MXPA99011786A - Method and system for incrementally moving teeth - Google Patents

Abstract

A system for repositioning teeth comprises a plurality of individual appliances. The appliances are configured to be placed successively on the patient's teeth and to incrementally reposition the teeth from an initial tooth arrangement, through a plurality of intermediate tooth arrangements, and to a final tooth arrangement. The system of appliances is usually configured at the outset of treatment so that the patient may progress through treatment without the need to have the treating professional perform eachsuccessive step in the procedure.

Description

METHOD AND SYSTEM TO MOVE THE TEETH IN INCREMENTS This application is a continuation in part of U.S. Patent Application Serial No. 08 / 947,342; filed on October 8, 1997, which claims the priority of provisional application No. 60 / 050,342; filed on June 20, 1997, the exhibits of both are incorporated herein by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates in general to the field of orthodontics, more particularly, the invention relates to a method and system for moving teeth incrementally from an initial array of teeth. towards a final arrangement of teeth. The repositioning of a tooth for aesthetic or other reasons is conventionally achieved using what we commonly call "brake". The brakes include a variety of devices such as so-called brackets, arch wires, ligatures and O-rings. Sticking the devices to the patient's teeth is a tedious and laborious task that requires many sessions with the orthodontist in charge. Consequently, the P1737 / 99MX conventional orthodontic treatment is limited by the patient's ability of the orthodontist and makes the orthodontic treatment quite expensive. Before fastening the brakes to a patient's teeth, at least one session is scheduled with the orthodontist, dentist, and / or X-ray labs so that X-ray impressions and photographs of the patient's teeth and teeth can be taken. structure of your jaw. Although during this preliminary session or possibly in a later session, an alginate mold is typically made from the patient's teeth. This mold provides a mold of the patient's teeth that the orthodontist uses in conjunction with the X-ray impression of the photographs to formulate the treatment strategy. The orthodontist then schedules one or more sessions during which the brakes will be placed on the patient's teeth. In the session in which the brakes are placed in principle, the surface of the teeth is initially treated with weak acid. This acid makes optimal the adhesion properties of the surface of the teeth to the brackets and bands that are going to stick to them. The brackets and bands serve as anchors for other devices that will be added later. After the acid treatment step, the brackets and bands are applied with cement to the patient's teeth using a material P1737 / 99MX suitable binder. No force-inducing devices are added until the cement has set. For this reason, it is common for the orthodontist to schedule a later session to make sure that the brackets and bands are well attached to the tooth. The primary force-inducing apparatus in a conventional brake assembly is an arc wire. The arc wire is resilient and joins the brackets by means of grooves that are in them. The arch wire joins the brackets together and exerts force on them to move the teeth over time. Commonly used twisted wires or elastomeric O-rings to reinforce the union of the archwire to the brackets. The joining of the arc wire to the brackets is known in the orthodontic technique as "ligado" and the wires used in this procedure are called "ligatures". The elastomeric O-rings are called "plastics". After the archwire is in place, periodic sessions with the orthodontist are required, during which the patient's brakes will be adjusted by initiating a different arch wire that has different force induction properties or replacing or tightening existing ligatures . Typically, these sessions are scheduled every three to six months. As illustrated in the above, the use of P1737 / 99MX conventional brakes is a tedious and laborious process and requires many visits to the orthodontist's office. further, from the patient's perspective, the use of braces is unpleasant, uncomfortable, presents risks of infection and makes brushing, flossing and other dental hygiene procedures difficult. For these reasons, it is desired to provide alternative methods and systems for the repositioning of teeth. These methods and their subjects should be economical and, in particular, should reduce the time required by the orthodontist to plan and monitor each patient individually. The methods and their subjects should also be more acceptable to the patient, in particular being less visible, less uncomfortable, less prone to infections and more compatible with daily dental hygiene. At least some of these objectives will be met with the methods and systems of the present invention described below.

