US 20040115586 A1 Abstract A system and method by which an orthodontic appliance is automatically designed and manufactured from digital lower jaw and tooth shape data of a patient provides for preferably scanning a model of the patient's mouth to produce two or three dimensional images and digitizing contours and selected points. A computer may be programmed to construct archforms and/or to calculate finish positions of the teeth, then to design an appliance to move the teeth to the calculated positions. The appliance may include archwires and brackets. Machine code is generated and appliances are automatically produced that will straighten the teeth of the patient. Custom placement jigs may also be automatically designed and fabricated and are provided with the custom appliance to position the appliance on the patient's teeth.
Claims(54) 1. A method of making a custom orthodontic appliance to move teeth of a patient from malocclused positions toward finish positions, the method comprising the steps of:
sensing the shapes of a plurality of the teeth of a patient; from the sensed shapes, producing three-dimensional digital tooth-shape data representing shapes of individual teeth of the patient; from the digital tooth shape data, producing in a digital computer, tooth finish position defining data that locate and orient the teeth in finish positions relative to each other; processing the three dimensional digital tooth shape data and the tooth finish position defining data to derive appliance design data of an orthodontic appliance for urging the teeth of the patient from the malocclused positions toward the finish positions, the design data including data of tooth interconnecting appliance geometry and data of three-dimensional tooth conforming surface geometry, the data of appliance geometry and of tooth-conforming surface geometry being related such that, when the orthodontic appliance having the appliance geometry is positioned on the teeth of the patient by fitting surfaces having the tooth conforming surface geometry to a plurality of the patient's teeth, the appliance geometry is deformed so as to apply forces to the teeth to urge the teeth toward the finish positions; producing machine readable control signals containing geometric information correlated to the results of the appliance design data deriving step; and manufacturing, by controlling one or more fabricating machines in response to the machine readable control signals, the orthodontic appliance having the tooth-interconnecting appliance geometry and the three-dimensional tooth-conforming surface geometry. 2. A method of treating malocclused teeth comprising:
mounting an orthodontic appliance manufactured according to with the appliance on the teeth of the patient, moving the teeth away from the malocclused positions toward the finish positions with the force applied by the appliance having the deformed appliance geometry. 3. The method of the producing of the tooth finish position defining data includes processing the three-dimensional digital tooth-shape data in the computer to derive the tooth finish position data. 4. The method of the producing of the tooth finish position defining data includes processing the three-dimensional digital tooth-shape data in the computer to derive a mathematical representation of an ideal dental archform for the patient, the tooth finish position data being defined in relation to the derived mathematical representation of the ideal dental archform. 5. The method of the producing of the tooth finish position defining data includes processing the three-dimensional digital tooth-shape data in the computer to define the tooth finish position data that includes relative positions of the teeth arranged in a dental archform. 6. The method of the manufacturing includes controlling one or more fabricating machines in response to the machine readable control signals to produce an orthodontic archwire having the tooth-interconnecting appliance geometry. 7. The method of the manufacturing includes controlling one or more fabricating machines in response to the machine readable control signals to produce orthodontic brackets having the three-dimensional tooth-conforming surface geometry. 8. The method of the manufacturing includes controlling one or more fabricating machines in response to the machine readable control signals to produce orthodontic bracket placement jigs having the three-dimensional tooth-conforming surface geometry. 9. A method of making a custom orthodontic appliance for moving teeth that are initially in positions of malocclusion in the mouth of a patient toward treatment positions tending to correct the malocclusion, the method comprising:
scanning the shapes of the teeth while in their positions of malocclusion to generate 3-D data of the shapes of the teeth; determining treatment positions of the teeth that will tend to correct the malocclusion and storing data of the determined treatment positions; processing in a computer the stored data of treatment positions and designing thereby an orthodontic appliance for moving the teeth of the patient toward post appliance positions that are correlated to the determined treatment positions; the designing of the appliance including defining 3-D data correlated to three dimensional areas on the teeth, at least some of said areas to be contacted by surfaces of the appliance to apply forces to the teeth to move the teeth to the post-appliance positions; manufacturing one or more components of an orthodontic appliance having three dimensional surfaces thereon that conform to three dimensional areas of a patient's teeth by processing the defined 3-D data to operate a manufacturing apparatus to create structural shapes correlated to the three dimensional areas of the teeth. 10. The method of the manufacturing includes manufacturing a series of arch shaped appliances configured to progressively move the teeth toward treatment positions. 11. The method of the series of arch shaped components is a series of archwires. 12. The method of the series of archwires include archwires of increasing stiffness. 13. A method of making a custom orthodontic appliance for moving teeth that are initially in positions of malocclusion in the mouth of a patient toward treatment positions tending to correct the malocclusion, the method comprising:
scanning the shapes of the teeth while in their positions of malocclusion to generate 3-D data of the shapes of each of a plurality of the teeth; relating the 3-D data of the shapes of each of the plurality of the teeth in a computer in positions toward which they are to be moved by an orthodontic appliance; processing in a computer the generated data and thereby designing geometry of the orthodontic appliance, the designing including:
defining, from the 3-D data, three dimensional areas, on each of the plurality of the teeth, to be contacted to locate the appliance on the teeth and to apply forces to the teeth for urging the teeth toward the positions toward which they are to be moved, and
defining an appliance configuration that includes surfaces conforming to a plurality of the defined three dimensional areas and elastically deformable three dimensional structure interconnecting at least some of said surfaces to apply forces to the plurality of teeth; and
