated for the maxillary tooth brackets:
 As with the mandibular slot depth calculations, for each maxillary bracket, the deepest and shallowest slot depths is determined to develop a window into which the archwire must pass. Then the smoothest archwire curve that will pass between the depth limits is determined. Here to, the smoothest curve is considered to be one with the least variation in radius changes along the curve. A curve with no, or the least number of inflection points is preferred. A cubic spline equation is used to fit the points and the equation is then converted to one of circle segment form.
 (1800) The bracket placement jig designing step in which placement jigs are designed for use in properly positioning the custom designed brackets on the patient's teeth:
 After the brackets and archwires are completely defined as in the above steps, with the depth and angle of the slots finalized for the positioning of the brackets on the teeth and the shape of the desired archwires are described mathematically, bracket placement jigs are designed that will be used to assist the orthodontist in placing the brackets at the proper locations on the teeth. The designing of the jigs, in the preferred embodiment, is carried out in the software that generates the NC machine code in the performance of the jig manufacturing step (3500) below. This deferring of the jig design allows for consideration of appliance hardware modifications that may be made in the course of the bracket and archwire forming steps (3000) and (3200), respectively.
 The provision of the bracket placement jigs furthers a goal of the practice of orthodontics to treat cases to occlusal perfection with the least amount of effort, discomfort and time expended. The portion of this goal that can be accomplished by appliance design and manufacture has been described above. While the individualized appliance geometries thus defined will be fabricated, the ability to place the bracket portion of the appliance system on the teeth with sufficient accuracy to allow the appliance system to deliver the desired orthodontic relationship, heretofore not realized clinically, is provided as follows:
 The brackets are placed according to the three criteria:
 1. Height: The height is established so that the appliance causes the upper and lower teeth to contact each other in the prescribed manner.
 2. Mesio-Distally: The mesio-distal location is established so that the mesial and distal ridges of the teeth are parallel to the archform for that patient.
 3. Long Axis: The bracket is aligned relative to the long axis of the tooth so that the appliance system tips the tooth to the desired angle relative to the archwire.
 From the vertical profile data of step (500), and horizontal or three dimensional profile data of steps (300) and (400), the shape and size of each tooth is extracted, including particularly the profile in a mesio-distal view at the height of contour or along a plane perpendicular to the greatest prominence of the central developmental lobe of each tooth. Additionally, the geometry of the archwire slot has been accurately related to the respective teeth. This geometry includes the intersection of the archwire plane with the tooth profile curve, the slot inclination angle and the slot in-out dimensions. In addition, the wire size and bracket geometry information are assembled, and tool size and clearance information are taken into account.
 With this information, a bracket placement jig is designed for NC controlled manufacture to position the slot, and thereby the bracket, precisely on the tooth.
 In FIG. 8D, a plastic jig 82 is shown which engages the walls and bottom of the bracket slot fully. Additionally, the portion of the jig 82 contacting the tooth designed to be formed to precisely fit the known contour of the tooth, as determined by the profiles input in step (500). This assures that the bracket slot and hence the bracket is placed at precisely the correct height when bonded to the tooth.
 Brackets are placed so that the slots are not necessarily perpendicular to the long axis of the tooth but at varying degrees of cant. The jig 82 accomplishes this goal by the use of an adapter 84 that fits into the bracket slot 82 b and a coplanar slot 84 a (FIG. 9T) to engage the plastic blade jig 82, as illustrated in FIG. 8D. The jig design substeps, which are preferably performed in step (3500) and included in the detailed flowchart of the jig manufacturing step of FIG. 2Z, are summarized in the flowchart of FIG. 2V. The design is converted into CNC code in step (3500) for controlling the jig forming machinery 41 primarily to cut a contoured surface that conforms the profiles of the tooth so that the jig fits in a precise position on the tooth to position the bracket for adhesion to the teeth.
 In installation performed in the treatment operation (89), the jig 82 is lined up with the long axis of the tooth crown when viewed from either the front or facial surface of the tooth and from the biting or occlusal surface. A plastic blade form of jig 82 offers visual reference to the height of contour of the tooth and alignment of the bracket with the marginal ridges.
 (97) Appliance Manufacturing Procedure:
 The appliance manufacturing procedure (97), as illustrated in the flowchart of FIG. 2D, entails the generation of controller codes for NC machinery to produce the brackets, archwires and bracket placement jigs designed in the appliance design procedure (96), and the manufacture of the appliance components with the use of the machinery controlled by the codes. The procedure (97) includes the steps of:
 (3000) Controlling and operating the bracket forming machinery 39 to produce the custom brackets:
 The bracket manufacturing procedure of the preferred embodiment involves the generation of NC code for the bracket slot cutting mill 39 of FIG. 1D, as illustrated in the flowchart of FIG. 2X. The step involves the geometric relating of the tooth profile information PF for each tooth, and other tooth contour information of the shape of the surface of the tooth to which the bracket is to be attached from steps (300) and (400), and the archwire plane, slot inclination angle and slot depth information from steps (1200) through (1700). In addition, the bracket forming step performs the function of selecting the bracket blank from which the bracket is to be fabricated. The bracket blank is made up of a base or pad that is attached to the tooth and an outwardly projecting support into which an archwire slot is formed.
 The preferred embodiment includes the forming of brackets by cutting custom slots in bracket blanks while preserving the base inclination angle. Brackets could be alternatively fabricated by inclining the bracket bases or pads. Additionally, bracket bases may be contoured to conform to the surfaces of the teeth, or a bonding agent may fill the space between the bracket base and the tooth. Furthermore, while in the preferred embodiments, a mechanical cutter blade forms the bracket, other means such as wire EDM, machining, casting or stereo lithography may be employed.
 (3200) Controlling and operating the Wire-bending machinery 40 to produce the custom archwires:
 The software that operates the computer 30 c to drive the wire bending apparatus 40 reads data files generated for the mandibular and maxillary archwires in steps (1600) and (1700) respectively. Also read by the computer 30 c are data on the characteristics of the unformed wire 69, including that relating to the material of which the wire is made, as well as its cross-sectional shape and dimension. The file that is read contains coordinated data regarding calculated archwire segment lengths and radii which cumulatively describes geometrically the desired archwire shapes. As explained above, the archwires consist of a sequence of tangential arc segments with each segment a particular length and radius.
 The arch forming software determines the position of the roller 70 b of the anvil 70 that is required to produce a given radius in the particular wire material and cross-section by going to a look-up table, previously derived and stored in a file accessible by the computer 30 c, containing constants necessary to correct for each wire material and cross-section. The anvil 70 is driven to the desired position to produce the required radius and the feed roll motor 70 c is driven to create the desired length of wire at that radius. By adjusting the position of the anvil roller 70 b and length of wire fed with the roller 70 b so adjusted, archwires 64 of the calculated final sequential tangential radii are fabricated.
 (3500) Controlling and operating the jig forming machinery 41 to make custom placement jigs for the location of the brackets on the patient's teeth:
 The machine control codes for controlling the jig forming machinery 41 are produced directly from the tooth profiles generated in step 500 and from the archwire plane location of steps (1200) and (1400), the slot inclination steps (1300) and (1500), and the slot in-out dimensions from the steps (1600) and (1700). As stated above, the jig design step (1800) is preferably performed in the course of, and is described herein as part of, the jig manufacturing step.
 The profile data, which represents the profile curves with a fairly high resolution of data points is a series of straight line segments for developing the codes for driving the NC equipment. Tool and bracket dimensions and design clearances are also taken into account, and CNC codes are generated to cut jigs from circular plastic wafers on a standard CNC mill using a small carbide endmill tool. The details of the substeps of the step (3500) are included in the flowchart of FIG. 2Z.
 (98) Appliance Transmission Procedure:
 One of the ultimate objectives is to place the custom orthodontic appliance into the hands of the orthodontist 14, along with the tools and information necessary for the proper installation of the appliance 25 in the mouth of the patient 12 to treat the patient by moving the patient's teeth to the calculated finish positions. This is best understood by reference to FIG. 1.
 Referring to FIG. 1, as set forth above, the configuration of the preferred system 10 will vary depending on the nature and scale of the orthodontist's practice. Preferably, all or much of the appliance design portion of the procedure (87) takes place at an appliance design facility 13, although in a large scale orthodontic clinic, the entire process could be carried out at the patient treatment location. Usually, however, the functions performed in the design computer 30 b, or design portion of the computer 30, are carried out at the appliance facility 13, together with some of the manufacturing functions performed by the manufacturing control computer 30 c and the appliance manufacturing equipment 38.
 In the configuration where, as illustrated, some or all of the appliance 25 is made at the appliance facility 13, the custom appliance 25 is transmitted to the orthodontist 14. Along with the appliance 25 is communicated documentation in the form of a hard copy printout of information 37 generated by the design computer 30 b, which could also include documentation of the input data that made up the data 26 and the prescription information 27, and a printout of parameters recorded by the manufacturing computer 30 c.
 The transmitted appliance 25 includes a set of archwires 64, as illustrated in FIGS. 8E and 8F, a complete set of custom brackets 80, as illustrated in FIGS. 8D and 8F, and the placement jigs as illustrated in FIGS. 8D and 9T through 9W. Along with the jigs 82 are included a set of adapters 84 that are used to align the slots 80 b of the brackets 80 with coplaner slots 84 a of the jigs 82. The appliance and the bracket placement jigs therefor are similar in the case of lingual appliances, a bracket for which is illustrated on a tooth in FIG. 8G while the lingual appliance is shown positioned on the mandibular teeth in FIG. 8H.
 In addition, custom archwires 64 are transmitted to the orthodontist 14. These archwires include archwires in the exact form, as illustrated in FIG. 8E, to move the teeth to their finish calculated positions, as illustrated, for example for the lower teeth, in FIG. 4D. In FIG. 4D, the archwire 64 is shown in the unstressed state (or having nominal residual stress sometimes motivating some orthodontists to prescribe overcorrection) that it will attain when the appliance 25 has moved the patient's teeth to the calculated finish positions. This is the same shape as the archwire of FIG. 8E shipped to the orthodontist 14. This finish archwire will be of a material and stiffness determined to be appropriate for the final positioning of the teeth. Depending on the severity of the initial malpositioning of the patient's teeth, however, less stiff archwires, or temporary archwires may be desired for beginning the orthodontic treatment. Thus, additional archwires 64 of various properties but in the shape shown in FIG. 8E will be provided the orthodontist 14. In addition or in the alternative to the provision of these additional archwires, an actual size drawing or template having thereon the shape shown in FIG. 8E will be provided the orthodontist 14 to enable him to form archwires for preliminary treatment and rough positioning.
 In alternative configurations, information may be sent from the design computer 30 b in machine readable form, for example by diskette 34 or modem, to a manufacturing computer 30 c to which is attached one or more of the appliance component manufacturing machines 38.
 The patient treatment involves, first, the assembly of the respective bracket 80, jig 82 and adapter 84 combinations, as illustrated in FIG. 8D, and the application of the brackets 80 thereby to the patient's teeth. This involves the application of adhesive to the area generally in the center of the face of the tooth, either labial or lingual, to which the brackets 80 are to be applied. This is illustrated in FIG. 8D, for example, with the application of a bracket 80 to the labial face of a maxillary incisor TU,1. The assembly is positioned on the tooth with the blade of the jig 82 positioned on a generally vertical labial lingual cross section through the approximate center of the tooth, in the plane that may be said to contain the crown long axis CLA of the tooth.
 When the bracket adhesive has set, the bracket placement jig 82 is removed by first sliding out the adapter 84 mesiodistally and then sliding the jig 82 off of the incisal edge of the tooth, leaving the bracket in the calculated position.
 Then, with the brackets 80 set on the teeth the archwire 64 is installed. Often, the first archwire installed will be one of lower stiffness than the final archwire. In the example of FIG. 8F, the mandibular teeth in their initial position as illustrated in FIGS. 4 and 4A are shown. The brackets 80 are positioned on the teeth in the exact same positions as shown in the calculated finish position diagram of FIG. 4D. Because the teeth are not yet in this ideal finish position, the archwire 64, when inserted into the archwire slots and tied to the brackets 80, will be stressed into the elastically deformed condition shown in FIG. 8F. This stressed condition of the archwire 64 operates, without the need of the orthodontist to artfully bend the wire, to apply the forces to the teeth to urge them toward the ideal positions of FIG. 4D. This force will continue to be applied until the teeth have moved to the finish positions. In some prescribed forms of treatment, the wire and brackets are designed to move the teeth to a slightly overcorrected position to allow for a relaxation movement of the teeth when the appliance 25 is removed.
 The analysis, design and manufacturing operation (87), as stated above, includes the (94) input, (95) analysis, (96) design, (97) manufacturing, and (98) transmission procedures of a computerized custom designed appliance manufacturing operation. The steps of those procedures, as outlined above, include the following:
 The input of digitized information includes the (100) input of patient and doctor identifying information, (200) the input of patient background information, (300) the input of digitized information of the horizontal dimensions of the mandibular teeth and the mandibular bone, (400) the input of horizontal dimensions of the maxillary teeth, and (500) the input of vertical labial-lingual profile information of each of the individual teeth.
 (100) Identification Information Input Step:
 The first step in the procedure (82), as illustrated in. flowchart of FIG. 2A, is (100) to input the doctor-patient identification information 17. This step (100), as illustrated in the detailed flowchart of FIG. 2E, includes the substeps, performed by an operator 28 in response to prompts for text input at a terminal of the computer 30, of (105) input of the doctor's name, (110) input of the doctor's identification number, and (115) input of the patient's name. Then, the computer 30 (120) assigns a patient identification number. With this information, (125) a patient-specific floppy disk or diskette 34 is automatically formatted.