DESCRIPTION OF THE PREVIOUS TECHNIQUE The tooth positioners for a finished orthodontic treatment are described by Kesling in Am. J Orthod. Oral . Surg. 31: 297-304 (1945) and 32: 285-293 (1946). The use of silicone positioners for the realignment of integral orthodontics of a patient's teeth is described in P1737 / 99MX Warunek et al. (1989) J. Clin. Orthod. 23: 694-700. Clear plastic retainers for finishing and preservation of teeth are commercially available from Raintree Essix, Inc., New Orleans, Louisiana 70125, and Tru-Tain Plastics, Rochester, Minnesota 55902. The manufacture of orthodontic locators is described in U.S. Patent Nos. 5,186,623; 5,059,118; 5,055,039; 5,035,613; 4,856,991; 4,798,534; and 4,755,139. Other publications describing the manufacture and use of Dental Positioners include Klee ann and Janssen (1996) J. "Clin Orthodon 30: 673-680; Cureton (1996) J .. Cl in. Orthodon .30: 390-395; Chiappone (1980) J. Cl in. Orthodon 14: 121-133; Shilliday (1971) Am. J. Orthodon ti cs 59: 596-599; Wells (1970) Am. J.

Orthodonti cs 58: 351-366; and Cottingha (1969) Am. J. Orthodontics 55.23-31. Kuroda et al. (1996) Am. J. Orthodon ti cs 110: 365-369 discloses a method for laser scanning a dental plaster mold to produce a digital image of the mold. See United States Patent No. 5,605,459. The Patents of the United States Nos. 5,533,895; 5,474,448; 5,454,717; 5,447,432; 5,431,562; 5,395,238; 5,368,478; and 5,139,419, assigned to Ormco Corporation, describe methods for handling P1737 / 99MX digital images of the teeth to design orthodontic appliances. U.S. Patent No. 5,011,405, discloses a method for forming the digital image of teeth and determining the optimal position of the bracket for orthodontic treatment. Laser scanning of a tooth mold to produce a three-dimensional model is described in U.S. Patent No. 5,338,198. U.S. Patent No. 5,452,219 discloses a method for laser scanning in a tooth model and grinding a tooth mold. Digital computer manipulation of tooth contours is described in U.S. Patent Nos. 5,607,305 and 5,587,912. The computerized digital imaging of the jaw is described in U.S. Patent Nos. 5,342,202 and 5,340,309. Other patents of interest include U.S. Patent Nos. 5,549,476; 5,382,164; 5,273,429; 4,936,862 3,860,803; 3,660,900; 5,645,421; 5,055,039 4,798,534; 4,856,991; 5,035,613; 5,059,118 5, 186, 623; and 4,755, 139.

SUMMARY OF THE INVENTION The present invention provides improved methods and systems for repositioning the teeth from an initial tooth arrangement to an arrangement P1737 / 99MX end of tooth. The repositioning is achieved with a system comprising a series of apparatuses configured to receive the teeth in a cavity and to reposition each individual tooth more and more in a series of at least three successive steps, which usually include at least four successive steps , they usually include at least ten steps, and sometimes include at least twenty-five steps, and occasionally include forty or more steps. More often, the methods and systems will achieve the replacement of the tooth in a range of ten to twenty-five successive steps, although the more complex cases that indicate many patient's teeth can take forty to more steps. The successive use of the number of apparatuses allows each apparatus to be configured to move each tooth individually in small increments, typically less than 2 mm, preferably less than 1 mm and more preferably less than 0.5 mm. These limits refer to the maximum linear translation of any point on a tooth as a result of the use of a single device. The movements provided by successive apparatuses, of course, will not normally be the same for any particular tooth. Therefore, a point on a tooth can move at a particular distance as the result of using an appliance and subsequently moving at a different distance and / or on a P1737 / 99MX different address by a later device. The individual apparatuses preferably will comprise a polymeric shell having therein formed the tooth receiving cavity, typically molding it as described below. Each individual apparatus will be configured so that its tooth receiving cavity has a corresponding geometry a final or intermediate tooth arrangement intended for that apparatus. That is, when an appliance is first used by the patient, some of the teeth will be misaligned with respect to a non-deformed geometry of the appliance cavity. The apparatus, however, is resilient enough to accommodate or adjust the misaligned teeth and will apply sufficient resilient force against these misaligned teeth in order to reposition the teeth to the desired intermediate or final arrangement for that treatment step. The systems according to the present invention include at least a first apparatus having a selected geometry for repositioning a tooth of a patient from an initial array of teeth to a first intermediate array, wherein the individual tooth will reposition in increments. The system further comprises at least one intermediate apparatus having a selective geometry to progressively reposition the tooth from the first intermediate array towards one or more arrays.