operating manufacturing equipment to produce a tangible form of the designed geometry and therefrom producing an orthodontic appliance having the defined appliance configuration. 14. The method of the operating of manufacturing equipment includes producing an appliance in which the surfaces thereon that are for contacting three dimensional areas on each of the plurality of the teeth to locate the appliance on the teeth are located on positioning jigs that are a removable part of the appliance. 15. The method of the operating of manufacturing equipment includes producing the orthodontic appliance in which the surfaces thereon that are for contacting three dimensional areas on each of the plurality of the teeth to apply forces thereto for urging the teeth toward the positions toward which they are to be moved are the bases of orthodontic brackets. 16. The method of the operating of manufacturing equipment includes producing the orthodontic appliance in which the appliance configuration that includes elastically deformable three dimensional structure interconnecting surfaces to apply forces to the plurality of teeth includes an archwire having individualized geometry for customizing the appliance for the patient. 17. A method of providing a custom orthodontic appliance for the treatment of an orthodontic patient by moving teeth that are in initial positions in the mouth of the patient toward treatment positions, the method comprising:
providing a three-dimensional scanner at a dental facility operable for scanning three-dimensional information of the mouth of a patient defining shapes of the teeth of the patient while the teeth are in initial positions; providing an appliance facility having a computer and appliance fabrication machinery located thereat; receiving, at the appliance facility from the dental facility, three-dimensional digital information defining the shapes of the teeth scanned by the scanner at dental facility; and from information received at the appliance facility, fabricating, with the appliance fabrication machinery, an orthodontic appliance configured for treating the patient by moving teeth from their initial positions toward the treatment positions. 18. The method of the three-dimensional digital information is received at the appliance facility over an electronic communications network. 19. The method of the three dimensional information is scanned by the scanner directly from the mouth of a patient at the dental facility. 20. The method of from the received data, determining at the appliance facility optimum bracket placement locations on each of the teeth. 21. The method of based on the received data, selecting at the appliance facility an optimum set of brackets from sets of different bracket configurations stored in an electronic file. 22. The method of based on the received data, selecting, at the appliance facility, an optimum set of brackets from sets of different bracket profiles stored in an electronic file. 23. The method of determining the treatment positions of the teeth of the patient; and based on the determined treatment positions, selecting one or more archwire parameters selected from the group of parameters consisting essentially of appliance archforms, archwire materials and archwire cross-sections. 24. A method of fabricating a custom orthodontic appliance to position teeth of a patient to preferred finish positions in the mouth of the patient, the method comprising:
scanning anatomical shapes of the mouth of the patient and producing thereby anatomical tooth-shape data; deriving an arrangement of the teeth of the patient using the anatomical tooth-shape data with a specially programmed computer; determining bracket mounting locations on each of a plurality of the teeth of the patient; based on the anatomical tooth-shape data, the determined bracket mounting locations and the derived arrangement of the teeth, designing an orthodontic archwire which, when engaged to brackets mounted at the bracket mounting locations, will move the teeth to the derived arrangement; producing machine code to implement the designed orthodontic archwire; and fabricating an orthodontic archwire in response to the machine code. 25. The method of the fabricating includes the forming of a series of bends along the length of an archwire in response to the machine code. 26. An apparatus for manufacturing a custom orthodontic appliance, the apparatus comprising:
a scanner located at a patient examination facility for generating data signals containing information of anatomical shapes directly from the mouth of an individual patient at the facility; at least one computer programmed to calculate finish positions of the teeth of the patient, to calculate a design of an orthodontic appliance for placement on the teeth of the patient to move the teeth of the patient to the calculated finish positions, and to produce machine readable records of the calculated design; and a fabricating machine at an appliance manufacturing facility, the machine being responsive to the machine readable records to fabricate an orthodontic appliance for the individual patient having the calculated design. 27. The method of at least one computer is programmed to calculate finish positions of the teeth of the patient, including deriving at least one dental archform for the individual patient and to calculate the finish positions in relation to the archform. 28. The method of at least one computer is programmed to derive at least one dental archform for the individual patient and to calculate the finish positions of the teeth of the patient in relation to the archform and is located at the patient examination facility; and at least one computer is programmed to calculate the design of an orthodontic appliance for placement on the teeth of the patient to move the teeth of the patient to the calculated finish positions on the derived dental archform and to produce machine readable records of the calculated appliance design and is located either at the patient examination facility or at an appliance manufacturing facility. 29. A custom orthodontic archwire manufacturing apparatus comprising:
an archwire former operable in response to a wire shape control signal communicated thereto to form a length of orthodontic archwire material into an archwire shape; a scanner operable to produce a digital record of anatomical shapes of the mouth of an individual patient; and a programmed computer operative to generate a wire shape control signal responsive to the digital record so as to cause the archwire former to produce an orthodontic archwire having a shape that takes into account the anatomical shapes of the mouth of the individual patient. 30. The apparatus of the wire shape control signal includes wire length data that is correlated to a length component of the archwire and wire curvature data that respectively correspond to the wire length data; and the archwire former includes a wire feeder operable in response to the wire length data of the control signal to longitudinally feed the orthodontic archwire material and wire bending elements operable in response to the wire curvature data of the control signal to bend the archwire material to the shape that takes into account the anatomical shapes of the mouth of the individual patient. 31. The apparatus of the wire length data is a digital representation of a connected series of wire segments and the wire curvature data are digital representations of the curvatures of the respective wire segments; and the archwire former is operative to longitudinally feed the series of wire segments of the orthodontic archwire material according to the respective wire length components and to bend segments of the orthodontic archwire material to curvatures corresponding to the respective curvatures. 32. The apparatus of a computer programmed to calculate preferred finish positions of the teeth of the patient from the digital record, the archwire shape control signal being generated in response to the calculated finish positions; and the wire shape control signal being effective to cause the archwire former to produce an orthodontic archwire that will urge the teeth of the individual patient toward the calculated finish positions. 33. A method of forming an orthodontic appliance based on individual anatomy of a patient for applying mutual forces between or among a plurality of teeth of the patient to move teeth to desired positions in the mouth of the patient, the method comprising the steps of:
sensing tooth shapes of a plurality of teeth of a patient; from the sensed tooth shapes, producing tooth shape signals containing digital three-dimensional tooth shape data of the shapes of each of a plurality of the teeth of the patient; producing desired tooth position signals containing digital tooth position data of the desired positions; based on the tooth shape data and the desired tooth position data, displaying images of the teeth of the patient in the desired positions; calculating, from the digital tooth shape data and digital tooth position data, geometry for configuring an orthodontic appliance to apply mutual forces between or among a plurality of the teeth of the patient to move the teeth toward the desired positions; based on the results of the calculating step, generating a machine control signal carrying machine control instructions for producing the calculated geometry and communicating the generated control signal to a forming machine; and imparting an orthodontic appliance with the calculated geometry by operating the machine in response to the control signal to produce structure having the calculated geometry. 34. A method of fabricating a custom orthodontic archwire comprising:
sensing anatomical shapes of an individual patient's mouth; producing anatomical shape data corresponding to the sensed anatomical shapes; processing the anatomical shape data to derive data of preferred positions to which the teeth of the patients are to be moved by the appliance; deriving digital data of an archwire shape based on the anatomical shape data and the derived data of the preferred positions; generating a wire shape control signal containing information from the digital data of the archwire shape, such that, when the control signal is communicated to an archwire former, the archwire former produces an orthodontic archwire that is based on the anatomical shapes of the individual patient's mouth, and such that when the appliance is placed on the patient's teeth, the appliance urges the teeth toward the preferred positions; and forming, in response to the wire shape control signal and from a length of orthodontic archwire material, an orthodontic archwire having the archwire shape. 35. The method of the derived digital data of archwire shape includes wire length data and wire curvature data, the length data and the curvature data being based on the anatomical shapes and the curvature data being correlated to the length data; the wire shape control signal includes a wire feed control signal carrying the wire length data and a wire bending control signal carrying the wire curvature data; the wire shape control signal generating step includes the step of generating the wire feed control signal and the step of generating the wire bending control signal; and the archwire forming step includes the step of longitudinally feeding the orthodontic archwire material in response to the wire feed control signal and bending the archwire material so fed in response to the wire bending control signal and in synchronism with the feeding of the archwire material to thereby form the archwire having the archwire shape. 36. The method of the derived digital data the archwire shape is a digital representation of a connected series of wire segments, each having a length component and a curvature component, the components being based on the anatomical shape data and the preferred position data; and the feeding step includes longitudinally feeding a series of lengths of the orthodontic archwire material corresponding to the respective wire length components in accordance with the wire length data and the step of bending each length of archwire material so fed into a curvature corresponding to the respective wire curvature component in accordance with the wire curvature data. 37. A method of forming an individualized archwire for use with individualized brackets based on the anatomy of the mouth of a patient including anatomy of the individual patient's teeth, the method comprising the steps of:
sensing anatomical shapes of the patient's mouth, including the shapes of the patient's teeth; from the sensed anatomical shapes, producing signals containing digital anatomical shape data, including three-dimensional tooth shape data; establishing a digital representation of an ideal arrangement of the patient's teeth in the mouth of the patient; establishing bracket mounting locations on each of a plurality of the teeth of the patient; providing orthodontic brackets for mounting on the teeth at the established bracket mounting locations; calculating, with a digital computer, the geometry of brackets and the shape of an archwire such that the brackets and archwire operate in conjunction with each other, when the brackets are mounted on the teeth at their respective bracket mounting locations and are interconnected by the archwire, to position the teeth in the ideal arrangement; generating machine control signals correlated to the calculated shape of the archwire and communicating the generated control signals to an archwire forming machine; and operating the archwire forming machine in response to the control signals to form an individualized archwire having the calculated shape. 38. The method of 39. A method of fabricating a custom orthodontic appliance to position teeth of a patient to preferred finish positions in the mouth of the patient, the method comprising the steps of:
sensing anatomical shapes of the mouth of a patient; from the sensed anatomical shapes, producing signals containing anatomical shape data including three dimensional tooth shape data representing the shapes of individual teeth of the patient; deriving an ideal arrangement of the teeth of the patient by processing the anatomical shape data contained in the signals on a digital computer, including positioning and orienting the teeth in the derived arrangement based at least in part upon the three dimensional tooth shape data for the individual teeth; designing with the computer from the three dimensional tooth shape data, an orthodontic appliance configured to apply forces to urge the teeth toward the ideal arrangement; producing machine readable control signals containing geometric information correlated to the results of the appliance designing step; and operating a machine in response to the control signals and according to the geometric information to carry out at least one process selected from the group consisting of:
forming an orthodontic appliance configured to apply forces to the teeth to urge the teeth toward the ideal arrangement,
shaping three-dimensional surfaces corresponding to at least portions of the surfaces of the teeth of the patient and fabricating bracket positioning jigs having such surfaces thereon,
shaping three-dimensional surfaces corresponding to at least portions of the surfaces of the teeth of the patient and fabricating an appliance having three-dimensional tooth engaging surfaces derived therefrom, and
shaping three-dimensional surfaces corresponding to at least portions of the surfaces of the teeth of the patient and cutting slots in brackets positioning jigs having such surfaces thereon.