 (200) Patient Background Input Step:
 The next step in the information input procedure (94), as illustrated in FIG. 2A, is (200) the entry, in response to prompts, of the patient background information 19, and the prescribed treatment information 27 from the doctor. This step, as illustrated in the detailed flowchart of FIG. 2F, involves the substeps of (205) entering, from the background information 19, the patient's age as numerical data, and selecting (210) the patient's sex and (215) the patient's race from options on the screen. Then, from the prescription information 27, the data are entered, by selecting choices from multiple choice prompts, from information such as the following:
 (220) Whether or not the treatment is to include an extraction, and if so, which teeth are to be extracted;
 (225) Whether the occlusion type is a group function or a cuspid rise, and if a cuspid rise, whether averages or individual head film is to be used;
 (230) Whether the prescribed procedure is to preserve lower intercuspid distance or allow expansion, and if expansion is to be allowed, how much expansion;
 (235) Whether or not the occlusion is mutilated;
 (240) Whether a Steiner compromise is to be allowed to accommodate skeletal discrepancy;
 (245) Whether a Roth or Ricketts inset is to be used on upper laterals, and if so which;
 (250) Whether a Roth or Andrews upper lateral overbite is indicated, and if so, which;
 (255) Which is the preferred slot size, from traditional sizes 0.018″ or 0.022″ (0.45 mm or 0.55 mm), or other available size, of which 0.20″ (0.50 mm) would often be acceptable;
 (260) Whether the case is to be treated with labial or lingual appliances;
 (265) Whether the case is to be diagnosed using symmetry or not;
 (270) How inter-incisal angle is to be determined, using the Andrews Norms, the Parallel Upper Central to Facial Axis Norm, or Ricketts Norm.
 (300) Mandible Digitized Video Input Step:
 The forming of the computerized mathematical model of the teeth of the patient 12 begins with (300) the inputting of video or other graphics top view image of the patient's lower jaw, including the teeth, as illustrated in the detailed flowchart of FIG. 2G. Such an image as input by the video scanner 43, is illustrated in FIG. 3.
 The step (300) includes the digitizing and processing of the data of the widths of the mandibular teeth and size and shape of the mandibular bone or bone of the lower jaw 22 of the patient 12 from the horizontal plan view of the lower jaw as in FIG. 4. The mandible 22 is composed of hard or cortical bone on the external surface and soft or cancellous bone in the interior. This bone is not as orthodontically alterable as is the maxilla. Since the lower teeth must remain in the mandible, determination of its shape and boundaries is made so that a skeletal arch can be defined to be used as a starting point in the calculation of the finish position of the teeth.
 The lower teeth must lie on the mandible 22 in an arch that may be defined as the mandibular trough MT, as illustrated in FIG. 4. The roots of the lower teeth of the patient are contained within the mandibular trough MT, which is defined as the space between boundaries BL and BB of FIG. 4. The outer, or buccal, and inner, or lingual, boundaries BB and BL, respectively, are preferably digitized by interactive selection by the operator 28 from an image 48 of the cortical bone of the mandible 22 on the screen 35. Furthermore, the mandibular teeth must lie in the arch in contact with one another. They each occupy a portion of the arch equal to the distances between their mesial and distal contact points with the adjacent teeth. These tooth extremities are also preferably digitized by interactive selection from the image 48.
 To (300) input data of the patient's mandibular teeth and lower jaw 22, as illustrated in the detail flow chart of FIG. 2G, (305) a video graphics image 48 (FIG. 3) of mandibular model 21 is first input to the screen 35 of the computer 30 c. Then (310) a grid G is overlaid on the video image of the mandibular 22 as illustrated in FIG. 4. The grid G presents grid lines that intersect the image 48 on the screen. The operator 28 (315) resizes the grid G, if necessary, and orients the image relative to grid G to define X,Y coordinates with a Y axis on a midline ML of the lower jaw 22 and an X axis perpendicular to the Y axis through a selected intersection point or origin 0,0, preferably set at the mesial contact points of the lower central incisors.
 Next, the computer 30 prompts the operator sequentially to select each point, first for the individual tooth contact points, then the jaw bone boundaries. With the pointing device 47, (320) the operator 28 moves the cursor on the screen 35 and selects (e.g., clicks with a mouse on) the prompted point, thereby initiating the software for digitizing the X,Y Cartesian coordinates of the mesial and distal extremities MX,Y DX,Y, respectively, for each mandibular tooth. The mesial extremity MX,Y of a tooth is the point on its surface closest the midline ML along the mandibular arch (the mesial direction m) while distal extremity of a tooth is the point on its surface closest the rear of the mouth along the mandibular arch (the distal direction d). From the X, Y coordinates of MX,Y, MX and MY, and of DX,Y, DX and DY, (325) the mesio-distal width MDWI of each tooth I, on each side of the mandible 22, is calculated using Pythagorean theorem:
 MX is mandibular X coordinate.
 MY is mandibular Y coordinate.
 DX is distal X coordinate.
 DY is distal Y coordinate.
 These widths are then summed to calculate the total length MAL required of the arch to accommodate the mandibular teeth. Since all of the teeth will be finally positioned to be in contact with the adjacent teeth, this length remains a constant length of any arch on which the mandibular teeth are placed in the calculations.
 Then, by moving the pointing device 47 to the intersections of the lines of the grid G with the visible boundaries BB and BL and selecting the intersection points, data is input for determination of the shape of the mandibular trough MT. The point selection function can be made with conventionally available CAD/CAM, imaging or illustration software and the pointing device 47. (330) From the selected intersections of the lines of the grid G with the mandible boundaries BB and BL, Cartesian coordinates LaX,Y and LiX,Y of labial and lingual limits, respectively, of cortical bone on both sides of mandibular jaw are generated. The X, Y coordinates La and Li so chosen are digitized as above on the boundary lines BL and BB of the cortical bone, between and interproximate the teeth.
 After the points La and Li are chosen representing the cortical bone limits, (335) midpoint coordinates MPXY are calculated between each of the individual labio-lingual pairs of La and Li. Also, calculated are the bone width distances between each of the respective labio-lingual pair DLL, as follows:
 LaX is labial X coordinate of point La.
 LaY is labial Y coordinate of point La.
 LiX is lingual X coordinate of point Li.
 LiY is lingual Y coordinate of point Li.
 These midpoints MPX,Y one of which is the designated origin MP0,0, lie on an arch that describes the size and shape of the center of the cancellous portion of the mandibular bone 22.
 At this point, the beginning of the analysis for the calculation of the finish positions of the teeth is carried out. The coordinates of points MPX,Y are recalculated relative to a new origin 0,0 at the calculated midpoint between the mandibular centrals, to normalize the mandibular trough equation to its own independent midpoint when calculated below. The sum of the individual mandibular tooth widths MDW equals the total dental length or mandibular arch length MAL contained in the mandibular trough equation MTE that will be constructed through the points MPX,Y. MAL is referred to as the arch perimeter.
 At this stage, (340) the midpoints are typically averaged right to left to eliminate any asymmetry that may be present due to slight measurement errors. If, however, the patient has been diagnosed by the orthodontist 14 to be of asymmetrical anatomy, the averaging process is not performed. Such a determination will have been made by the orthodontist 14 in the examination procedure (90) described above and specified of the prescription 27 in step (265) of the procedure (92) described above. An advantage of the averaging process is that, when used, it assists the final positioning of the teeth symmetrically about the midline ML and will make it easier for an archwire to be produced that is symmetrical from right to left, and thus can be made such that it can be installed in inverted orientation.
 The midline ML shown in FIG. 4 is the axis of such symmetry corrections. These corrections for each point MPX,Y are calculated as follows:
 SX,Y is the symmetricalized point MPX,Y
 MPX,Y is mid-point of mandibular trough
 PRX,Y is a point MPX,Y on the right side
 PLX,Y is the corresponding point on left side of the trough
 With the completion of this symmetricalization process, a mathematical equation MTE, which describes the size and shape of the mandibular trough according to steps (345), (350) and (355), is derived by fitting a curve to the points MPX,Y. Preferably, this curve is derived by fitting a series of cubic equations, such as a cubic spline equation, to pass smoothly through the points, for example, through the averaged midpoints SX,Y. The cubic equations allow the determination of the slope of the curve at each of the midpoints.
 The cubic equations are then preferably converted in form to a series of segments of tangent circle equations with slopes equal to the slopes of the cubic spline at the midpoints, and equal to the slopes of the adjacent circle segments at the segment end points, or their points of intersection, along the curve. To fit a cubic equation with quadratics, two circles CS and CL are used to describe each segment of the MTE between midpoints, as illustrated in FIG. 5. This allows a smooth curve consisting of tangential circles to represent the mandibular trough.
 The cubic equation calculations are preferably those performed by (345) calculating cubic spline parameters required to pass a smooth curves through symmetricalized midpoints SX,Y as illustrated in FIG. 5A. This includes (350) calculating the slope of the cubic spline curve at each symmetricalized mid-point SX,Y or SX,Y, and (355) calculating a series of tangential circle equations whose slopes are equal at the mid-points and at points of intersection along the curve.
 (345) The cubic spline method preferred uses a cubic, or third degree, polynomial to interpolate between each pair of data points SX,Y. A different polynomial is used for each interval, and each one is constrained to pass through the original data with the same slope as the data. (350) The slopes of the cubic equation are computed by solving the slope of a parabola that passes through each data point and its two nearest neighbors points. The cubic spline method is described in more detail in the discussion of the cubic spline subroutine (2000) below.
 (355) Any point on the cubic spline equation can now be calculated by using a cubic spline interpolation. Using this, the cubic spline equation is subjected to a circle segment conversion by which the form of the equation MTE is converted to a series of circle segments that interconnect tangentially. Once the spline equation is derived, the slopes at each data point are calculated using the point slope method. These slopes are utilized to derive, between each pair of data points on the spline equation, the description of two circle segments, each from one of two circles as illustrated in FIG. 5, to convert the MTE to a series of circle segments throughout its length. This facilitates the setup of the teeth, the description of the configuration of archwires, and the generation of NC code for the manufacture of the appliance. The spline-to-circle conversion routine is described in further detail under routine (2100) below.
 The input procedure continues. (360) Cartesian coordinates are input for right and left mandibular cuspid cusp tips CR and CL, respectively, as illustrated in FIG. 4. (365) A distance DCT between the cusp tips CR and CL of the two mandibular cuspids is then calculated:
 CRX=right cuspid X coordinate.
 CRY=right cuspid Y coordinate.
 CLX=left cuspid X coordinate.
 CLY=left cuspid Y coordinate.
 This information is used to calculate if and how much the mandibular intercuspid distance is to be altered, and to evaluate whether the calculated final position is acceptable. Similarly, (370) Cartesian coordinates or right and left mesio-buccal cusp tips, MR and ML, respectively, of mandibular first molars are calculated, and (375) the distance between these points DMT is calculated:
 MRX=right first molar cusp X coordinate.
 MRY=right first molar cusp Y coordinate.
 MLX=left first molar cusp X coordinate.
 MLY=left first molar cusp Y coordinate.
 This information is used to determine if and how much the mandibular intermolar distance is to be altered.
 (400) Maxilla Digitized Video Input Step:
 As with the mandibular jaw information described in connection with FIG. 4, (400) a computer image is made from input in the same manner from the upper model 23 of the maxillary jaw 24 of the patient 12, as illustrated in the flowchart detail of FIG. 2H. This involves the substeps of (405) inputting a video image 48 a of maxillary model 23 to the computer screen 35. The image 48 a is illustrated in FIG. 4A. With the maxilla, it is not necessary to overlay the grid G on maxillary image on the screen, since the bone of the maxilla is a variable that will be altered orthodontically to accommodate the finish positions of the teeth. The orientation of the axes and position of the origin are immaterial to the calculation of the relative distances such as MDW of the teeth. Only the scale must be maintained. As with the mandibular information, the image of the maxillary jaw 24 is displayed at a scale predetermined by the scanner 33. The scale is involved in the calculation of the maxillary tooth widths MDW.
 (420) Cartesian coordinates of mesial and distal extremities Mx,y and Dx,y of each maxillary tooth are then input as with the mandibular teeth and (425) the mesio-distal width MDW of each maxillary tooth is calculated using Pythagorean theorem, thus:
 MX is mesial X coordinate.
 MY is mesial Y coordinate.
 DX is distal X coordinate.
 DY is distal Y coordinate.
 This information is used first to determine whether the maxillary and mandibular teeth are correct in proportion to the mesiodistal widths MDW of the other. If the proportions are incorrect, a tooth size discrepancy TDS is said to exist, and the information is recorded to report to the orthodontist. The MDWs of the maxillary teeth are later used to place the maxillary teeth upon the mandibular arch.
 Next, (430) coordinates of the central fossae of right and left maxillary first molars are input. Then, (435) the distance between central fossae DCF is calculated as follows:
 RX is right side central fossa X coordinate.
 RY is right side central fossa Y coordinate.
 LX is left side central fossa X coordinate.
 LY is left side central fossa Y coordinate.
 This information is recalculated after the tooth finish positions are calculated to coincide with the DMT spacing of the mandibular first molars, and compared with this initial measurement as an indicator of whether the intermolar width will be changed by treatment and the amount of such change, if any.
 (500) Digitized Probe Tooth Profile Input Step:
 The next input step (500) involves an analysis of the dentition, as illustrated in the detailed flowchart of FIG. 21. In this step, selected profiles of each of the teeth are generated from either the model 20, or from a digitized three dimensional representation of the patient's teeth or the model 20 as illustrated in FIGS. 3A and 3B. In the illustrated embodiment, the use of the probe assembly 57 of FIG. 1C is used in this step.
 Where the full three dimensional scan has been employed in step (300), as could be produced with the use of the laser image generator (FIG. 1B), or as could be produced with moire image generator or other technique, a digitized computer model is produced. From such a computer model, which is an electronic version of the model 20 in the form illustrated in FIGS. 3A and 3B, planes or other cross-sections through the teeth are selected that contain extremities of the teeth. The three dimensional images may be displayed on the screen 35 and profiles generated either with the pointing device 47 in a manner similar to the use of the mechanical probe described below, or automatically using available CAD or illustration imaging software. Whether the profiles are generated from a physical model 20 or an electronic version thereof, much of the input step (500) and/or the landmark selection step (600) may be similarly employed.