P1737 / 99MX successive intermediates. This system further comprises a final apparatus having a geometry selected to progressively reposition the tooth from the last intermediate array toward the desired final tooth arrangement. In some cases, it will be desirable to form the final apparatus or several apparatuses to "overcorrect" the final position of the tooth, as discussed in more detail below. As will be described in more detail below in relation to the methods of the present invention, the systems can be planned and all the individual apparatuses can be manufactured at the beginning of the treatment, and the apparatuses can therefore be provided to the patient in a single system or package . The order in which the devices will be used will be clearly marked (for example by sequential number), so that the patient can place the devices on their teeth at the frequency prescribed by the orthodontist or by another professional in charge of the treatment. Unlike the brakes, the patient does not need to visit the professional in charge of the treatment whenever a treatment adjustment is required. While patients will normally want to visit the treatment manager on a regular basis to ensure that the treatment is following the original plan, eliminating the necessary visits to the treatment manager each time P1737 / 99MX requires an adjustment, allows the treatment to be carried out in many more successive but small stages, thus reducing the time that the professional in charge of the treatment devotes to each patient individually. In addition, the ability to use polymeric breastplate devices that are more comfortable, less visible and can be removed by the patient greatly reduces patient compliance, comfort and satisfaction. According to a method of the present invention, the teeth of a patient are repositioned from an initial tooth arrangement to a final tooth arrangement by placing a series of incremental position adjustment devices in the patient's mouth. Conveniently, the devices are to be fixed and the patient can place and reposition the device at any time during the procedure. The first apparatus in the series will have a selected geometry to reposition the teeth from an initial tooth array to a first intermediate array. After the first intermediate arrangement has been achieved or approached, one or more additional (intermediate) devices will be placed successively on the teeth, and these additional devices will have the selected geometries to progressively reposition the teeth from the first arrangement P1737 / 99MX intermediate through successive intermediate arrangements. The treatment will be finished when a final device is placed in the patient's mouth, the final apparatus has a selected geometry to progressively reposition the teeth from the last intermediate arrangement towards the final tooth arrangement. The final apparatus or several devices in the series may have a geometry or geometries selected to overcorrect the arrangement of the tooth, ie they have a geometry that (if fully achieved) would move the teeth individually beyond the tooth arrangement that is has selected as the "end". This overcorrection is desirable in order to compensate for potential relapses after the repositioning method has ended, ie to allow some movement of the individual teeth back to their previously corrected positions. Overcorrection is also beneficial for accelerating the correction speed, i.e., having an apparatus having a geometry that is positioned beyond a desired end or intermediate position, the individual's teeth will move toward the position at a higher speed . In these cases, the treatment can be terminated before the teeth reach the positions defined by the final device or devices. The method will normally include placing at least two P1737 / 99MX additional equipment, which usually involves placing at least ten additional appliances, and sometimes involves placing at least twenty-five additional appliances and occasionally placing at least forty or more additional appliances. The successive apparatuses will be replaced when the teeth arrive (within a selected tolerance) or they have reached the final final fix for that treatment stage, they are typically replaced in a range of between 2 and 20 days, normal in a range of 5 and 10 days. Often, it may be desirable to replace the appliances at a time before the "final" tooth arrangement is reached for that stage of treatment. It will be appreciated that as the teeth gradually reposition and arrive at the geometry defined by a particular apparatus, the repositioning force of the individual teeth will greatly diminish. Therefore, it may be possible to reduce the overall treatment time by replacing a prior apparatus with the succeeding apparatus at the time when the teeth are only partially repositioning by the previous apparatus. Therefore, the FDDS can presently represent an overcorrection of the final position of the tooth. This reduces the speed of the treatment and can compensate for the relapse of the patient.