40. A method of providing custom orthodontic treatment comprising:
providing a scanning device for producing three-dimensional digital data of the shapes of the teeth of a patient; receiving, from a dental practitioner, instructions relating to prescribed orthodontic treatment of the patient; displaying three-dimensional digital data from the scanner with a computer; interactively selecting surface features of the patient's teeth from the data displayed with the computer; manipulating the three-dimensional data with a computer to position the selected surface features of different teeth relative to each other so as to produce a digital arrangement of the teeth in accordance with the instructions from the dental practitioner; designing an orthodontic appliance for moving the teeth of the patient in accordance with the digital arrangement and the instructions from the dental practitioner; and fabricating an orthodontic appliance as so designed. 41. The method of the manipulating of the data to produce the digital arrangement of the teeth includes manually adjusting the digital arrangement on the computer. 42. The method of the fabricating of the orthodontic appliance includes forming an orthodontic archwire. 43. The method of the fabricating of the orthodontic appliance includes forming a series of bends along the length of an orthodontic archwire. 44. The method of analyzing the anatomy of the teeth from the produced three dimensional data; and fabricating the appliance based in part on the analyzing of the anatomy. 45. The method of the fabricating of the custom orthodontic appliance is based in part on identified placement positions on the teeth of the patient and specified bracket geometry. 46. The method of providing bracket placement jigs based the three-dimensional data for the positioning the orthodontic appliance for bonding to the teeth of the patient. 47. A method of making a custom orthodontic appliance comprising:
capturing three-dimensional anatomical data of the teeth of a patient while in initial positions; based on the anatomical data, determining treatment positions of the teeth and storing data of the determined treatment positions; processing in a computer the stored data of treatment positions and designing thereby an orthodontic appliance for moving the teeth of the patient toward the determined treatment positions; and manufacturing a series of custom orthodontic appliances for applying forces to the teeth of the patient to move them progressively toward the determined treatment positions. 48. The method of the series of appliances includes a series of archwires. 49. The method of the series of appliances includes a series of archwires of increasing stiffness. 50. The method of the treatment position determining step includes manipulating the digitized three-dimensional data to produce a three-dimensional digital model of the teeth in the treatment positions. 51. A method of making a custom orthodontic appliance comprising:
producing digital three-dimensional data of the shapes of the teeth of a patient, the data including relatively simple data sets of tooth representations and relatively high resolution data sets of tooth representations; determining treatment positions of the teeth and storing data in a computer the determined treatment positions by manipulating the relatively low simple data sets of tooth representations; processing in a computer the stored data of treatment positions and designing thereby an orthodontic appliance for urging the teeth of the patient toward the determined treatment positions; and fabricating surfaces of material in accordance with the relatively high resolution data sets of tooth representations to conform surfaces of the material to the surfaces of the teeth for locating the appliance on the teeth. 52. The method of the relatively high resolution sets of tooth representations are produced by scanning a model of the teeth; and the relatively simple data sets of tooth representations are produced by simplifying the data of the relatively high resolution data sets of tooth representations. 53. The method of the relatively high resolution data sets of tooth representations are produced by scanning a model of the teeth; and the surfaces fabricated in accordance with the relatively high resolution data sets of tooth representations include surfaces of bracket positioning jigs that conform to the surfaces of the teeth for locating brackets on the teeth of the patient. 54. A method of providing for the accurate placement of orthodontic appliances on the teeth of patients comprising:
providing a scanner for producing three-dimensional data of the shapes of the teeth of patients; defining in a computer placement positions of orthodontic brackets on teeth; generating control signals with the computer for controlling a fabricating machine; producing with the fabricating machine in response to the control signals bracket placement jigs having tooth conforming surfaces thereon defined by three-dimensional data from the scanner for locating the orthodontic brackets at the defined placement positions on the teeth of patients. Description [0120] 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. [0121] The overall configuration of the system [0122] 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. [0123] 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. [0124] 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. [0125] 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. [0126] Throughout this description, the various teeth of the patient, up to thirty-two in number, may be identified as T [0127] 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). [0128] 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 M [0129] Referring to the system diagram of FIG. 1, an orthodontic appliance manufacturing and patient treatment system [0130] The records [0131] In the illustrated embodiment of the invention, the records [0132] In other embodiments of the invention, the orthodontist [0133] The entry of the information into the input computer [0134] The combined information from the scanner [0135] In a configuration in which the scanner [0136] Preferably, the digital input process utilizes interactive methods by which an operator [0137] In embodiments where some or all of the extraction of the digitized anatomical information [0138] An analysis and design computer [0139] The computer [0140] The manufacturing equipment [0141] The equipment [0142] The appliance manufacturing machines [0143] Certain components of the system 33 [0144] Three steps in the information input procedure ( [0145] The input information [0146] The various types of and components of the scanner [0147] Video Scanning Data Input Assembly [0148] One preferred form or component of the scanner [0149] Referring to FIG. 1A, the video imaging assembly [0150] The input computer [0151] In the alternative to selecting points from the video image display [0152] Laser Three-dimensional Image Input Assembly [0153] One preferred form or component of the scanner [0154] Illustrated in FIGS. 3A and 3B are two sections of the mandibular digitized model, and include a section 57: [0155] The scanner may also include, alternatively or in combination with other scanning equipment such as the video scanner assembly [0156] Referring to FIG. 1C, the probe assembly [0157] The probe assembly [0158] In use, a half of the model [0159] With the curves such as the profile PF so formed, an operator can, with the use of the pointing device 38 [0160] The manufacturing equipment [0161] The manufacturing equipment [0162] Bracket Cutting Machine [0163] Referring to FIG. 1D, a bracket slot cutting machine [0164] Also fixed to the base [0165] At the remote end of the moveable arm [0166] Wire Bending Machine [0167] The wire bending apparatus [0168] The power supply [0169] The controller [0170] By coordinating the anvil [0171] A wire position sensor [0172] Bracket Placement Jig Forming Machine [0173] The bracket jig forming equipment [0174] The mill [0175] In the preferred and illustrated embodiment of the invention, the overall configuration of which is illustrated diagrammatically in FIG. 1, the full custom system [0176] The method of the present invention, in its preferred embodiment, includes three