 In the preferred use of the information from the probe assembly 57, a single digitized profile curve PFis constructed for each tooth in a generally vertical plane extending in an approximately labial-lingual orientation generally along the central developmental lobe perpendicular to the marginal ridges. While other profiles can be taken, the need to do so is reduced by intelligent plane selection made with an understanding of tooth anatomy, depending on the data required by the tooth positioning and appliance design criteria employed. The selection of the profile plane is illustrated in FIG. 6 where a first profile PFA through the center of the tooth is shown as missing the buccal cusp tip which is the maximum crown highpoint of the tooth. Profile PFB is then selected to include the buccal cusp, and the ridge of the profile is found to generally align with the lowpoint of PFA. Alternatively, the profile may be non-planar to pick the important features of both planes. As such, the profile produced will be comparable to a projection onto a plane of the relevant tooth extremities.
 The step (500) of analysis of the dentition includes, first (505) examination, by the operator 28 of the computer 30 a, of the marginal ridges of the upper central and upper lateral teeth. If ridges are excessive, a determination is made to take a profile twice with the probe 60, once by smoothing the teeth, for example with wax, for arch coordination and once without smoothing for placement jig geometry. Otherwise, a single profile taken across the buccal cusp will contain information of the crown height of the tooth as well as approximating the profile of the tooth through its mesiodistal center with accuracy that is usually sufficient. Then, (510) a determination is made as to whether one or two traces of maxillary incisor teeth are to be input as in step (505) above.
 (515) The computer 30 a is configured to receive sequential Cartesian coordinate pairs through an RS-232C serial port representing tooth profile anatomy from the orthogonally positioned displacement transducers 61. (520) The computer 30 a prompts the operator 28 to enter the profiles of each tooth sequentially. In response to the prompts, data points of each tooth are input, beginning with lower left molar T(B,L,6) and ending with upper right molar T(U,R,6), and a display 63 of profile PFI image is generated. The output circuits associated with the transducers 61 are configured to digitize data values at periodic time intervals as the probe 60 is moved across the teeth from the time the probe first starts to move across the tooth until the operator enters a command or key stroke indicating that the scan is complete. Then (525) the input profile data of each of the teeth is stored in memory by the computer 30. The resulting profiles PF, are illustrated in FIG. 3C. These profiles, at this stage, are not related to the positions of the teeth within the mouth or with respect to other teeth. Thus, each of the X-Y coordinates of the individual tooth profiles are independent of each other. In step (600) below, the coordinate axes of each tooth will be oriented with respect to each other, and thereafter, in later steps (800)-(1100), the coordinates of each profile are translated vertically for proper occlusion and horizontally for placement on their respective arches.
 The calculation of the finish positions of the teeth, as illustrated in the flowchart of FIG. 2B, includes (600) determining the relative positions of geometric landmarks on the surfaces of the teeth and establishing the axis inclinations of the teeth, (700) calculating cuspid rise, (800) initially positioning the mandibular teeth vertically and in relation to the mandibular trough, (900) calculating a best fit cusp tip equation for the mandibular teeth, (1000) calculating the finish positions of the mandibular teeth on the best fit equation, and (1100) calculating the finish positions of the maxillary teeth on three arches related to the best fit equation.
 (600) Tooth Landmark Identification Analysis Step:
 After the individual teeth have been digitized, the inputting of tooth shape data (94) is complete, with the digitized information 26 stored a file. Then, referring again to the flowchart of FIG. 2, (95) the input data 26 is analyzed to develop or derive further parameters for calculating the final positions of the teeth and for (96) the design of the appliance 25. In the tooth positioning analysis (95), as illustrated in the flowchart of FIG. 2B, (600) a tooth profile analysis is made in which, for example, certain anatomical landmarks are chosen, depending on the tooth to be analyzed. The details of the tooth profile analysis are illustrated in the flowchart of FIG. 2J.
 In the tooth profile analysis step, (605) individual images 63 of the profile curves PFI of each tooth (FIG. 3C) are recalled separately to the screen of the computer 30 b for selection of the landmarks.
 Using the displayed images 63 of the profile curves PFI, (610) specific landmark points are chosen, first on the mandibular molars and bicuspids. The selected points are digitized as illustrated in FIG. 6. The selected points are:
 Point P1: The Lingual (tongue side) gum/tooth intersection.
 Point P2: The prominence of the lingual cusp.
 Point P3: The prominence of the buccal (cheek side) cusp.
 Point P4: The buccal gum/tooth intersection.
 From these landmarks, (615) the crown long axis CLA of each molar and bicuspid profiled is determined. The determination is made by constructing a first line L1 between points P2 and P3 and a second line L2 between points P1 and P4. The crown long axis CLA of a tooth is the line between the midpoints of L1 and L2.
 Line L1 is constructed through point P2 and point P3 by the following equation:
 X2, Y2=X and Y coordinates of point P2.
 X3, Y3=X and Y coordinates of point P3.
 Line L2 is constructed through point P1 and point P4 by the following equation:
 X1, Y1=X and Y coordinates of point P1.
 X4, Y4=X and Y coordinates of point P4.
 A point equidistant between points P2 and P3 along line L1 is then calculated and defined as P2-3:
 X2, Y2=X and Y coordinates of point P2.
 X3, Y3=X and Y coordinates of point P3.
 A point equidistant between points P1 and P4 along line L2 is also calculated and defined as the Gingival Center Point GCP:
 X1, Y1=X and Y coordinates of point P1.
 X4, Y4=X and Y coordinates of point P4.
 The line defining the crown long axis CLA is constructed using the following equation:
 X2-3, Y2-3=X and Y coordinates of the center point P2-3.
 XGCP, YGCP=X and Y coordinates of gingival center point GCPX,Y.
 For molars and bicuspids, point P3, the buccal cusp tip, is defined as the Incisal Center Point ICP.
 Similarly, (610) the anatomical landmarks and crown long axis CLA for the mandibular cuspids, laterals and central teeth are determined, as illustrated in FIG. 6B. The points P1 through P4, as labeled in FIG. 6B, are selected as follows:
 Point P1: The lingual gum/tooth intersection.
 Point P2: The lingual aspect of the incisal edge.
 Point P3: The buccal aspect of the incisal edge.
 Point P4: The facial gum/tooth intersection.
 As with the bicuspids and molars, lines L1 and L2 are constructed. The landmarks in the cases of the teeth as illustrated in FIG. 6B, are chosen because they are relatively tolerant to operator error in selection. This can be seen by the set of broken lines that are possible alternatives to L2 in FIG. 6B. From these landmarks (615) the crown long axis CLA is determined as defined above, by connection of the midpoints of L1 and L2.
 The next step in the analysis is the determination of maxillary dentition for each upper molar and bicuspid. (610) Anatomical landmarks are identified and chosen as illustrated in FIG. 6C, which requires (612) the selection of a fifth point, P5, defined as follows:
 Point P1: The lingual gum/tooth intersection.
 Point P2: The prominence of the lingual cusp.
 Point P3: The prominence of the buccal cusp.
 Point P4: The buccal gum/tooth intersection.
 Point P5: The mesial marginal ridge of the tooth at central groove.
 Referring to FIG. 6C, from the landmarks, (615) the crown long axis CLA of each applicable maxillary tooth is determined.
 The (610) anatomical landmarks for the maxillary cuspids, laterals and central teeth are determined as illustrated in FIG. 6D. The points labeled P1 through P4 are selected, as follows as illustrated in FIG. 6D:
 Point P1: The lingual gum/tooth intersection.
 Point P2: The lingual aspect of the incisal edge.
 Point P3: The buccal aspect of the incisal edge.
 Point P4: The facial gum/tooth intersection.
 From each of these sets of landmarks, the crown long axis CLA of each such tooth is also determined as described (615) above.
 This completes the loop (620) for all of the teeth.
 Next, as further illustrated in FIG. 6D, (620) seed values for setting the crown long axis inclinations LAI of the teeth. Initially, such seed values may be derived from analyses that identified the facial axis plane FAP through the facial axis point FA of the tooth (the midpoints of the height of the clinical crowns along the facial axes of the clinical crowns) as described by Dr. Lawrence Andrews. It is, however, contemplated that CLA seed values for various population groups will be statistically derived in the course of the practice of the present invention, and will produce improved treatment results.
 The seed values shown in Table 1 below are typical for Caucasian males. These seed values for tooth LAI, tabulated in degrees from the horizontal lingual (-X) axis, will vary to reflect known variations due to such things as sex,
 The preferred seed values are shown in Table 1 below are typical for Caucasian males. These seed values will vary to reflect known variations due to such things as sex, race or treatment plan.
TABLE 1 Tooth Maxillary Mandibular Type Crown LAI Crown LAI Central 117 107 Lateral 112 107 Cuspid 108 100 1st Bicuspid 94 83 2nd Bicuspid 94 80 1st Molar x x 2nd Molar x x
 The computer images as summarized in FIG. 3C for each tooth (630) are then rotated so that the CLA is oriented at the angle LAI, the long axis inclination angle, to the mandibular trough plane MT according to the values in Table 1. This computes the final inclinations of the teeth that will be preserved in the calculations below. This produces the oriented profiles PF summarized in FIG. 6E.
 In the analyses of Andrews referred to above, the LAIS were established with a line LFA drawn tangent to the facial surface at FA, and line representing the relative inclination of the archwire plane drawn through FA point. The angle between the lines was established at the inclinations reported by Andrews for patients with no skeletal discrepancies. The angle LAI between the crown long axis CLA and a line representing the maxillary arch plane in which lies the mandibular trough equation MTE is related to the facial inclination angles of Andrews' studies by taking into account statistically the thicknesses and contours of the teeth. Table 1 above was derived, after statistical processing, to produce the seed value used for the final inclination of the crown long axis in preferred occlusal design.
 Once the tooth profiles have been rotated to the inclination angles LAI, certain precise vertical dimensions and extremities can be determined. From the digitized profile curves, which are stored in memory in the form of a series of closely spaced points, the precise incisal tip IC, as illustrated in FIGS. 6F, 6H and 6I, are identified on the cuspids, laterals and centrals.
 Additionally the elevation of the marginal ridge P5 is identified. The marginal ridge elevation MRE, which is the vertical distance from P3 to P5, is identified on the maxillary posterior teeth because they are the centric stops for the buccal cusps of the mandibular molars and bicuspids. In other words, point P3 on the mandibular molars and bicuspids contacts point P5 on the maxillary molars and bicuspids when the teeth are together, as illustrated in phantom line PH1, in FIG. 6C. For a more precise placement in a less common case where the maxillary ridge is narrow in relation to the mandibular tip (phantom line PH2), a more detailed three dimensional analysis of the tooth shape can take into account additional correction needed. The calculation of MRE (FIG. 6C) is made after rotation of the teeth to their proper LAI inclinations so that MRE will be a vertical distance, where LAI is measured relative to the plane of the dental arch. The MRE is used as the buccal cusp height BCH in the calculation of cuspid rise and archwire plane placement as described below in the discussion of FIGS. 7A and 8, 471 respectively.
 (700) Cuspid Rise Determination Step:
 The next step of the analysis procedure (87) is (700) the calculation of cuspid rise, illustrated in detail in the flowchart of FIG. 2K.
 Most orthodontists currently desire a cuspid rise occlusion, in which, in lateral movement of the lower jaw, the cuspids cause the other teeth to disclude or to come apart. In order for this to happen, the overlap of the cuspids must be greater than that of the other teeth when the teeth are together. This is complicated by the fact that the cuspids (I=3) are close to the front of the mouth and are therefore further from the condyle or pivot point PP of the jaw than are the posterior teeth (I>3), as illustrated by distances DJI in FIG. 7. This results in the teeth closer to the back of the mouth moving less than the cuspids on opening. This differential rate of movement must be included in the calculation of cuspid rise or the back teeth will remain in contact after the cuspids have cleared each other. Also, the distance DPP from the occlusal plane to the pivot point PP of the condyle of the jaws must be considered, as illustrated in FIG. 7. A failure to provide for this distance results in what is known as working interferences.
 According to the preferred embodiment of the present invention, where cuspid rise is prescribed to control occlusion, the contribution of cuspid rise is distributed between the maxillary and mandibular cuspids, with two parts of the cuspid rise provided by the maxillary cuspids and one part by the mandibular cuspids. This distribution is applicable where occlusion is solely to be a cuspid rise function. Where occlusion is to be a group function, as specified by the orthodontist 14 in the prescription 27, the distribution between the upper and lower teeth is generally equal.
 In the substeps performed in the calculation of the cuspid rise (700), illustrated in detail in the flowchart of FIG. 2K, the first substep is (705) to acquire the initial vertical distance or buccal cusp height BCH from P3 to the marginal ridge for each of the right and left maxillary first bicuspids T(U,4), second bicuspids T(U,5), first molars T(U,6), and second molars T(U,7), as illustrated in FIG. 6C. This is the marginal ridge elevation MRE calculated for each of these teeth in substep (615) of step (600). Then, from anatomical study, (710) the ues in Table 2.
TABLE 2 1.67 × BCH of T(U,7) 1.50 × BCH of T(U,6) 1.36 × BCH of T(U,5) and 1.20 × BCH of T(U,4).
 Then, (715) from the products of the buccal cuspid rise vertical height CR required to clear each respective pair of teeth is determined by first computing the values in Table 2, which are derived from the jaw dimensions DPP and DJI in FIG. 7. required to clear each respective pair of teeth is determined by first computing the val height BCH for each such tooth multiplied by the rise factor listed above, the largest value is selected. This selected product is the cuspid rise required to clear the most prominent cusp and provide group function occlusion. This is illustrated as BCH6 in FIG. 7A for the case where the first molars are the last to clear.