P1737 / 99 X In general, the transition to the next device can be based on several factors. More simply, the apparatuses can be replaced with a predetermined schedule or with a fixed time interval (ie number of days for each device) that is determined at the beginning based on a typical or expected patient response. Alternatively, the actual response of the patient can be taken into account, for example, a patient can advance to the next appliance when that patient no longer feels pressure on their teeth with a current appliance, that is, the appliance they have been using fits easily on The patient's teeth and the patient experience little pressure or no pressure or discomfort in their teeth. In some cases, for patients whose teeth are responding very quickly, it may be possible for the treating professional to decide to skip one or more intermediate devices, ie to reduce the total number of devices being used to a number smaller than that determined at start. In this way, the overall treatment time for a particular patient may be reduced. In another aspect, the methods of the invention comprise the repositioning of the teeth using apparatus comprising polymeric shells having shaped cavities for P1737 / 99MX receive and resiliently reposition the teeth and produce a final tooth arrangement. The present invention provides improvements to these methods, which comprise determining at the beginning of the treatment the geometries for at least three of the apparatuses that are going to be used by the patient in successive form to achieve the replacement of the teeth from an initial tooth arrangement. towards the final tooth arrangement. Preferably, at least four geometries will be determined at the beginning, usually at least ten geometries, frequently at least twenty-five geometries and sometimes forty or more geometries. Normally, the tooth positions defined by the cavities of each successive geometry differ from those defined by the previous geometry by no more than 2 mm, preferably no more than 1 mm and normally no more than 0.5 mm, as described above. In another aspect, methods are provided for producing a set of digital data representing a final tooth array. The methods comprise providing a set of initial data representing an initial tooth array and representing a visual image based on the initial data set. The visual image is manipulated to reposition the teeth individually in the visual image. A final set of digital data is then produced and P1737 / 99MX represents the final tooth arrangement that repositions the teeth as seen in the visual image. Conveniently, the initial set of digital data can be provided by conventional techniques, including digitized X-ray imaging, images produced by computer-assisted tomography (CAT scans), images produced by magnetic resonance imaging (MRI), and the similar. Preferably, the images will be three-dimensional images and the digitalisation can be achieved using conventional technology. Normally, the initial set of digital data is provided by producing a plaster cast of the patient's teeth (before treatment) obtained by conventional techniques. The plaster mold produced in this way can then be swept using a laser or other scanning equipment to produce a high resolution digital representation of the plaster cast of the patient's teeth. The use of plaster mold is preferred since it does not expose the patient to X-rays or subject it to the inconveniences of an MRI scan. In a preferred embodiment, a wax bite is also obtained from the patient using standard methods. The wax bite allows the plaster molds of the upper and lower dentition of the patient to be placed, one in relation to the P1737 / 99MX other, in the centric occlusal position. The pair of molds are then swept to provide information about the relative position of the jaw in this position. This information is then incorporated into the IDDS for the two arcs. Once the digital data set is acquired, an image can be presented and manipulated on an appropriate computer system equipped with computer-aided design software, as will be described in more detail below. Image manipulation will typically involve defining the boundaries in at least some of the individual teeth and causing the images of the teeth to move relative to the jaw and other teeth by manipulation of the image via a computer. Methods for detecting tip information for the teeth are also provided. Image manipulation can be done in a totally subjective way. That is, the user can simply reposition the teeth in an aesthetically and therapeutically desired manner based on the observation of the image alone. Alternatively, the computer system could be provided with rules and algorithms that help the user to reposition the teeth. In some cases, it would be possible to provide rules and algorithms that reposition the teeth in a fully automatic way. That is, without the intervention of the P1737 / 99MX user. Once the individual's teeth have been repositioned, a final set of digital data will be generated that will represent the desired final arrangement of the tooth, and will be stored. A preferred method for determining the final tooth arrangement is that the professional in charge of the treatment defines the final position of the tooth, for example in a written prescription. The use of prescription is to define the desired results of the orthodontic procedure is well known in the art. When a description or other final designation is provided, the image can be manipulated to match the prescription. In some cases, it would be possible to provide software that could interpret the prescription in order to generate the final image and thus the set of digital data representing the final tooth arrangement. In yet another aspect, the methods according to the present invention are provided to produce a plurality of digital data sets representing a series of discrete tooth arrays that progress from an initial tooth array to a final tooth array. These methods comprise providing a set of digital data representing an initial tooth array (which can be achieved according to any of the aforementioned techniques). A set of P1737 / 99MX digital data representing a final tooth arrangement is also provided. This final set of digital data can be determined by the previously described methods. The plurality of successive sets of digital data is produced based on the initial set of digital data and the final set of digital data. Normally, the set of successive digital data is produced by determining the positional differences between the selected individual teeth and the initial set of data and the final data set and interpolating these differences. This interpolation can be carried out in several very discrete stages, as desired, usually in at least three, often at least four, more often at least ten, sometimes at least twenty-five and occasionally forty or more. Many times, interpolation will be a linear interpolation for some or all of the positional differences. Alternatively, the interpolation may be non-linear. In a preferred embodiment, non-linear interpolation is calculated automatically with the computer, using collision detection techniques and route programming to avoid interference between the individual teeth. The positional differences correspond to tooth movements where the maximum linear movement of any point on a tooth is 2 mm or P1737 / 99MX less, usually 1mm and often 0.5mm, or less. Normally, the user will specify certain intermediate, objective tooth arrays, referred to as key frames, which are incorporated directly into the intermediate set of digital data. The methods of the present invention then determine successive sets of digital data between the key frames in the manner described above, for example, by linear or non-linear interpolation between the key frames. The keyframes can be determined by a user, for example, the individual manipulation of a visual image on the computer used to generate the digital data sets, or alternatively, it can be provided by the practitioner as a prescription, in the same way that the description was made for the final tooth arrangement. In still another aspect, the methods according to the invention provide for the manufacture of a plurality of dental appliances for incremental position adjustment. The methods comprise providing an initial set of digital data, a final set of digital data and producing a plurality of successive sets of digital data representing the successive, white tooth arrangements, generally as just described. The P1737 / 99MX dental braces are manufactured based on at least some of the sets of digital data that represent the successive tooth arrangements. Preferably, the manufacturing step comprises controlling a manufacturing machine based on the successive sets of digital data to produce positive models of desired tooth arrangements. Dental appliances are then produced as negatives of the positive models using conventional manufacturing techniques by positive pressure or vacuum. The manufacturing machine may comprise a stereo lithograph or any other similar machine which is based on selective hardening of a volume of uncured polymer resin by scanning with a laser or selective hardening of the resin in a form that is based on the whole of digital data. Other manufacturing machines that could be used in the methods of the present invention include machine tools and wax deposition machines. Still, in another aspect, the methods of the present invention for manufacturing a dental apparatus comprise providing a digital data set representing a modified tooth array for a patient. A manufacturing machine is then used to produce a positive model of the modified tooth arrangement with P1737 / 99MX base in the digital data set. The dental device is then produced as a negative of the positive model. The manufacturing machine can be a stereo lithograph or any other machine that is described above and the positive model is produced by conventional pressure or by vacuum molding techniques. In still another aspect, the methods for manufacturing a dental appliance according to this invention comprise providing a first digital data set representing a modified tooth array for a patient. A second set of digital data is then produced from a first set of digital data, wherein the second set of data represents a negative model of the modified tooth array. The manufacturing machine is then controlled based on the second set of digital data to produce the dental apparatus. The manufacturing machine will normally rely on the selective hardening of a non-hardened resin in order to produce the apparatus. The apparatus typically comprises a polymer shell that has a cavity shape to receive and resiliently reposition the teeth that are in an initial tooth array to arrive at a modified tooth array.