general operations. The first operation, is ( 85) Patient Evaluation Operation [0177] Referring to the system diagram of FIG. 1 and the flow chart of FIG. 2, the orthodontic evaluation operation ( [0178] During the examination procedure ( [0179] In assembling the information [0180] Then, further based on the diagnosis [0181] The orthodontist [0182] Alternatively, the orthodontist 87) Analysis, Design and Manufacture Operation [0183] When the information [0184] The operation ( [0185] In accordance with certain embodiments of the present invention, some or all of the appliance manufacturing step ( [0186] ( [0187] In the input procedure ( [0188] The input steps ( [0189] ( [0190] This information is used to identify the records of the patient and the products produced. [0191] ( [0192] 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 [0193] This information also includes diagnostic determinations and treatment option decisions made by the orthodontist [0194] ( [0195] In implementing a treatment to correct the tooth alignment of the patient [0196] 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 [0197] In step ( [0198] 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. [0199] 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. [0200] Measured initial contra-lateral cusp spacing data are generated for use by the orthodontist [0201] 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. [0202] ( [0203] 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. [0204] In step ( [0205] Measured initial contra-lateral cusp and central groove/fossa spacing data are generated for use by the orthodontist [0206] As with step ( [0207] ( [0208] 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 [0209] 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. [0210] 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. [0211] 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. [0212] ( [0213] The computer analysis procedure is illustrated in the flowchart of FIG. 2B. In the computer analysis procedure ( [0214] ( [0215] 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 ( [0216] 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 ( [0217] 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 ( [0218] 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. [0219] ( [0220] The orthodontist [0221] 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 ( [0222] ( [0223] The step ( [0224] 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 ( [0225] 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 ( [0226] 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 ( [0227] 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. [0228] 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. [0229] ( [0230] 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. [0231] ( [0232] 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 ( [0233] This placement is the finish position of the mandibular teeth. [0234] ( [0235] 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 ( [0236] 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. [0237] 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. [0238] 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 ( [0239] Placement of the maxillary posterior teeth places the intersections of the marginal ridges and the central grooves from steps ( [0240] The vertical positioning of the remaining teeth takes into account the occlusion and other prescription information input in step ( [0241] ( [0242] The appliance design procedure ( [0243] ( [0244] 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. [0245] 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. [0246] ( [0247] 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. [0248] ( [0249] 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. [0250] ( [0251] 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. [0252] ( [0253] 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. [0254] ( [0255] 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. [0256] ( [0257] 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 ( [0258] 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: [0259] The brackets are placed according to the three criteria: [0260] 1. Height: The height is established so that the appliance causes the upper and lower teeth to contact each other in the prescribed manner. [0261] 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. [0262] 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. [0263] From the vertical profile data of step ( [0264] 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. [0265] In FIG. 8D, a plastic jig [0266] 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 [0267] In installation performed in the treatment operation ( [0268] ( [0269] The appliance manufacturing procedure ( [0270] ( [0271] The bracket manufacturing procedure of the preferred embodiment involves the generation of NC code for the bracket slot cutting mill [0272] 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. [0273] ( [0274] The software that operates the computer [0275] The arch forming software determines the position of the roller [0276] ( [0277] The machine control codes for controlling the jig forming machinery [0278] 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 ( [0279] (98) Appliance Transmission Procedure: [0280] One of the ultimate objectives is to place the custom orthodontic appliance into the hands of the orthodontist [0281] Referring to FIG. 1, as set forth above, the configuration of the preferred system [0282] In the configuration where, as illustrated, some or all of the appliance [0283] The transmitted appliance [0284] In addition, custom archwires [0285] In alternative configurations, information may be sent from the design computer 89) Patient Treatment Operation [0286] The patient treatment involves, first, the assembly of the respective bracket [0287] When the bracket adhesive has set, the bracket placement jig [0288] Then, with the brackets 87) [0289] The analysis, design and manufacturing operation ( 94) [0290] The input of digitized information includes the ( [0291] ( [0292] The first step in the procedure ( [0293] ( [0294] The next step in the information input procedure ( [0295] ( [0296] ( [0297] ( [0298] ( [0299] ( [0300] ( [0301] ( [0302] ( [0303] ( [0304] ( [0305] ( [0306] ( [0307] The forming of the computerized mathematical model of the teeth of the patient [0308] The step ( [0309] The lower teeth must lie on the mandible [0310] To ( [0311] Next, the computer [0312] where: [0313] M [0314] M [0315] D [0316] D [0317] 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. [0318] Then, by moving the pointing device [0319] After the points La and Li are chosen representing the cortical bone limits, ( [0320] where: [0321] La [0322] La [0323] Li [0324] Li [0325] These midpoints MP [0326] 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 MP [0327] At this stage, ( [0328] The midline ML shown in FIG. 4 is the axis of such symmetry corrections. These corrections for each point MP [0329] where: [0330] S [0331] MP [0332] PR [0333] PL [0334] With the completion of this symmetricalization process, a mathematical equation MTE, which describes the size and shape of the mandibular trough according to steps ( [0335] 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. [0336] The cubic equation calculations are preferably those performed by ( [0337] ( [0338] ( [0339] The input procedure continues. ( [0340] where: [0341] CR [0342] CR [0343] CL [0344] CL [0345] 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, ( [0346] where: [0347] MR [0348] MR [0349] ML [0350] ML [0351] This information is used to determine if and how much the mandibular intermolar distance is to be altered. [0352] ( [0353] As with the mandibular jaw information described in connection with FIG. 4, ( [0354] ( [0355] where: [0356] M [0357] M [0358] D [0359] D [0360] 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. [0361] Next, ( [0362] where: [0363] R [0364] R [0365] L [0366] L [0367] 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. [0368] ( [0369] The next input step ( [0370] Where the full three dimensional scan has been employed in step ( [0371] In the preferred use of the information from the probe assembly [0372] The step ( [0373] ( 95) Analysis and Finish