 (720) If the group function has been selected in the prescription 27 provided by the orthodontist 14, the calculated rise is used as is. If cuspid guidance has been selected in the prescription 27 of the orthodontist 14, the calculated cuspid rise factor must further be modified to give typically 0.5 to 0.75 mm of clearance over the largest rise factor by multiplying the buccal cusp height BCH for each tooth by the rise factor listed above and selecting the largest figure, then adding 0.5 to 0.75 mm additional cuspid overlap to obtain and adjusted cuspid guidance cuspid rise.
 (725) Calculation of cuspid overlap or cuspid rise CR for maxillary and mandibular cuspids is preferably as follows: If group function has been selected, mandibular rise equals 50% total group function rise, and maxillary rise equals 50% of the total group function rise. If cuspid function has been selected, mandibular rise equals 34% of the total cuspid guidance rise, and maxillary rise equals 66% of the total cuspid guidance rise.
 (800) Mandibular Tooth Placement Step:
 The next step in the analysis procedure (87) is (800) the mathematical construction of the mandibular occlusion to calculate the position of the mandibular teeth. The details of this step are illustrated in the flowchart of FIG. 2L. The first calculation places the tips of the mandibular teeth on an occlusal plane pending final refinement of the placement, as diagrammatically illustrated in FIG. 6E. In this step, the inclinations of the mandibular tooth crown long axes CLA are preserved, and the teeth are moved upward along their CLA's until their tips are in alignment with the plane of the top of the tallest tooth. The CLA's are placed to intersect the MTE below the tooth GCP. Because the teeth are inclined at different LAIs, or long axis inclination angles, the tooth tips will each be differently offset from the MTE, and thus not in a smooth arch.
 The substeps of the mandibular placement step (800), illustrated in the flowchart of FIG. 2L, are as follows:
 (805) The tallest mandibular tooth, with the exception of the cuspids, is identified. In FIG. 6F this is illustrated as the left mandibular central. The tallest tooth is the tooth with the greatest crown height CH. The crown height CH is the distance, in the Y direction (with the teeth profiles oriented as described in step (600), from the GCP, the point of intersection of line L2 and crown long axis CLA, to highest point on buccal cusp, e.g. P3 (for posterior teeth) as illustrated in FIG. 6F and (for the anterior teeth) to either the incisal center point ICP or, preferably to the incisal tip IC, as illustrated in FIG. 6G. The crown height CH of the tallest tooth, shown as the left mandibular central incisor in FIG. 6F, is the maximum crown height MCH of the mandibular teeth.
 Then, (810) three parallel planes are established:
 a) an MCH reference plane MCHP parallel to the X-axis, and passing through an origin 0,0, set at the GCP of the tallest tooth (FIGS. 6F and 6I);
 b) a Buccal Cusp Plane BCP parallel to X-axis and passing through coordinates 0, MCH on the tallest tooth (FIGS. 6F and 6I); and
 c) a Cuspid Rise Plane CRP parallel to X-axis and passing through coordinates 0, where CR is the cuspid rise calculated in step (700), where the cuspid rise option has been selected.
 With the planes defined, (815) the oriented mandibular teeth are placed such that the highest point on buccal cusp tip P3 or incisal tip IC of each contacts the buccal cusp plane BCP, for all teeth except the cuspids, as illustrated further in FIG. 6F. The BCP thereby is established as the occlusal plane MOC. The reference plane MCHP is set equal to the plane of the mandibular trough MT This sets the GCP of the tallest tooth on the MT, with the GCPs of the remaining mandibular teeth above it. It also sets the occlusal plane MOC a distance MCH from the mandibular trough MT. The absolute highest point on a tooth crown is preferably used to align the teeth with the BCP. Such a point can be determined by additional point selection in step (500), such as by the direct selecting of the point IC for the precise incisal tip, or preferably by calculating the highest point directly from the profiles of FIG. 3C or from three dimensional images as in FIGS. 2A, 2B after rotation of the teeth to their final inclination angles LAI, at the end of step (600).
 The next stage in this step is to establish the mandibular component of cuspid rise. This involves (820) vertically moving the cuspids by, for example, sliding the cuspids along their crown long axes, such that the cuspid cusp tips are at the appropriate height above the mandibular occlusal plane, that is, in the plane CRP.
 At this stage, the vertical positions of the mandibular teeth relative to each other are calculated, providing a basis for relating the Y coordinates of the individual mandibular tooth profiles with respect to each other as illustrated in FIGS. 6F and 7C.
 Then, with the mandibular teeth vertically positioned, the teeth are horizontally set at temporary positions with respect to the MTE, which lies in the plane of the mandibular trough MT (MCHP). This horizontal positioning, in effect, relates the X axes of the individual tooth profiles in a horizontal in-out direction with respect to the mandibular arch and special mesiodistally along the mandibular arch.
 Because the preferred goal, however, is to position the tips of the teeth in the smoothest arch in an occlusal plane MOC rather than their gingival aspects in a smooth arch at the mandibular trough MT, (825), a horizontal distance OFFSET for each tooth is calculated, based on the tooth and the crown long axis inclination LAI determined in step (600). This offset is the horizontal distance from the MTEto the tooth tips when their GCPs are placed on the MTE.
 For mandibular centrals and laterals and cuspids, the OFFSET is calculated by dividing, by the tangent of LAI, the vertical distance from (1) the intersection of crown long axis CLA and the incisal tip IC to (2) the intersection of CLA and maximum cusp height reference plane MCHP. The vertical distance may be calculated from the IC to the MCHP (equal to the Y coordinate of point IC, producing the incisal center vertical distance ICD.) For mandibular laterals and centrals, ICD equals MCH. For mandibular cuspids, ICD equals the mandibular cuspid rise component, which is MCH+(Total CR)/3 when cuspid rise function occlusion has been selected. The calculation of the OFFSET for centrals, laterals and cuspids would thus be as follows for the incisors and laterals:
 (831) For mandibular bicuspids and molars, referring to FIG. 6F, the OFFSET is calculated as the horizontal distance from point P3 to the intersection of the CLA and the MCHP as follows:
 where HD equals the horizontal distance from point P3 to incisal center point ICP.
 Then, (835) the mandibular trough placement point MTPP is defined as the intersection of MCHP and CLA, as illustrated in FIGS. 6G and 6H. For the tallest tooth, MTPP is its GCP, as illustrated in FIG. 6I. The MCHP is at the level of the mandibular trough and contains the MTE. The MTPP is the point on the tooth that is initially placed on the MTE.
 Next, referring to FIGS. 7B and 7C, the teeth are placed with their MTPPs on the mandibular trough, one side at a time. To achieve this, (840) the subroutine (2200) is called twice, once for the left side, and once for the right side, as follows:
 The mandibular trough equation MTE is first adjusted for the mandibular centrals to increase the radii by the amount of the central OFFSET for that particular tooth, as defined above, to form a mandibular trough offset curve MO(1) of FIG. 4B. The radii of the MTE referred to are those of the MTE defined in the circle segment form of the equation generated in step (300) with the spline to circle conversion routine (2100). Since the OFFSETs of the teeth differ, the MO may be viewed as a discontinuous equation when constructed in this manner, made up of segments, each containing the tip of one tooth and spaced labial-lingually from the MTE by the amount of the individual tooth's OFFSET
 Beginning with the left side, the central is placed, as illustrated in FIG. 7B, by placing its mesial contact point MCP at the intersection of the midline ML with the offset curve MO for the tooth. This has the effect of the placing MTPP of the tooth, which is the intersection of the CLA with the MCHP or MT, on the MTE and the incisal tip IC of the tooth on MO1. The tooth placement on the circle segment form of an equation is explained in detail in the description of the tooth placement routine (2200) below. In the placement of the central, a circle C1 is constructed with a radius equal to the mesiodistal width MDW1 of the central tooth and with the center of the circle C1 at the mesial contact point MCP of the tooth at intersection of the midline ML with the offset curve MO1. Then, circle C2 is constructed with a radius equal to MDW/2 and with its center coincident with the center of circle C1. Then, the intersections of trough offset curve MO with the circles C1 and C2 are found, its intersection with the circle C1 being the distal contact point DCP of the tooth and its intersection with the C2 being the tooth midpoint TMP of the central tooth. The tooth midpoint TMP is here defined as the midpoint of the mesiodistal width of the tooth placed on an archform, which is the intersection of the archform with a vertical labial-lingual plane that contains the CLA. This mid-point TMP of the central tooth on the MO is the approximate position of the incisal tip IC.
 Determining the intersections of the circles with the offset trough curve MO, or expanded mandibular trough, requires identification of which circle sector lines (FIG. 5) the circles C1 and C2 intersect. These are identified by comparison of the X coordinates of the intersections with the X coordinates of the distal contact points DCP of each of the central teeth to determine which segments of the trough equation will be used, as explained more fully in the description of the tooth placement routine (2200) below.
 Finally, a distal contact point line DCPL is constructed for the central tooth through the DCP, at the intersection of circle C1 with the MO, and through the center of the identified circle segment of the MO, the expanded MTE, on which the DCP of the tooth lies. This line lies along a radius of the circle segment of the MO curve through the distal contact point of the central tooth. Similar lines DTMP are constructed for the center of the tooth TMP.
 (845) For each of the remaining mandibular teeth on the same side of the arch, in distal sequence, a new mandibular trough offset MO1 is calculated, by expanding the MTE with radii of curvature increased by the amount of the next tooth's OFFSET and with center of the circles C1 and C2 moved labially or outwardly from the MTE along the prior tooth's distal contact point line DCPL by the amount of the current tooth's OFFSET This is the MCP for the next tooth. Circle C1 for the tooth is constructed with a radius equal to the mesiodistal width of the tooth and with its center at their center point MCP. Circle C2 is constructed with a radius equal to MDW/2 and with centers coincident with circles C1.
 For bicuspids and molars, the tooth midpoints TMP can be considered as their points P3. Then, as with the central, the intersections of MO and circles C1 and C2 are calculated for these teeth. The distal contact points DCT of these teeth are at the intersections of MO for the tooth and the respective C1s. The centers of the teeth TMP are at the intersections of MO for the tooth and the respective circles C2. The MO sector segments which the circles intersect are identified. Selection of the segments is made by comparing the X and Y coordinates of intersections to X and Y coordinates of distal contact points DCPs. Finally, a distal contact point line DCPL is constructed from selected segment center to the plane DCP. The same is done for the centers of the teeth TMP.
 (848) The substeps (842) are repeated for all of the remaining mandibular teeth on the same side of the arch. Then, (849) substeps (840)-(848) are repeated for the teeth on the opposite side of arch.
 (900) Best Fit Mandibular Arch Equation Step:
 The above step (800) leaves the crown long axes CLA of the mandibular teeth intersecting the MCHP reference plane, which is at the level of the mandibular trough MT at or just below the gingival center points GCP of the teeth, along the mandibular trough equation MTE. The discontinuous offset equation MO, however, contains the approximate tips of the teeth in the occlusal plane MOC, with the teeth irregularly offset as represented by the discontinuous MO lines in FIG. 4B. To place the tips of the teeth into an ideal arch, (900) a final equation for better placement of the buccal cusp tips and incisal edges of the mandibular teeth in a continuous arch is developed. The development of the best fit equation is illustrated in the detailed flowchart of FIG. 2M.
 When viewed perpendicularly to the occlusal plane as in FIGS. 4B and 7B, it can be seen that the buccal cusp tips and incisal tips of all of the individual teeth do not lie along either the mandibular trough equation or the same geometrical expansion of that equation. In fact, due to small anatomical variations, it is unlikely that the tips will fall on any smooth curve when the tooth CLAs intersect a smooth curve at the mandibular trough in the MCHP and the LAIs are preserved. To remedy this, the equation is statistically developed that best fits the cusp tips and incisal edges of the individual teeth; a Best Fit Buccal Cusp Equation BFBCE. In the formulation of the equation, the coordinates of the right and left tooth midpoints TMP, the ICPs or ICs in FIG. 7B, are preferably averaged. The equation BFBCE may be obtained (910) by use of polynomial or other bezier or least square statistical techniques to arrive at a best fit equation. These are available in any of a number of off-the-shelf software packages.
 Such a BFBCE equation is plotted in FIG. 4B. Once the BFBCE is determined, it may be (915) converted to a circle segment equation in a manner such as with the spline to circle conversion routine (2100). This equation provides a basis for moving the teeth labially or lingually from the discontinuous offset equation MO to place the tips of the mandibular teeth in a smooth arch in the occlusal plane CP, as illustrated in FIG. 7C. To do this, in the next step the profile planes will be translated bodily in their own horizontal X-directions (which is an X-Y movement in the coordinates of the horizontal planes), moving their MTPPs off of the MTE in the MCHP (or MT).
 (1000) Mandibular Best Fit Arch Placement Step:
 After statistically deriving a best fit equation BFBCE, (1000) positions of the individual mandibular teeth are calculated to translate then facially, either labially or lingually, so that their tips fall on the best fit curve. This step is illustrated in detail in the flowchart of FIG. 2N.
 To achieve this, (1005) the mesiodistal contact point of the mandibular central, the point MCP, as in FIG. 7B, is first placed on the intersection of the midline ML with the BFBCE in the same manner as it was placed on the MO in step (800). Then (1010) circles C1 and C2, as defined above, for the tooth are constructed and their intersections with the BFBCE curve are found. As with the placement in step (800) above, the intersection of C1 with BFBCE is the distal contact point DCP of the tooth, and the intersection of C2 with the BFBCE curve, is the center point TMP (which aligns with IC) of the tooth. This, in effect, moves the tooth normal to the circle segment of the BFBCE associated with the TMP. Then, (1015) new circles C1 and C2 are constructed with centers at the distal center points DCP and (1020) substeps (1005) and (1015) are repeated for all teeth on the same side of the mandibular arch. Then, (1025) steps (1005) through (1020) are repeated for the teeth on the other side of the mandibular arch. The placement uses the tooth placement routine (2200), the description of which below explains in detail the placement of the mandibular teeth on the BFBCE.