P1737 / 99MX BRIEF DESCRIPTION OF THE DRAWINGS Figure IA illustrates a jaw of a patient and provides a general indication of how the teeth of a patient can be moved by the methods and apparatus of the present invention. Figure IB illustrates a single tooth of Figure IA and defines how the distances of tooth movements are determined. The figure. 1C illustrates the jaw of Figure IA together with an incremental position adjusting apparatus that has been configured according to the methods of the present invention. Figure 2 is a block diagram illustrating the steps of the present invention to produce a system of incremental position adjustment apparatuses. Figure 3 is a block diagram that establishes the steps for manipulating a set of initial digital data representing an initial tooth array to produce a final set of digital data corresponding to a desired final tooth arrangement. Figure 4A is a flow chart illustrating a deletion tool for the method herein. Figure 4B illustrates the volume of space being erased with the program of Figure 4A. Figure 5 is a flow diagram that P1737 / 99MX illustrates a program for matching the high and low resolution components in the manipulation of the data sets of the Figure 3. Figure 6A is a flow chart illustrating a program for performing the "detection" step of the tip detection algorithm. Figure 6B is a flow chart illustrating a program for performing the "reject" step of the tip detection algorithm. Figure 7 illustrates the method for generating multiple intermediate digital data sets that are used to produce the adjustment apparatuses of the present invention. Figure 8A is a flow diagram illustrating the steps performed by the route programmer algorithm. Figure 8B is a flow chart illustrating the steps to perform the "visibility" function according to one embodiment of the present invention. Figure 8C is a flow diagram illustrating the steps for performing the "children" function according to one embodiment of the present invention. Figure 8D is a flow chart illustrating the steps for performing the route programming step 128 of Figure 8A. Figure 9A is a flow diagram that P1737 / 99MX illustrates the steps to perform the recursive collision test during collision detection. Figure 9B is a flow diagram illustrating the node division effected during collision detection according to an embodiment of the present invention. Figure 9C is a flowchart illustrating the steps to provide greater movement information to the collision detection process. Figure 10 illustrates alternative processes for producing a plurality of apparatuses according to the methods of the present invention, using digital data sets representing the intermediate and final device designs. Figure 11 is a simplified block diagram of a data processing system incorporating an embodiment of the present invention.