Tooth Position Calculation Procedure [0374] The calculation of the finish positions of the teeth, as illustrated in the flowchart of FIG. 2B, includes ( [0375] ( [0376] After the individual teeth have been digitized, the inputting of tooth shape data ( [0377] In the tooth profile analysis step, ( [0378] Using the displayed images [0379] Point P [0380] Point P [0381] Point P [0382] Point P [0383] From these landmarks, ( [0384] Line L [0385] where: [0386] X [0387] X [0388] Line L [0389] where: [0390] X [0391] X [0392] A point equidistant between points P [0393] where: [0394] X [0395] X [0396] A point equidistant between points P [0397] where: [0398] X [0399] X [0400] The line defining the crown long axis CLA is constructed using the following equation: [0401] where: [0402] X [0403] X [0404] For molars and bicuspids, point P [0405] Similarly, ( [0406] Point P [0407] Point P [0408] Point P [0409] Point P [0410] As with the bicuspids and molars, lines L [0411] The next step in the analysis is the determination of maxillary dentition for each upper molar and bicuspid. ( [0412] Point P [0413] Point P [0414] Point P [0415] Point P [0416] Point P [0417] Referring to FIG. 6C, from the landmarks, ( [0418] The ( [0419] Point P [0420] Point P [0421] Point P [0422] Point P [0423] From each of these sets of landmarks, the crown long axis CLA of each such tooth is also determined as described ( [0424] This completes the loop ( [0425] Next, as further illustrated in FIG. 6D, ( [0426] 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, [0427] 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. [0428] The computer images as summarized in FIG. 3C for each tooth ( [0429] In the analyses of Andrews referred to above, the LAIS were established with a line L [0430] 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 [0431] Additionally the elevation of the marginal ridge P [0432] ( [0433] The next step of the analysis procedure ( [0434] 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 DJ [0435] 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 [0436] In the substeps performed in the calculation of the cuspid rise ( [0437] Then, ( [0438] ( [0439] ( [0440] ( [0441] The next step in the analysis procedure ( [0442] The substeps of the mandibular placement step ( [0443] ( [0444] Then, ( [0445] 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. [0446] b) a Buccal Cusp Plane BCP parallel to X-axis and passing through coordinates 0, MCH on the tallest tooth (FIGS. [0447] c) a Cuspid Rise Plane CRP parallel to X-axis and passing through coordinates 0, where CR is the cuspid rise calculated in step ( [0448] With the planes defined, ( [0449] The next stage in this step is to establish the mandibular component of cuspid rise. This involves ( [0450] 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. [0451] 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. [0452] 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, ( [0453] 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: OFFSET=ICD/tan(LAI) [0454] ( OFFSET=[MCH/tan (LAI)]+HD [0455] where HD equals the horizontal distance from point P [0456] Then, ( [0457] 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, ( [0458] 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( [0459] 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 MO [0460] 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 C [0461] Finally, a distal contact point line DCPL is constructed for the central tooth through the DCP, at the intersection of circle C [0462] ( [0463] For bicuspids and molars, the tooth midpoints TMP can be considered as their points P [0464] ( [0465] ( [0466] The above step ( [0467] 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 ( [0468] Such a BFBCE equation is plotted in FIG. 4B. Once the BFBCE is determined, it may be ( [0469] ( [0470] After statistically deriving a best fit equation BFBCE, ( [0471] To achieve this, ( [0472] 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 ( [0473] 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. [0474] ( [0475] The construction of occlusion requires ( [0476] For the maxillary incisors, the modification of the BFBCE first involves averaging the distances from point P [0477] 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 ( [0478] In the ( [0479] ( [0480] 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, TMP [0481] ( [0482] where: [0483] t=number of teeth (4), [0484] Avg=2 (to find midpoint), and [0485] Clearance=0.25 mm, typically. [0486] P [0487] ( [0488] The next substep in the construction of the maxillary occlusion is ( [0489] For the maxillary cuspids, ( [0490] Alternatively, the cuspids may be placed with their mesial contact points MCP [0491] 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 ( [0492] In relating the profile and archform drawings and equations above, it should be noted that the X dimension of the profiles on which P [0493] At this point, information from the prescription [0494] Where ( [0495] Facial intersection with MOC=FIMOC, [0496] Lingual intersection with MOC=LIMOC, [0497] The distance from LIMOC to FIMOC, DLF, is computed as follows: DLF=/X [0498] where LIMOC is the contact point with MAAF. [0499] Where ( [0500] Facial intersection with MOC=FIMOC [0501] Lingual intersection with MOC=LIMOC [0502] Distance DLF from LIMOC to FIMOC=/X [0503] where LIMOC is contact point with MAAF [0504] Where ( [0505] Facial intersection with MOC=FIMOC. [0506] Lingual intersection with MOC=LIMOC. [0507] Distance DLF from LIMOC to FIMOC=/X [0508] LIMOC is contact point with MAAF [0509] The ( [0510] If ( [0511] First, in calculating the positions of the teeth to provide the horizontal occlusion, ( MAO=/LIMOC [0512] ( MBO=/P [0513] ( [0514] Calculation of the positions of the maxillary incisors on the MAAFO, preferably in accordance with the tooth placement routine ( [0515] The intersection of MAAFO and the arch midline ML is the mesial contact point MCP of the tooth. A circle C [0516] The intersection of MAAFO and circles C [0517] 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. [0518] 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 C [0519] 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. [0520] 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 ( [0521] 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 ( [0522] At this point, the final positions of the maxillary teeth have been calculated, and thus, the finish positions of all of the teeth. 96) [0523] The appliance design procedure includes the steps of ( [0524] ( [0525] The next step is ( [0526] 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. [0527] More particularly, as illustrated in the flowchart of FIG. 2P and FIG. 8, ( [0528] ( [0529] Once the archwire planes have been defined with respect to the teeth, as illustrated in the flowchart of FIG. 2Q, ( [0530] 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 ( [0531] Bracket angle determination (
[0532] ( [0533] h,k=coordinates of circle center [0534] X [0535] X [0536] Then, as illustrated in FIG. 8A for labial appliances, π/2 radians are then subtracted to produce the slot inclination angle SIA: SIA=FIA−π/2 [0537] ( [0538] The next step is ( [0539] For maxillary centrals, ( [0540] where K is the conversion factor from Table 3. [0541] ( [0542] Once the archwire plane is determined, as illustrated in the flowchart of FIG. 2S, (
[0543] Where: h,k=coordinates of the circle center [0544] X [0545] X [0546] X [0547] Then, as illustrated in FIG. 8A, ( SIA=FIA−π/2 [0548] ( [0549] The next step, as illustrated in the flowchart of FIG. 2T, is ( [0550] Still viewing the tooth in the ICPCSCPP, (
[0551] Similarly, (
[0552] ( [0553] Then, ( [0554] Where: [0555] S [0556] MP is the mid-point of BCBCE. [0557] PR is a point on the right side of the midline. [0558] PL is a point on the left side of the midline. [0559] The smoothest curve SC that will pass between all AWLL [0560] a) The mid-point of each AWLL [0561] b) Then, as described above, a cubic spline equation is passed through these points. [0562] c) The existence of any inflection points is determined. [0563] 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. [0564] Then, ( [0565] Finally, ( [0566] ( [0567] The next step, as illustrated in the flowchart of FIG. 2U, is ( [0568] The calculation proceeds with ( [0569] Still viewing the tooth in the ICPCSCPP, (