 This step bodily translates the teeth in a generally horizontal direction, and rotates the teeth of the mandible about their CLAs to place incisal edges and cusp tips, as determined in step (800), on the BFBCE. With the completion of this step the finished positions of the mandibular teeth are calculated and the mandibular occlusion is finalized. At this point the mandibular occlusion can be envisioned as an ideal setup cast in stone, to which the maxillary occlusion will be fitted and related.
 The finish positions of the mandibular teeth are illustrated in FIG. 7C in which the X-Y coordinates are those of the horizontal arch planes. A vertical Z coordinate, perpendicular to the horizontal X-Y plane, is aligned with the Y axes of the individual tooth profile planes. The X coordinates of the profile planes are aligned with the labial-lingual directions La-Li in FIG. 7B.
 (1100) Maxillary Tooth Placement Step:
 The construction of occlusion requires (1100) the fitting of the maxillary teeth to the already positioned mandibular teeth. This is accomplished by deriving a modified best fit buccal cusp equation BFBCE for the maxillary teeth in the step illustrated in detail in the flowchart of FIG. 2O. Unlike with the mandibular teeth, with the maxillary teeth, the cusp tips of the posterior teeth and incisal edges of the anterior teeth are not set in a single arch. The maxillary teeth are rather set: (1) with the central groove-marginal ridge points of the maxillary bicuspids and molars on the BFBCE, (2) with the maxillary anteriors spaced labially off of the BFBCE to allow for incisal overlap and a clearance between the lingual surfaces thereof and the labial surfaces of the mandibular teeth, and (3) with the cuspid tips in the arch generally between the first maxillary bicuspid and the lateral incisor. The arches on which the maxillary teeth are placed as illustrated in FIG. 4C, as explained above.
 For the maxillary incisors, the modification of the BFBCE first involves averaging the distances from point P2 to point P3 on the mandibular incisor incisal edge, and dividing by two, to locate the arch that will contain the labial surface of the tooth adjacent the incisal center point ICP of the tooth, which is generally the point P3. This produces a uniform distance from the best fit equation to the contact point of the facial surface on the labial side of the mandibular anterior teeth with the facial point on the lingual side of the maxillary anterior teeth. An additional distance, of typically one-quarter millimeter, is added to the averaged distance to provide a slight Clearance between the upper and lower anterior teeth. This is illustrated in FIG. 7D.
 The maxillary anterior dentition is set for vertical position relative to the occlusal plane MOC according to occlusion criteria selected to provide a predetermined overlap. From the cuspid rise calculation of step (700), the vertical positions of the maxillary cuspids are known relative to the mandibular occlusal plane MOC. For maxillary laterals and centrals, the vertical positions provide the overlaps according to the prescribed criteria, putting their lingual facial contact points with their mandibular counterparts on the MOC plane. All teeth are inclined at the prescribed crown long axis CLA inclination values LAI from Table 1 in step (600).
 In the (1100) placement of the teeth of the maxilla, or upper jaw 24, with respect to those of the mandibular, or lower jaw 22, (1105) three arch forms are mathematically defined. These are (1106) the maxillary anterior arch form MAAF, (1110) the central groove marginal ridge arch form CGMRAF, and (1115) the maxillary cuspid arch form MCAF, as illustrated in FIG. 4B. The MAAF is established to position the maxillary incisors with respect to the BFBCE so that their lingual faces contact or clear the labial faces of the mandibular incisors. The CGMRAF is established separate from the MAAF because the maxillary bicuspids and molars contact their mandibular counterparts with their central groove marginal ridge intersection points juxtaposed on the mandibular buccal cusps. The MCAF is established separate from the MAAF and the CGMRAF because the cuspids have a still different relation to their mandibular counterparts.
 (1106) Location of the MAAF relative to the BFBCE requires a circle segment radius expansion of the BFBCE equation such that the lingual surfaces of the maxillary incisors, after being adjusted vertically to provide a predetermined overlap, will contact the labial face of the mandibular incisors at points spaced labially from the BFBCE with the predetermined Clearance. This expansion is calculated as the average distance between points P3 and P2 on the four maxillary incisors and adding the predetermined Clearance of typically 0.25 mm. This expansion, so calculated, is added to the BFBCE circle segment radii to define the maxillary anterior contact arch form MAAF. The MAAF is thus also expressed as a circle segment equation.
 The calculation of the amount of circle segment radius expansion of the BFBCE needed to define the MAAF is made at the midpoint of the mesiodistal width of either maxillary central, TMP1 in FIG. 4C. This would be the intersection with BFBCE of circle C2 in FIG. 7C. The tooth is placed on the maxillary contact arch form equation MAAF such that the mesial contact point of the tooth is on intersection of the midline ML and the maxillary contact arch form MAAF (FIG. 4C).
 (1108) The MAAF is defined as follows with respect to upper laterals and centrals:
 t=number of teeth (4),
 Avg=2 (to find midpoint), and
 Clearance=0.25 mm, typically.
 P2 and P3 are points on the maxillary central as defined in step (600). As described above, the crown long axes CLA of these teeth are angulated relative to the occlusal plane at the crown long axis seed values stated in Table 1.
 (1109) The tooth placement proceeds in accordance with the tooth placement routine (2200) described below. The placement positions the lingual faces of the central teeth on the MAAF, with the central mesial contact point MCP1 on ML. The midpoint TMP2 of the mesiodistal width of the next maxillary tooth is then placed on the maxillary contact arch equation MAAF such that the mesial contact point MCP2 touches a line normal to the curve MAAF and through the distal contact point DCP1 of the previous tooth. This procedure applies on one side of the occlusion up to the cuspid. The other maxillary side is constructed similarly.
 The next substep in the construction of the maxillary occlusion is (1110) the definition of the location of the arch for horizontal placement of the posterior teeth. The teeth are again set at the LAI values of Table 1 from step (600). (1111) The intersections of the marginal ridge and the central groove, which, if not separately selected in step (600) may be taken as point P5 in FIG. 6C, are placed over the buccal cusp of the appropriate mandibular tooth whose cusps were previously positioned on the best fit buccal cusp equation BFBCE. Thus, the CGMRAF coincides with the BCBFE as shown in FIG. 4B.
 For the maxillary cuspids, (1115) the cusp tips are placed on some smooth arch between the MAAF and the CGMRAF Preferably, their tips are placed on the BFBCE expanded by the average of the distances therefrom to the incisal tip of the lateral and to the buccal cusp tips of the first maxillary bicuspids. This labial distance from this point to the buccal cusp tip of the first bicuspid may alternatively be used to place the distal contact point of the cuspid, with its mesial contact point in contact with the distal contact point of the lateral. The point to which the BFBCE must be expanded to locate the buccal cusp tip of the first bicuspid for the two above alternatives is P3X(U,4)-P5X(U,4). The cuspids will thereby be spaced out from the BFBCE by the average of a distance equal to the horizontal or X distance from P5 to P3 on the first maxillary molar, as illustrated in FIG. 6C, and the MAAF.
 Alternatively, the cuspids may be placed with their mesial contact points MCP3 on the MAAF and with their distal contact points DCP in line with the mesial contact points or with the buccal cusp tips of the first maxillary bicuspids.
 A third alternative in placing the cuspids is to use the same criteria for clearance with the mandibular teeth used for the definition of the MAAF. Following the determination of the MCAF, the cuspids placed adjacent the laterals with the tips thereof on the MCAF, followed by the successive placement of the posterior teeth with the marginal ridges thereof on the CGMRAF (BFBCE), all according to routine (2200).
 In relating the profile and archform drawings and equations above, it should be noted that the X dimension of the profiles on which P3 and P5 are defined are vertical planes, and that the X direction in these planes corresponds to the labial direction in the horizontal planes of the archforms, as was explained for the mandibular teeth in connection with FIG. 7C. Thus, addition of an X component of a point on a tooth profile to an archform curve results in a labial expansion of the archform, or an increase in the radius of the corresponding circle segment of the archform circle series equation.
 At this point, information from the prescription 27 from the orthodontist 14 is retrieved to determine (1120) which maxillary anterior vertical occlusion method has been selected. The methods may include, for example, (1121) Roth occlusion, (1122) Ricketts occlusion, or (1123) the preferred method, referred to by the inventors as Elan occlusion. These are discussed below.
 Where (1121) Roth occlusion has been selected, the maxillary cuspids will extend a distance CRU3 equal to the cuspid rise CR below the occlusal plane MOC, and for laterals and centrals, the teeth will extend a distance CRU2 equal to 0.5 the cuspid rise beyond the occlusal plane, as illustrated in FIG. 7D. From step (725), the treatment is selected to apply either group function or cuspid rise function, and the respective cuspid rise quantities for maxillary cuspids are determined. From the lowest point on buccal (facial) cusp, a distance is measure vertically upward equal to 0.5 CR to find the intersection of occlusal plane MOC and central and lateral teeth if two profiles were taken, the profile that includes marginal ridges is used. The intersections of MOC with each maxillary incisor are defined as follows:
 Facial intersection with MOC=FIMOC,
 Lingual intersection with MOC=LIMOC,
 The distance from LIMOC to FIMOC, DLF, is computed as follows:
 where LIMOC is the contact point with MAAF.
 Where (1122) Ricketts occlusion is prescribed, the maxillary cuspids also extend below the MOC by a distance CRU3 equal to the cuspid rise CR. The laterals are positioned such that the tips are the distance CRU2 of 1.0 mm above the cuspid tips, and the distance CRU1 is such that the tips of the centrals are 0.5 mm above the cuspid tips. From step (725), in which either group function or cuspid rise function were selected, the respective cuspid rise quantities are applied for the maxillary cuspids. Then, from lowest point on buccal (facial) cusp, a distance of 1.0 mm is measured upward on the laterals and a distance of 0.4 mm is measured upward on centrals to find the intersection of MOC with the central and lateral teeth. If two profiles were taken, a profile that includes the marginal ridges is used. A line is then constructed through the points on the buccal cusps parallel to the MOC. The intersections with the teeth are defined as follows:
 Facial intersection with MOC=FIMOC
 Lingual intersection with MOC=LIMOC
 Distance DLF from LIMOC to FIMOC=/XFIMOC−XLIMOC/
 where LIMOC is contact point with MAAF
 Where (1123) Elan occlusion has been selected, the maxillary cuspids will extend a distance CRU3 equal to 0.67 of the cuspid rise CR below the occlusal plane MOC, laterals extend a distance CRU2 equal to 0.33 of the cuspid rise CR below the plane MOC, and the centrals extend a distance CRU1 equal to 0.50 of the cuspid rise CR below the plane MOC. As with the above, from step (725), in which either group function or cuspid rise function were selected, the respective cuspid rise quantities are applied for the maxillary cuspids. Then, from the lowest point on buccal (facial) cusp, a distance of 0.33 of the cuspid rise CR is measured upward on the laterals, and a distance of 0.50 of the cuspid rise CR is measured upward on the centrals, and the intersection of the teeth with the plane MOC is found. If two profiles were taken, a profile that includes marginal ridges is used. The MOC plane and the intersections with the teeth are defined as follows, as illustrated on the cuspid in FIG. 7D:
 Facial intersection with MOC=FIMOC.
 Lingual intersection with MOC=LIMOC.
 Distance DLF from LIMOC to FIMOC=/XFIMOC−XLIMOC/.
 LIMOC is contact point with MAAF
 The (1125) elected horizontal occlusion is selected. If (1126) the Roth maxillary anterior horizontal occlusion has been selected, no further changes are required. This results in the lingual surfaces of the teeth forming a smooth arc. If (1127) the Ricketts maxillary anterior horizontal occlusion has been selected, changes are made to cause the labial surfaces of the teeth to form a smooth arc. This requires finding the largest DLF, or LIMOC-FIMOC distance for the centrals, subtracting the other LIMOC-FIMOC distances of the incisors from this largest distance, adding the respective differences to each tooth to extend the LIMOC point lingually along line LIMOC-FIMOC, and establishing a new point at which the LIMOC is to intersect the MOC.
 If (1128) the Elan horizontal occlusion is selected, which is the preferred and illustrated embodiment, the horizontal tooth placement proceeds as set forth below. Because, given the overlap of the maxillary incisors, the labial-lingual thicknesses of the anterior teeth are greater in the plane of occlusion than the distance P3-P2 used to calculate the MAAF and the MCAF, offsets must be calculated and the maxillary teeth placed again on the offset versions of these archforms.
 First, in calculating the positions of the teeth to provide the horizontal occlusion, (1130) a distance is calculated from LIMOC to ICP for the maxillary centrals and the laterals. This distance is referred to as the maxillary anterior offset MAO, thus:
 (1135) The maxillary first bicuspid offset MBO is calculated:
 (1140) The maxillary tooth positions are then recalculated, one side at a time, with respect to the offset maxillary arch forms defined above that contain the buccal cusp tips and incisal edges of the maxillary teeth. This is achieved by sending the relevant parameters to the placement routine (2200) and calculating placement in the same manner as shown in FIG. 7B for the mandibular teeth. For the maxillary centrals, (1141) MAAF is adjusted such that the MAAF radii are increased by the amount of the MAO. This curve is now called maxillary contact archform offset MAAFO and is illustrated in FIG. 4C.
 Calculation of the positions of the maxillary incisors on the MAAFO, preferably in accordance with the tooth placement routine (2200), closes the spaces between the teeth that results from expanding MAAF to MAAFO.
 The intersection of MAAFO and the arch midline ML is the mesial contact point MCP of the tooth. A circle C1 is constructed with a radius equal to the mesiodistal width MDW of the central incisor. Its center is at the intersection point of MAAFO and ML. The intersection of the circle C1 with MAAFO is the distal contact point DCP. Then, circle C2 is constructed with a radius equal to MDW/2, that is half the mesiodistal width MDW. Its center is coincidental with that of C1. The intersection of the circle C2 with the MAFFO curve is the mid-point of tooth TMP and the incisal center point ICP.
 The intersection of MAAFO and circles C1 and C2 are then constructed. The curve defined by MAAFO and the intersection of circle C1 is the distal contact point DCP. The intersections of MAAFO and MAAFO circle segment lines are found. The X coordinates of the intersections are compared to the X coordinates of DCP to determine which segment's center will be used.
 A distal contact point line DCPL is constructed from the selected segment center to the DCP. Similarly a center of tooth line TMPL is constructed from the sector center to the TMP. Thus, the tooth LIMOC is on MAAF and the tooth mesiodistal width line is on the MAAFO arch. The location of FIMOC is accordingly determined by adding DFL to the MAFFO circle segment radius through the TMP.
 The MAAFO, like the MO for the mandibular teeth, is discontinuous, with the archform being offset differently for the different maxillary teeth. Accordingly, for the maxillary laterals, the prior MAAFO is replaced with the MAAF adjusted such that the MAAF radii are increased by amount of MAO for lateral. The tooth's MCP is the tooth's MAO distance from the MAAF along the prior tooth's distal contact point line DCPL. Circle C1 is constructed with a radius the mesiodistal width of the tooth and with a center at the tooth's MCP. The intersection of C1 with the MAAFO is the tooth's DCP. Circle C2 is constructed with a radius equal to half of the tooth's MDW and with a center coincident with that of circle C1. The intersection of circle C2 with MAAFO is the tooth's ICP.
 Then, the intersections of MAAFO and the MAAFO sector lines are found. The X and Y coordinates of intersections are compared to the X and Y coordinates of DCP to determine which segment's center will be used. A distal contact point line DCP is constructed from the selected segment center to the DCP. Similarly a center of tooth line TMPL is constructed from the sector to the TMP.
 For the maxillary cuspids, the prior MAAFO is eliminated. A new arch form, the maxillary cuspid arch form MCAF, is computed to place the cuspid between the lateral and the first bicuspid. In one preferred approach, the MCAF is constructed offset from the BFBCE by the average of the OFFSETs of the first bicuspid and the lateral, as calculated in substep (1135) above. With exception of a new arch radius, the cuspid is placed as above.
 For the maxillary bicuspids and molars, the arch form CGMRAF, which is the BFBCE, is offset by MBO. CGMRAF is adjusted by adding MBO for the respective teeth. The cuspid tips on the MCAF, which was offset from the BFBCE to align with the buccal cusp tips of the first bicuspids in (1115) above, are thus in line with the posterior buccal cusp tips. From the cuspid DCP, circles C1 and C2 are constructed and DCPLs are established. This sequence is repeated for remainder of the teeth, completing the relation of the maxillary and mandibular occlusions. The finish positions of the maxillary teeth are illustrated FIG. 4D.
 At this point, the final positions of the maxillary teeth have been calculated, and thus, the finish positions of all of the teeth.
 The appliance design procedure includes the steps of (1200) determining the location of the mandibular archwire plane relative to the calculated finish positions of the mandibular teeth, (1300) calculating the angle of each mandibular bracket slot relative to the mounting surface of the respective tooth, (1400) determining the location of the maxillary archwire plane relative to the calculated finish positions of the maxillary teeth, (1500) calculating the angle of each maxillary bracket slot relative to the mounting surface of the respective tooth, (1600) calculating the shape of the mandibular archwire and the slot in-out dimension of each mandibular bracket, (1700) calculating the shape of the maxillary archwire and the slot in-out dimension of each maxillary bracket, and (1800) calculating the contours of bracket placement jigs for each tooth.
 (1200) Mandibular Archwire Plane Step:
 The next step is (1200) to establish the position of the archwire plane for the mandibular teeth, which is illustrated in detail in the flowchart of FIG. 2P. The archwire plane can be located in an infinite number of vertical positions since the brackets and archwire will be designed to accommodate any chosen location. Since the overlap of the maxillary teeth is known, for labial bracket placement, the mandibular archwire plane is set to provide bracket clearance for the maxillary teeth in the finished occlusion. For lingual bracket placement, this consideration is given to the maxillary archwire plane instead, in step (1300) below.
 Since the maxillary teeth do not pose a bracket interference dilemma with labial bracket placement, the brackets can be positioned for ease of placement, cosmetic considerations and gingival health. This applies to the mandibular bracket positioning where lingual bracket placement is used. Typically, these brackets are located more centrally than the brackets of the other arch.
 More particularly, as illustrated in the flowchart of FIG. 2P and FIG. 8, (1200) to establish the archwire plane, (1205) the selected vertical occlusion and respective vertical overlap from MOC for cuspids, laterals and centrals is recalled from (1110). Then, (1210) with the information from (705), the buccal cusp height BCH is recalled for each bicuspid and molar. Next, (1215) the maximum BCH or anterior vertical overlap is chosen as the maximum vertical overlap MVO. Then, (1220) a distance equal to the MVO is measured downward from the MOC. Finally, (1225) half of the bracket height (typically 3.0 mm) plus an additional 0.75 mm is added for occlusal clearance. This defines the mandibular archwire plane MAWP. This places brackets as occlusal as possible with an 0.75 mm clearance from the worst case from the maxillary occlusion.
 (1300) Mandibular Slot Inclination Step:
 Once the archwire planes have been defined with respect to the teeth, as illustrated in the flowchart of FIG. 2Q, (1300) the angle between the bracket mounting surface of the teeth and archwire plane is determined. This angle minus 90° is the facial torque or inclination angle to be formed into the brackets. This also defines the bracket slot placement height which is the distance from the top of the incisal edge to the archwire plane. This distance is calculated perpendicular to the archwire plane.
 Slotless bracket bodies (vanilla brackets) have now been positioned appropriately. A smooth archwire is then designed such that it will pass through the bodies of the brackets. The archwire must not cut too deeply into the bracket or pass even partially outside the face of the brackets. Brackets are chosen having different heights according to need. Without modifying buccal tube assemblies, standard bracket distances from the tooth surface to the center of the slot may be used as a seed values. The archwire equation is then mathematically derived from cubic spline and tangential circle techniques as previously described and provided in the routines (2000) and (2100). Both archwires are developed similarly.
 Bracket angle determination (1300), more particularly, is achieved by (1305) taking the intersection of the MA WP and labial (buccal) surface of each mandibular tooth in the case of labial appliances. and the intersection of the MAWP with the lingual surface of each tooth in the case of lingual appliances. Then, (1310) circles are constructed with centers at the intersections and with diameters that represent the occluso-gingival (vertical) dimensions of the bracket bonding pad (typically 3.0 mm). Then, (1315) X, Y coordinates of the circle intersections with labial (buccal) tooth surface are taken, and, with the equations:
R 2=(X 1 −h)2+(Y 1 −K)2
Y 2 =mX 2 +b 2
Y 3 =mX 3 +b 3
 (1320) The slopes between the points of intersection are calculated to produce the facial inclination angle FIA, where:
 h,k=coordinates of circle center
 X1, Y2, b2=definition of first line segment
 X3, Y3, b3=definition of second line segment
 Then, as illustrated in FIG. 8A for labial appliances, π/2 radians are then subtracted to produce the slot inclination angle SIA:
 (1400) Maxillary Archwire Plane Step:
 The next step is (1400) locating the maxillary archwire plane as illustrated in the flowchart of FIG. 2R and diagram of FIG. 8. For the maxillary centrals, this involves (1405) finding the vertical distance from incisal edge to point P4. (1410) The smallest value is selected and divided by two to produce the slot placement height for the maxillary centrals. (1415) For terminal maxillary bicuspids the vertical distance from buccal cusp to point P4 is found. (1420) Again, the smallest value is selected and divided by two. This produces the slot placement height SPH for the terminal maxillary bicuspids.
 For maxillary centrals, (1425) the Y value of FIMOC is subtracted from the Y value for the slot placement height SPH. This is the distance from MOC to the slot centerline. For terminal maxillary bicuspids, (1430) the Y value of MOC is subtracted from the Y value for the slot placement height SPH. This is the distance from MOC to the slot centerline. Then, (1435) the SPH for the terminal bicuspid from SPH for the maxillary centrals. This is elevation change DH of the maxillary archwire relative to the MOC from the centrals to the terminal maxillary bicuspids. (1440) The elevation of the maxillary archwire MXAWP from the MOC, or archwire height AHTon each tooth, is calculated as follows:
AHT=K+DH+SPH−MOC Y+Vertical overlap from (1110)
 where K is the conversion factor from Table 3.
TABLE 3 Extraction Non- (e.g. 2nd Tooth Type Extraction Bicuspid) Maxillary Central 0.0 0.0 Maxillary Lateral −0.19 −0.28 Maxillary Cuspid −0.42 −0.62 Maxillary First Bicuspid −0.68 −1.00 Maxillary Second Bicuspid −1.00 NA Maxillary First Molar −1.32 −1.46
 (1500) Maxillary Slot Inclination Step:
 Once the archwire plane is determined, as illustrated in the flowchart of FIG. 2S, (1500) the slot inclination angle SAI for each of the maxillary tooth brackets is determined in a manner similar to the slot inclination determination step for the mandibular brackets (1300). This step (1505) begins by finding the intersection of the maxillary archwire plane MXAWP with the labial or buccal surface of each maxillary tooth. Then, (1510) circles are described, for each maxillary tooth, having centers at this intersection point and having diameters equal to the occluso-gingival, or vertical, dimensions of the bracket bonding pad, which is typically 4.0 mm. From these circles, (1515) X, Y coordinates of the intersections of the circles with the labial or buccal tooth surface are found, as follows:
R 2=(X 1 −h)2+(Y 1 −k)2
Y 2 =mX 2 +b 2
Y 3 =mX 3 +b 3
 Where: h,k=coordinates of the circle center
 X1, Y1=possible coordinates on the circle
 X2, Y2, b2=definition of a first line segment
 X3, Y3, b3=definition of a second line segment
 Then, as illustrated in FIG. 8A, (1520) π/2 radians are then subtracted to produce the slot inclination angle SIA:
 (1600) Mandibular Archwire and Slot Depth Step:
 The next step, as illustrated in the flowchart of FIG. 2T, is (1600) to determine the mandibular archwire and bracket in-out dimension. First, (1605) the circle segment of the BFBCE with which the ICP of the right central is associated is determined, as illustrated in FIG. 8B. Then, (1610) the incisal center point and circle segment center point plane ICPCDCPP is created normal to the arch planes. An incisal center point line ICPL is struck that will pass through the ICP and a particular circle segment center point CSCP associated with the tooth. Then (1615) the Pythagorean distance PD from CSCP to ICP is determined. Then, (1620) viewing the tooth in the ICPCSCPP, as illustrated in FIG. 8C, a line NL is struck normal to the BFBCE plane through the ICP, which is the intersection of CLA and BFBCE. Next, (1625) still viewing the tooth in this plane, the intersection point XP of NL and MAWP is determined.
 Still viewing the tooth in the ICPCSCPP, (1630) the X distance XD to the labial surface of the tooth from the XP is determined, and (1635) PD is added to XD and the lower limit of the bracket slot LLBS. The LLBS is a distance associated with the particular bracket that will be placed on this tooth. It is the deepest slot allowable for that bracket. Then, the lower limit LL is calculated thus:
 Similarly, (1640) PD is added to the XD and the upper limit of the bracket slot ULBS. The ULBS is also a distance associated with the particular bracket that will be placed on this tooth. It is the shallowest slot allowable for that bracket. The, the upper limit UL is calculated thus:
 (1645) Then, viewing the mandibular occlusion in a plan view and moving out along the ICPL from its CSCP by the LL distance, X and Y points, AWLLX,Y, are determined relative to an origin at the intersection of BFBCE and the mandibular midline ML. Then, (1650) viewing the mandibular occlusion in a plan view and moving out along the ICPL from its CSCP by the UL distance, X and Y points, AWULX,Y are determined relative to the intersection of BFBCE and the mandibular midline ML. Then, (1655) the mid-point of AWLLX,Y and AWULX<Y is found and steps (1605) through (1650) are then repeated for all mandibular teeth.
 Then, (1660) the average mid-point and distance from right to left is calculated to force mandibular archwire symmetry:
 SX,Y is the symmetricalized point.
 MP is the mid-point of BCBCE.
 PR is a point on the right side of the midline.
 PL is a point on the left side of the midline.
 The smoothest curve SC that will pass between all AWLLX,Y and AWULX,Y points is then determined, as illustrated in FIG. 4E. This is accomplished by the following procedure:
 a) The mid-point of each AWLLX,Y and AWUKX,Y pair is found.
 b) Then, as described above, a cubic spline equation is passed through these points.
 c) The existence of any inflection points is determined.
 d) The curve with the least variation in radius changes along the curve is considered the smoothest curve. Preferably, it has no inflection points. If there are one or more inflection points, a logical alternative bracket solution will be derived based upon where the inflection occurred.
 Then, (1665) the intersection point XSCICPL of the mandibular right central's ICPL is determined as well the smoothest curve as defined above in substep (1660). Next, (1670) the in-out IO of that particular tooth is determined as the distance along ICPL from ICP to XSCICPL minus that tooth's XD. Then, (1675) steps (1665) and (1670) are repeated until all in-out dimensions are calculated.
 Finally, (1675) all XCSICPL points are passed into the cubic spline routine (2000) and to circle routine (2100) and (1680) all circle segment information gathered therefrom are converted to linear distance LD moves needed to bend the appropriate wire, as will be further explained in connection with the wire bending step (3200) below. The bracket slot cutting is described in connection with step (3000) below.