[0570] Similarly, (
[0571] ( [0572] Then, ( [0573] Where: [0574] S [0575] MP=the mid-point of BCBCE. [0576] PR=a point on the right side of the midline. [0577] PL=a point on the left side of the midline. [0578] Then the smoothest curve SC that will pass between all AWLL [0579] a) The mid-point of each AWLL [0580] b) Then, as described above, a cubic spline equation is passed through these points. [0581] c) The existence of any inflection points is determined. [0582] 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 AWLL [0583] Then, ( [0584] Finally, ( [0585] ( [0586] 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 ( [0587] Referring to FIG. 2V, ( [0588] 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 ( [0589] Three subroutines are used in calculating various archforms and calculating the positions of the teeth thereon. These are ( [0590] ( [0591] 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 M [0592] 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. [0593] The iterations necessary to compute the cubic polynomial are as follows: [0594] 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. [0595] 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. [0596] 3) The spline coefficients are computed. [0597] 4) The polynomial is evaluated. [0598] These steps are described in [0599] 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: [0600] 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. [0601] 2) The slope array is then filled with slopes corresponding to data points on either side of the original data points. [0602] 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: [0603] Where: [0604] SLOPE=the slope of the curve at that point. [0605] X1=the X point 0.001 to left of original data point. [0606] Y1=the Y point associated with X1. [0607] X2=the X point 0.001 to right of original data point. [0608] Y2=the Y point associated with X2. [0609] 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. [0610] ( [0611] 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: [0612] P1 [0613] P2 [0614] MT1=tangent slope of spline at point P1 [0615] MN1=normal slope of MT1 [0616] MT2=tangent slope at point P2 [0617] MN2=normal slope of MN2 [0618] P3 [0619] CL=a Cord Line, a line connecting points P1 [0620] CNL=a Cord Normal Line, a line normal to CL through P3 [0621] hs,ks=the center of the smaller of the two circle segments [0622] The iterations to convert a spline segment into two circle segments are, as follows: [0623] 1) Determine MN1 and MN2. They are the negative inverse of MN1 and MT2, respectively. [0624] 2) Determine the intersection point P3 [0625] 3) Determine the slope of the CL. [0626] 4) Determine the slope of CLN. [0627] 5) Determine the distance from P1 [0628] 6) Determine the distance from P2 [0629] 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 P1 [0630] 8) Rename the variable associating to the size of the circle. See FIG. 5B in which: [0631] P1 [0632] P2 [0633] MNS=the normal slope of small circle segment, equivalent to MN1 or MN2 depending on the relative results of test one and test two [0634] MNL=normal slope of large circle segment [0635] hs,ks=the center of the smaller of the two circle segments [0636] hl,kl=the center of the larger of the two circle segments [0637] P6 [0638] MNF=is the slope of the final line [0639] 9) Determine the intersection of the line described by slope of CNL and passing through P3 [0640] 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. [0641] 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 P6 [0642] 12) Strike a line from P6 [0643] 13) The negative inverse of the slope of the line from P6 [0644] 14) Determine the midpoint of the line from P6 [0645] 15) Determine the intersection of the line described by a slope of mnf and passing the point described in step [0646] 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. [0647] 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. [0648] 18) Accommodate an arc length calculation dependent upon which spline point is closer to P3 [0649] If the test one result is greater than that of test two, then: [0650] Theta1=A TN(m)−ATN(MSI) [0651] Theta2=ATN(MLI)−ATN(m) [0652] otherwise: [0653] Theta1=A TN(msl)−ATN(m) [0654] Theta2=A TN(m)−ATN(mll) [0655] where: [0656] Theta1=the arc angle of the smaller circle [0657] Theta2=the arc angle of the larger circle. [0658] 19) Calculate arc length for each segment. [0659] s1=rs (Theta1) [0660] s2=rl (Theta2) [0661] where: [0662] s1=arc length of smaller segment [0663] s2=arc length of larger segment [0664] 20) Calculate the running arc length. [0665] 21) Continue distally until all spline segments are converted. [0666] FIGS. [0667] ( [0668] The individual tooth placement upon an equation is required in many steps of the tooth finish position calculation procedure ( [0669] 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: [0670] DCP=Distal Contact Point [0671] ICP=Incisal Center Point [0672] MCP=Mesial Contact Point [0673] MCPL=is the Mesial Contact Point Line. [0674] 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. [0675] The iterations to place the teeth onto the circle segments are: [0676] 1) Determine the offset distance for the mandibular central tooth on the side of the jaw under consideration. [0677] 2) Expand all circle segments about their centers by the offset amount. [0678] 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. [0679] 4) Place the first circle C [0680] 5) Determine which circle segment in the distal direction circle C [0681] X [0682] X [0683] X [0684] X and Y axes are oriented at X [0685] The two following circle equations are then solved simultaneously: [0686] Where: [0687] h1,k1=the center coordinates of the first circle [0688] h2,k2=the center coordinates of the second circle [0689] R [0690] R [0691] X,Y=coordinates of possible intersection points [0692] The following solutions are possible: (1) two real solutions which are labeled X1 [0693] 6) Construct a line passing through the DCP and the center of the circle segment that intersects C [0694] 7) Place circle C [0695] 8) Determine which circle segment in the distal direction intersects circle C [0696] 9) Eliminate all expanded circle segments. [0697] 10) Determine the offset distance for the mandibular lateral. [0698] 11) Expand all circle segments about their centers by the offset amount. [0699] 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. [0700] 13) Place circle C [0701] 14) Determine which circle segment in the distal direction circle C [0702] 15) Construct a line passing through the DCP and the center of the circle segment that intersects C [0703] 16) Place circle C [0704] 17) Determine which circle segment in the distal direction intersects circle C [0705] 18) Continue distally until all teeth are placed. [0706] 19) Perform the same iterations for the co-lateral side of the arch. [0707] The appliance manufacturing procedure ( [0708] ( [0709] The bracket manufacturing step ( [0710] Referring to FIG. 2X, the bracket manufacturing step ( [0711] For each tooth and bracket, as a default or initial selection, ( [0712] Then, ( [0713] Then, ( [0714] ( [0715] The archwire manufacturing step ( [0716] As illustrated in the flowchart of FIG. 2Y, the archwire manufacturing step ( [0717] Based upon the wire type selected, ( [0718] Then, using the cubic spline subroutine ( [0719] Then, ( [0720] When all circle segments have been formed, ( [0721] ( [0722] The jig manufacturing step ( [0723] 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 ( [0724] In the preferred and illustrated embodiment, the jig manufacturing equipment [0725] The jig manufacturing step ( [0726] Then, ( [0727] Then, ( [0728] Then, ( [0729] Then, ( [0730] Next, ( [0731] Then, ( [0732] 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: [0037] FIGS. [0038]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. [0039]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. [0040]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. [0041]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. [0042]FIG. 1D is an isometric diagram of one embodiment of a bracket cutting device of the system of FIG. 1. [0043]FIG. 1E is an isometric diagram of one embodiment of a wire forming device of the system of FIG. 1. [0044]FIG. 1F is an isometric diagram of a bracket placement jig forming device of the system of FIG. 1. [0045] FIGS. [0046]FIG. 2 is a flow chart of one preferred embodiment of the process of the present invention performed with the system of FIG. 1. [0047]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. [0048]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. [0049]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. [0050]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. [0051]FIG. 2E is a detailed flow chart illustrating the substeps of the identification data input step of the input procedure of FIG. 2A. [0052]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. [0053]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. [0054]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. [0055]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. [0056]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. [0057]FIG. 2K is a detailed flow chart illustrating the substeps of the cuspid rise calculation step of the analysis procedure of FIG. 2B. [0058]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. [0059]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. [0060]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. [0061]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. [0062]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. [0063]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. [0064]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. [0065]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. [0066]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. [0067]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. [0068]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. [0069]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. [0070]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. [0071]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. [0072]FIG. 2Z is a detailed flow chart illustrating the substeps of the jig manufacturing step of the appliance manufacturing procedure of FIG. 2D. FIGS. [0073] FIGS. [0074]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. [0075]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. [0076]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. [0077]FIG. 3C is an example of a set of vertical tooth profile images produced by the scanner of FIG. 1C. [0078] FIGS. [0079]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. [0080]FIG. 4A is a geometric diagram similar to FIG. 4 for the maxillary teeth. [0081]FIG. 4B is a geometric diagram plotting horizontal mandibular archforms calculated through the analysis procedure of FIG. 2B. [0082]FIG. 4C is a geometric diagram plotting horizontal maxillary archforms calculated through the analysis procedure of FIG. 2B. [0083]FIG. 4D is a horizontal plan diagram showing the maxillary teeth in their finish positions. [0084]FIG. 4E is a horizontal plan diagram showing the mandibular teeth in their finish positions and with the custom appliance in place. [0085] FIGS. [0086]FIG. 5 is a horizontal plan diagram illustrating the placement of a tooth on an archform equation described in circle segment form. [0087] FIGS. [0088] FIGS. [0089] FIGS. [0090]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. [0091]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. [0092]FIG. 6B is a mathematical tooth profile plot, similar to FIG. 6A, of a mandibular cuspid or incisor showing selected landmark parameters. [0093]FIG. 6C is a mathematical tooth profile plot, similar to FIG. 6A, of a maxillary molar or bicuspid showing selected landmark parameters. [0094]FIG. 6D is a mathematical tooth profile plot, similar to FIG. 6A, of a maxillary cuspid or incisor showing selected landmark parameters relevant thereto. [0095]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. [0096]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. [0097]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. [0098]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. [0099]FIG. 6I is mathematical tooth profile plot, similar to FIG. 6H, of the tallest mandibular tooth. [0100] FIGS. [0101]FIG. 7 is an elevational diagram of the relationship of the jaws of a patient for illustration of cuspid rise occlusion calculation. [0102]FIG. 7A is an enlarged view of a portion of FIG. 7. [0103]FIG. 7B is a plan mathematical diagram illustrating certain of the mathematics of tooth placement on the mandibular offset arch. [0104]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. [0105]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. [0106] FIGS. [0107]FIG. 8 is a diagram similar to FIG. 7D illustrating archwire plane and bracket slot design on positioned teeth. [0108]FIG. 8A is an elevational diagram illustrating a bracket and slot configuration in connection with the diagram of FIG. 8. [0109]FIG. 8B is a top view illustrating the relation of a tooth to an archform by placement routine of FIG. 2W. [0110]FIG. 8C is a tooth profile diagram illustrating the slot in-out dimension calculation. [0111]FIG. 8D is a perspective diagram illustrating the placement of a custom bracket onto a tooth with the use of a custom placement jig. [0112]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. [0113]FIG. 8F is a plan diagram illustrating the labial installed appliance on the teeth of the patient in their initial positions. [0114]FIG. 8G is a plan diagram, similar to FIG. 8F, illustrating a lingual appliance installed on the teeth of the patient. [0115]FIG. 8H is an elevational diagram illustrating an orthodontic lingual bracket of the appliance of FIG. 8G. [0116]FIG. 8I is a top view of a bracket having a base slot curvature conforming to that of an archwire supported therein. [0117] FIGS. [0118] FIGS. [0119] FIGS. [0009] 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. [0010] 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. [0011] 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. [0012] 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. [0013] 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. [0014] 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. [0015] 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. [0016] 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. [0017] 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. [0018] 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. [0019] 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. [0020] 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. [0021] 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. [0022] 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. [0023] 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. [0024] 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. [0025] 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. [0026] 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. [0027] 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. [0028] 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. [0029] 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. [0030] 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. [0031] 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. [0032] 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. [0033] 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. [0034] 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. [0035] 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. [0036] 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: [0001] 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, [0002] 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, [0003] 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: [0004] Ser. No. 07/973,973 entitled Method of Forming Custom Orthodontic Appliance, now U.S. Pat. No. 5,431,562, [0005] Ser. No. 07/973,965 entitled Custom Orthodontic Brackets and Bracket forming Method and Apparatus, now U.S. Pat. No. 5,454,717, [0006] Ser. No. 07/973,947 entitled Custom Orthodontic Archwire forming Method and Apparatus, now U.S. Pat. No. 5,447,432, and [0007] 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, [0008] all of which are hereby expressly incorporated by reference herein. Referenced by
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