 (1700) Maxillary Archwire and Slot Depth Step:
 The next step, as illustrated in the flowchart of FIG. 2U, is (1700) to determine the maxillary archwire and bracket in-out dimension. As with the mandibular determination step (1600), (1705) the circle segment of the BFBCE with which the ICP of the right central is associated is determined. The step is similar to that for the mandibular slot in-out dimension calculation of FIGS. 4E and 8C, except that the maxillary centrals and laterals are associated with the MAAF rather than the BFBCE, the maxillary cuspids are associated with MCAF, and teeth posterior to the cuspid are associated with the BFBCE.
 The calculation proceeds with (1710) the incisal center point and circle segment center point plane ICPCDCPP being created, with a line being struck that will pass through the incisal center point line ICPL which will pass through the ICP and a particular circle segment center point CSCP associated with the tooth. The plane passing through the ICP and the CSCP and normal to the mandibular trough MT is the ICPCSCPP. Then (1715) the Pythagorean distance PD from CSCP to ICP is determined. Then, (1720) viewing the tooth in the ICPCSCPP, a line NL is struck normal to the BFBCE through the intersection of CLA and BFBCE. Next, (1725) still viewing the tooth in this plane, the intersection point XP of NL and MAWP is determined.
 Still viewing the tooth in the ICPCSCPP, (1730) the X distance XD to the labial surface of the tooth from the XP is determined, and (1735) PD is added to XD and the lower limit of the bracket slot LLBS. The LLBS is a distance associated with the particular bracket that will be placed on this tooth. It is the deepest slot allowable for that bracket. Then, the lower limit LL is calculated thus:
 Similarly, (1740) PD is added to the XD and the upper limit of the bracket slot ULBS. The ULBS is also a distance associated with the particular bracket that will be placed on this tooth. It is the shallowest slot allowable for that bracket. Then, the upper limit UL is calculated thus:
 (1745) Then, viewing the mandibular occlusion in a plan view and moving out along the ICPL from its CSCP by the LL distance, X and Y points, AWLLX,Y, are determined relative to the intersection of BFBCE and the mandibular midline ML. Then, (1750) viewing the mandibular occlusion in a plan view and moving out along the ICPL from its CSCP by the UL distance, X and Y points, AWULX,Y are determined relative to the intersection of BFBCE and the mandibular midline ML. Then, (1755) The mid-point of AWLLX,Y and AWULX,Y is found and steps (1705) through (1750) are then repeated for all mandibular teeth.
 Then, (1760) the average mid-point and distance from right to left is calculated to force mandibular archwire symmetry:
 SX,Y=the symmetricalized point.
 MP=the mid-point of BCBCE.
 PR=a point on the right side of the midline.
 PL=a point on the left side of the midline.
 Then the smoothest curve SC that will pass between all AWLLX,Y and AWULX,Y points is determined. This is accomplished by the following procedure:
 a) The mid-point of each AWLLX,Y and AWUKX,Y pair is found.
 b) Then, as described above, a cubic spline equation is passed through these points.
 c) The existence of any inflection points is determined.
 d) If there are no inflection points, this is considered the smoothest curve. If there is an inflection point, a logical alternative bracket solution will be derived based upon where the inflection occurred. The relevant information necessary to determine a new pair of AWLLX,Y and AWULS,Y and their midpoints is undertaken. It should be noted that there are varying LLBS and ULBS possibilities available for each tooth.
 Then, (1765) the intersection point XSCICPL of the mandibular right central's ICPL is determined as well as the smoothest curve as defined above in substep (1760). Next, (1770) the in-out of that particular tooth is determined as the distance along ICPL from ICP to XSCICPL minus that tooth's XD. Then, (1775) steps (1765) and (1770) are repeated until all in-out dimensions are calculated.
 Finally, (1775) all XCSICPL points are passed into the spline to circle program and (1780) all circle segment information gathered therefrom are converted to linear distance LD moves needed to bend the appropriate wire, as will be further explained in connection with the wire bending step (3200) below. The bracket slot cutting is described in the discussion of step (3000) below.
 (1800) Placement Jig Design Step:
 With the shapes of the individual teeth determined, their finish positions calculated, and the brackets designed and their places on the individual teeth determined, the information necessary for the design of bracket placement jigs to aid the orthodontist in positioning the brackets in their proper positions on the individual teeth is available. In the preferred embodiment of the invention, the design of the placement jigs is carried out in the software associated with the jig manufacturing step (3500) described below, following a loading of the appropriate files with the necessary data from the calculations described above into the manufacturing control computer 30 c. An abbreviated presentation of the jig design substeps is set forth in the flowchart of FIG. 2V.
 Referring to FIG. 2V, (1805) a file containing data of the individual tooth profiles, the archwire plane location including data relating each of the tooth profiles to the relevant archwire plane, the bracket profiles relevant to each tooth, and the bracket design data including the slot size, inclination and depth, are prepared. Then, (1810) the tools that will form the jig are determined, and (1815) clearances are established. Then, (1820) data needed for instructions to cut an internal profile into each jig is assembled to hold a bracket and to locate the bracket at the proper position on the tooth by precise fitting of the jig over the tooth profile along a labial-lingual plane through the tooth midpoint TMP.
 The details of the jig design step, as it is performed along with the jig manufacturing step, is described in detail in connection with the description of the flowchart of FIG. 2Z under step (3500) below.
 Three subroutines are used in calculating various archforms and calculating the positions of the teeth thereon. These are (2000) the cubic spline equation curve calculation subroutine, (2100) the spline equation to circle segment equation conversion subroutine, and (2200) the tooth placement subroutine. These are illustrated in the flowchart of FIG. 2W.
 (2000) Cubic Spline Equation Fitting Subroutine:
 In the cubic spline interpolation, symmetrical data points are interpolated and a cubic spline equation is derived. As illustrated in FIG. 5A, a symmetrical mandibular trough or cubic spline equation SMT is shown for one side of the lower jaw. In FIG. 5A, the point MX,MY represents the intersection of the curve and the midline ML. The points SIX,SIY for I=1 to 6 represent the symmetricized points XML referred to above.
 The cubic spline method uses a cubic (3rd degree) polynomial to interpolate between each pair of data points. A different polynomial is used for each interval, and each one is constrained to pass through the original data points with the same slope as the data. At these points, slopes are computed by finding the slope of the parabola that passes through each data point and its two nearest neighbors.
 The iterations necessary to compute the cubic polynomial are as follows:
 1) For each data point, the X and Ycoordinates are made equal to zero and all other data points evaluated relative to this new original.
 2) The slopes of the cubic spline are computed by first computing the coefficients of the above described parabola, then a first point of a slope array is filled followed by the remaining points through the final slope array point.
 3) The spline coefficients are computed.
 4) The polynomial is evaluated.
 These steps are described in Science and Engineering Programs, Apple II Edition, Edited by John Heilborn, and published by Asborne/McGraw-Hill. Copyright, 1981, McGraw-Hill, Inc., and incorporated herein by reference.
 Once the polynomial has been evaluated, it is possible to acquire additional data points. A Y value can be determined for any given X value, with the constraint that additional data points be within the upper and lower limits of the original X values. The following iterations are performed before circle conversion:
 1) Determination of X and Y points on each side of the original data points. This is done by taking X points that are one thousandth (0.001) to each side of original X data points. Then X values two thousandths (0.002) less than the last data point are taken. Then Y points are determined for each arrayed X point by evaluation of the polynomial equation discussed above. Then the Y points of the array are calculated.
 2) The slope array is then filled with slopes corresponding to data points on either side of the original data points.
 3) The slope of the curve at each of the original data points is calculated. This involves retrieving X and Y points on either side of original data points, and calculating the slope at the original data points using the Point Slope method according to:
 SLOPE=the slope of the curve at that point.
 X1=the X point 0.001 to left of original data point.
 Y1=the Y point associated with X1.
 X2=the X point 0.001 to right of original data point.
 Y2=the Y point associated with X2.
 The slope is calculated using the arrayed point that is 0.002 less than the last data point and the last data point, and the slope is calculated using the point slope method as all array slopes are calculated.
 (2100) Circle Segment Conversion Subroutine:
 The circle segment conversion typically fits two circle segments into one spline segment. A spline segment is defined as the interpolated cubic spline equation which describes the shape of the curve between two original data points. A circle segment is defined as the arc associated with a beginning point, or end point, and the slope of tangency at that point. Two configurations of circle segments are possible when converting a spline segment into two circle segments, one where the first circle is larger than the second (FIG. 5B) and the other where the first circle is smaller than the second circle FIG. 5C, the variables in which are identified below. The iterations necessary to convert a spline segment into two circle segments are illustrated in FIG. 5D in which:
 P1X, P1Y=the beginning point of spline segment
 P2X, P2Y=end point of spline segment
 MT1=tangent slope of spline at point P1X, P1Y
 MN1=normal slope of MT1
 MT2=tangent slope at point P2X, P2Y
 MN2=normal slope of MN2
 P3X, P3Y=intersection of a line through point P1X, P1Y with a slope of MT1 and a line though point P2X, P2Y with a slope of MT2
 CL=a Cord Line, a line connecting points P1X, P1Y and P2X, P2Y
 CNL=a Cord Normal Line, a line normal to CL through P3X, P3Y
 hs,ks=the center of the smaller of the two circle segments
 The iterations to convert a spline segment into two circle segments are, as follows:
 1) Determine MN1 and MN2. They are the negative inverse of MN1 and MT2, respectively.
 2) Determine the intersection point P3X, P3Y.
 3) Determine the slope of the CL.
 4) Determine the slope of CLN.
 5) Determine the distance from P1X, P1Y to P3 X, P3Y. This is defined as test one.
 6) Determine the distance from P2X, P2Y to P3X, P3Y. This is defined as test two.
 7) Test to determine which length is smaller. If the test one result is shorter than the test result, the smaller circle is associated with P1X, P2Y, otherwise, the smaller circle is associated with P2X, P2Y.
 8) Rename the variable associating to the size of the circle. See FIG. 5B in which:
 P1X, P2Y=the beginning point of spline segment
 P2X, P2Y=the end point of spline segment
 MNS=the normal slope of small circle segment, equivalent to MN1 or MN2 depending on the relative results of test one and test two
 MNL=normal slope of large circle segment
 hs,ks=the center of the smaller of the two circle segments
 hl,kl=the center of the larger of the two circle segments
 P6X, P6Y=a distance, defined by the radius of the small circle, to a point along MNL from the spline segment point associated with it
 MNF=is the slope of the final line
 9) Determine the intersection of the line described by slope of CNL and passing through P3X, P3Y and the line described by MNS through the spline segment point associated with it. The intersection point of these two lines is the center of the smaller circle hs,ks.
 10) Determine the Pythagorean distance from the small circle center hs,ks to the spline segment points associated with it. This distance is the radius of the small circle rs.
 11) Move along the line described by MNL and passing through the spline segment point associated with it by the radius of the smaller circle rs. This point is P6X, P6Y.
 12) Strike a line from P6X, P6Y to hs,ks.
 13) The negative inverse of the slope of the line from P6X, P6Y and hs,ks is mnf.
 14) Determine the midpoint of the line from P6X, P6Y to hs,ks.
 15) Determine the intersection of the line described by a slope of mnf and passing the point described in step 14 and the line described by MNL and through the spline segment point associated with it. The intersection point of these two lines is the center of the larger circle hl,kl.
 16) Determine the Pythagorean distance from the large circle center hs,ks to the spline segment points associated with it. This distance is the radius of the larger circle rl.
 17) The intersection of the two circles is defined as the intersection of the line going through the large circle center hl,kl and the small circle center hs,ks and either of the circles. At this point the tangency of the two circles are equivalent.
 18) Accommodate an arc length calculation dependent upon which spline point is closer to P3X, P3Y:
 If the test one result is greater than that of test two, then:
 Theta1=A TN(m)−ATN(MSI)
 Theta1=A TN(msl)−ATN(m)
 Theta2=A TN(m)−ATN(mll)
 Theta1=the arc angle of the smaller circle
 Theta2=the arc angle of the larger circle.
 19) Calculate arc length for each segment.
 s1=rs (Theta1)
 s2=rl (Theta2)
 s1=arc length of smaller segment
 s2=arc length of larger segment
 20) Calculate the running arc length.
 21) Continue distally until all spline segments are converted.
 FIGS. 5E-5J illustrate the building of the mandibular trough data points into circle segments.
 (2200) Tooth Placement on Curve Subroutine:
 The individual tooth placement upon an equation is required in many steps of the tooth finish position calculation procedure (94). The preferred method is described here in connection with the first occurrence in the procedure for the placement of the mandibular teeth.
 There are four alternative equations upon which teeth can be placed: the mandibular trough MT equation, the maxillary anterior arch form MAAF equation, the maxillary cuspid arch form MCAF equation, and the central groove marginal ridge arch form MGMRAF equation. All occlusion equations will have been converted to circle segments before teeth are placed upon them. A typical tooth placement is illustrated in FIG. 5N, in which:
 DCP=Distal Contact Point
 ICP=Incisal Center Point
 MCP=Mesial Contact Point
 MCPL=is the Mesial Contact Point Line.
 The DCP is the point at which the tooth contacts the proceeding tooth. The ICP is the center of the tooth being placed. The MCP is the point at which the tooth contacts the preceding tooth. The MCPL is defined as the line through the DCP of the tooth being placed and the center of the circle segment associated with the DCP. The MCPL is the line upon which the DCP of the proceeding tooth will be found.
 The iterations to place the teeth onto the circle segments are:
 1) Determine the offset distance for the mandibular central tooth on the side of the jaw under consideration.
 2) Expand all circle segments about their centers by the offset amount.
 3) Determine the intersection of the first circle segment and the midline. This is the mesial contact point MCP of the central, as illustrated in FIG. 5K.
 4) Place the first circle C1, whose radius is the mesio-distal width of the tooth, at MCP, as illustrated in FIG. 5K.
 5) Determine which circle segment in the distal direction circle C1 intersects and identify the intersection point. This is accomplished by performing an iteration which begins by transferring the coordinate system to the beginning point of the circle segment, as illustrated in FIG. 5L, in which:
 XBEG, YBEG=beginning coordinates of the circle segment
 XEND, YEND=End points of the circle segment
 XINT, YINT=coordinates of circle intersection
 X and Y axes are oriented at XBEG, YBEG.
 The two following circle equations are then solved simultaneously:
R 1 2=(x−h1)+(y−k1)
R 2 2=(x−h2)+(y−k2)
 h1,k1=the center coordinates of the first circle
 h2,k2=the center coordinates of the second circle
 R1=the radius of the first circle C1
 R2=the radius of a second circle C2
 X,Y=coordinates of possible intersection points
 The following solutions are possible: (1) two real solutions which are labeled X1INT, Y1INT and X2INT, Y2INT, respectively. (2) imaginary solutions, which are discarded, whereupon the next circle segment is evaluated. If intersections are real, the circle segment is rotated, as illustrated in FIG. 2M, such that XEND, YEND is placed on the X axis. Then, XBEG, YBEG is subtracted from the rotated X intersection point X1INT or X2INT, and rotated XEND is subtracted from the rotated X intersection point X1INT or X2INT. If the signs of the results of the two subtractions are opposite, the rotated intersection point is tested for a value less than zero. If it is not less than zero, the other rotated intersection point is tested to determine if it is valid. The testing continues until a segment is found such that the subtractions produce opposite sign results and the associated rotated Y intersection point is less than zero. This is the distal contact point DCP of the tooth, as illustrated in FIG. 5N.
 6) Construct a line passing through the DCP and the center of the circle segment that intersects C1.
 7) Place circle C2, whose radius is one half the mesio-distal width MDW of the tooth, at the MCP.
 8) Determine which circle segment in the distal direction intersects circle C2 and identify the intersection point. This is the incisal center point ICP of the tooth, as illustrated in FIG. 5N.
 9) Eliminate all expanded circle segments.
 10) Determine the offset distance for the mandibular lateral.
 11) Expand all circle segments about their centers by the offset amount.
 12) Determine the intersection point of the expanded circle segment ECS associated with the DCP MCP Line. The intersection point is the mesial contact point MCP of the lateral, as illustrated in FIG. 5O.
 13) Place circle C1, with radius the mesio-distal width MDW of the lateral, at the current MCP point.
 14) Determine which circle segment in the distal direction circle C1 intersects and identify the intersection point, which is the DCP of the lateral.
 15) Construct a line passing through the DCP and the center of the circle segment that intersects C1.
 16) Place circle C2, whose radius is one half the mesio-distal width MDW of the tooth, at the MCP.
 17) Determine which circle segment in the distal direction intersects circle C2 and identify the intersection point. This is the incisal center point ICP of the tooth, as illustrated in FIG. 5P.
 18) Continue distally until all teeth are placed.
 19) Perform the same iterations for the co-lateral side of the arch.
 The appliance manufacturing procedure (97) includes the steps of (3000) manufacture of the custom brackets, (3200) manufacture of the custom archwires and (3500) manufacture of custom placement jigs for placement of the custom brackets on the patient's teeth. These steps are described in detail below for the embodiment in which all of the manufacturing is carried out at the appliance design facility 13.
 (3000) Bracket Manufacturing Step:
 The bracket manufacturing step (3000) produces the custom brackets, preferably by selecting bracket blanks and cutting a torque slot in the bracket for the archwire 64. This utilizes the modified CNC mill 40 illustrated in FIG. 2D. The bracket slot cutting step is illustrated in the detailed flowchart of FIG. 2X.
 Referring to FIG. 2X, the bracket manufacturing step (3000) begins with the computer 30 c (3005) loading the data for each bracket from the patient data file 36.
 For each tooth and bracket, as a default or initial selection, (3010) low profile brackets are assumed. Then, the slot angle FAI and the slot in-out dimension IO are read. Also, (3020) the radius of the archwire at the tooth midpoint is determined.
 Then, (3025) a main CNC program is created and (3030) the program loops to generate the code for the cutting of each bracket, beginning with the calculation of the variables for the bracket, (3040) assigning the variables for each bracket to (3045)-(3050) set the cutting of the slot at the appropriate angle by rotating the bracket support 73 and setting the cutter 77 c to a cooperating height Z and horizontal X position. If the position of the slot lies outside of the area of the bracket, a bracket of the appropriate higher profile is called for by the program, and loaded, either automatically or by an operator. The code is then generated (3055) to control the path of the cutter in the Y direction to cut the archwire radius in the slot bottom. (3060) then, the NC code is combined with the calculated variable values for the tooth and bracket and a subroutine is generated for the bracket, with (3065) the P-codes subroutines written the file. (3068) The program loops until codes for all of the brackets are complete.
 Then, (3070) the CNC code is preferably downloaded to an NC controller and the brackets are formed by the cutting of the slots in the series of bracket blanks, and (3080) a report is written.
 (3200) Arch wire Manufacturing Step:
 The archwire manufacturing step (3200) produces the archwire 64, as illustrated in FIG. 2E, preferably that is symmetrical about its archwire midline AML, having the appropriate terminal leg span TLS, formed of a series of circle segments.
 As illustrated in the flowchart of FIG. 2Y, the archwire manufacturing step (3200) executes a program with the manufacturing control computer 30 c to generate a CNC code to operate the wire forming machine 40. The program begins by (3215) opening one or more files from the calculated patient data 36 and reads therefrom the wire alloy and the wire cross-section prescribed, and an array of data that contains a series of j sets of data including the radius and sector length of each circle segment of which the archwire curve is formed, and the calculated total cumulative archwire length. To the archwire equation, (3220) a radii and sector lengths are added to produce a one half inch of straight segment at each end of the wire to form parallel terminal leg extensions. Then, calculating the cumulative slopes and sector lengths of the wire along the equation, (3225) the terminal leg span TLS is calculated.
 Based upon the wire type selected, (3230) one of several data files or tables are read. For rectangle wire, for example, four files would include: (1) 0.022″ thickness stainless steel (SS), (2) 0.025″ thickness SS, (3) 0.022″ thickness titanium molybdenum alloy (TMA), and (4) 0.025″ thickness TMA. Other files are provided for round wires of various diameters and types.
 Then, using the cubic spline subroutine (2000), (3235) the slopes of the cubic spline equation describing wire behavior are calculated by: (1) computing the coefficients of a parabola, (2) filling the first point of a slope array, (3) filling the intermediate points of the slope array, and (4) filling the last point of the slope array. Then, (3240) the cubic spline coefficients are calculated. Then, (3245) the vertical displacement of the bending lever arm LA (FIG. 2E) between the contact points of the roller 70 b with the wire 69 and the contact point of the rollers 68 with the wire 69 is determined for each circle segment of the archwire equation, and data added to the array.
 Then, (3255) temporary variables are defined for the sector length, lever arm displacement, radius and terminal leg span across the straight segments of the archwire, (3260) the controller card 65 of the computer 30 c is initialized, (3265) the controller base address is set, and (3270) default parameters are set. Then, (3275) a sequential series of sector lengths and lever arm displacements are sent respectively (1) through the circuits 66 a and 67 a to the drive of the feed rolls 68, and (2) through the circuits 66 b and 67 b to the anvil assembly 70.
 When all circle segments have been formed, (3280) the lever arm displacement is zeroed and (3285) the wire leg location is read by the sensor 71. This reading converted to a numerical value in the computer 30 b and any difference in the actual measured terminal leg span and the desired terminal leg span TLS is calculated. If (3290) the difference is out of tolerance, a correction is made and another wire is formed.
 (3500) Jig Manufacturing Step:
 The jig manufacturing step (3500) produces bracket placement jigs custom designed for each tooth to aid in the placement of the custom designed brackets in the proper positions on the teeth so that the custom designed archwire will, when installed in the custom designed and custom placed brackets, move the teeth to their calculated finish positions.
 The information necessary for the design of the custom placement jigs is contained in the patient data file of the calculations made in the appliance design procedure (96) and in the tooth profile data file of digitized information read in step (500), in the illustrated embodiment of the invention. The design of the custom jigs involves, primarily, an assembly of the information already generated, and, in the preferred embodiment, takes place in the course of generating the code for control of the NC controlled manufacturing equipment 41 that produces the jigs.
 In the preferred and illustrated embodiment, the jig manufacturing equipment 41 is a standard CNC mill equipped with a small carbide endmill tool of, for example, 0.020 inches in diameter (FIG. 1F). The jigs themselves 82 are made from circular ABS plastic wafers 83 of approximately one inch in diameter and approximately 0.040 inches in thickness, though considerable variation in size is acceptable.
 The jig manufacturing step (3500), as illustrated in the detailed flowchart of FIG. 2Z, begins with the execution of a program or routine in the manufacturing computer 30 b and the input of parameters identifying the patient or case. Upon beginning of the execution of the program, (3515) the file of patient data 36 generated in the tooth position calculation and analysis procedure (95) and the appliance design procedure (96) is opened and information is read for each tooth, as illustrated in the diagram of FIG. 9I, in relation to a tooth profile PF The variables read are (a) the intersection of the archwire plane and the labial (or lingual, if prescribed) surface of the tooth TS, which is in the form of a pair of X, Y coordinates TSX,Y in the tooth profile vertical-labial/lingual plane, (b) the slot in-out dimension Elan or IO, (c) the type of bracket, which provides access to the appropriate place in a lookup table of bracket dimensions, such as bracket base thickness BRel and bracket pad height BPH, and (d) the torque slot width, 0.018 or 0.022 from the prescription.
 Then, (3520) the bracket data file is opened and the bracket base thickness read, as illustrated in FIG. 9J. Then, a file name is assigned, (3530) a CNC file is created, and (3535) a CNC “main” program is written to it, as set forth, for example, in the flowchart of FIG. 2Z-1.
 Then, (3540) a sequential file is identified that contains the beginning and ending object number for each tooth profile, and (3545) a CAD program file containing the tooth profiles PF, is loaded. The profiles PF, as illustrated in FIG. 3C, are made up of a series of closely spaced points in the profile plane, each represented by X,Y coordinates, connected by straight line segments to define the profile curve PF. The endmill tool diameter Endmill is also entered, which must be less than the archwire diameter or archwire slot width (0.018 or 0.022). Constants are declared, including the diameter of the jig blank 83, the cut clearance on the outside of the jig, the number of loops, set at 23, and the counter initial settings.
 Then, (3560) the CNC P-code is generated for each tooth, by looping through substeps (3560) through (3639) until the code for each of the jigs 82 is generated. The loop begins by (3560) incrementing the tooth and P-code counters by 1. The loop begins with the lower left bicuspid, as brackets are usually not used on the molars, and proceeds left to right. Thus, (3565), when the incrementing of the counter advances the count to the lower right molar, (3565) the counter is advanced to skip to the upper left bicuspid.
 Then, (3570) the parameters for the particular tooth are set up as illustrated in the flowchart detail of FIG. 2Z-2. This is followed by creating the profile and bracket clearance compensation tool paths ITP and BCTP, respectively, as illustrated in the flowchart detail of FIG. 2Z-3. This involves (3590) the creation of an initial inside tool path line IITP made up of a series of straight line segments, one parallel to each of the line segments of the tooth profile curve, spaced a distance equal to the tool radius on the inside of the profile curve, as illustrated in FIG. 9K, (3595) the creation of an initial bracket base compensation tool path line IBCTP made up of a series of straight line segments, one parallel to each of the line segments of the tooth profile curve, spaced a distance equal to the bracket base dimension minus the tool radius outside of the profile curve, as illustrated in FIG. 9L, and (3600) creation of the final bracket base compensation tool path (d) to cut from the inside tool path line to the base compensation line at the top of the bracket base pad to cut off the jig at the bottom of the pad, as illustrated in FIG. 9M (“top” and “bottom” being used as an example for the lower teeth, and being opposite for the upper teeth).
 Next, (3605) the archwire slot tool path ASTP is created as illustrated in the flowchart detail of FIG. 2Z-4, which can be understood from the sequence set forth in the flowchart with reference to the diagrams of FIGS. 9N, 9O and 9P. Then, as set forth in the flowchart detail of FIG. 2Z-5, (3610) a reference tool path RefP is created on an image of a jig blank 83, as illustrated in FIG. 9Q, and with reference to it, (3615) the outside jig boundary cutout CTP is added as illustrated in FIG. 2R, and (3620) the actual tool path TP is then generated as illustrated in FIG. 9S.
 Then, (3625) the CNC machine code is generated, as illustrated in the detailed flowchart of FIG. 2Z-6, and written to the output file. Then, (3630) the variables are reset, (3635) the final results are displayed, and (3640) the program loops back to substep (3560) until all of the bracket jig code have been generated. Then, (3645) the completed CNC file is sent to the controller of the CNC mill and a pallet of wafers 83 a (FIG. 1F) is cut into a set of bracket placement jigs 82. An example of one of the jigs is illustrated in FIGS. 9T through 9W.
 What is described above includes the preferred embodiments of the invention. Those skilled in the art will appreciate that additions to and modifications of the system and method of the invention, and the detailed manifestations thereof, may be made without departing from the principles of the inventive concepts set forth herein. Accordingly, the following is claimed:
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|U.S. Classification||433/3, 433/24|
|International Classification||A61C13/00, A61C7/28, A61C7/14, A61C13/097, A61C7/16, A61C9/00, A61C7/00, A61C7/12, A61C7/20|
|Cooperative Classification||A61C7/146, A61C7/002, A61C13/097, A61C7/20, A61C7/12, A61C7/145, A61C2007/004, A61C9/0046, A61C13/0004, A61C7/00, A61C7/16|
|European Classification||A61C13/00C1, A61C7/12, A61C7/16, A61C7/14P, A61C7/20, A61C7/00|