DESCRIPTION OF SPECIFIC MODALITIES According to the present invention, systems and methods are provided for incrementally moving the teeth, using a plurality of discrete apparatuses, wherein each apparatus successively moves one or more of the patient's teeth in degrees relatively small. The movements of the tooth will be those that are normally associated with orthodontic treatment, including translation in all three P1737 / 99MX orthogonal directions in relation to a vertical center line, the rotation of the central line of the tooth in the two orthodontic directions (root angulation and "torque") as well as the rotation around the central line. Referring to Figure IA, a representative jaw 100 includes sixteen teeth 102. The present is intended to move at least high of these teeth from an initial tooth array to a final tooth array. To understand how the teeth can move, an arbitrary center line (CL) is drawn through one of the teeth 102. With respect to the center line (CL) the teeth can move in the orthogonal directions represented by the axes 104, 106 and 108 (where 104 is the center line). The center line may be rotated about axis 108 (root angle) and 104 (torque) as indicated by arrows 110 and 112, respectively. In addition, the tooth can be rotated about the central line, as represented by arrow 114. Therefore, all possible free-form movements of the tooth can be effected. Referring to Figure IB, the magnitude of any movement of the tooth achieved by the methods and devices of this invention will be defined in terms of the maximum linear translation of any point P on a tooth 102. Each point Pi will suffer P1737 / 99MX a cumulative translation as the tooth moves in any of the orthogonal or rotational directions defined in Figure IA. That is, while the point will normally follow a non-linear path, there will be a linear distance between any point on the tooth when it is determined at two different times during the treatment. Therefore, an arbitrary point Pi can in fact have a true side-to-side translation as indicated by the arrow di, while a second arbitrary point P2 can travel along an arcuate path, resulting in a final translation d2 . Many aspects of the present invention are defined in terms of the maximum permissible movement of a point i induced by the methods in any particular tooth. This maximum movement of the tooth, in turn, is defined by the maximum linear translation at that point Pi on the tooth, which suffers the maximum movement for that tooth at any stage of the treatment. With reference to Figure 1C, the systems according to the invention will comprise a plurality of incremental position adjustment apparatuses. The apparatuses are intended to effect the incremental repositioning of the individual teeth in the jaw, as generally described above. In a broader sense, the methods of the present invention may P1737 / 99 X employ any of the positioners, retainers or any other known removable appliance that is used for finishing and preserving the position of the teeth in relation to conventional orthodontic treatment. The systems of the present invention, in contrast to the previous systems and apparatuses, will provide a plurality of apparatuses intended to be used by a user in a successive manner, in order to achieve the gradual repositioning of the tooth, as described herein. A preferred apparatus 100 will comprise a polymer shell that has a cavity shaped to receive and resiliently reposition the teeth from a tooth array toward a successive tooth array. The polymeric shell preferably, but not necessarily, will fit over all the teeth present in the upper or lower jaw. Normally, only one or both of the teeth will be repositioned while others will provide a base or anchor region to hold the repositioning device in place, as it applies the resilient repositioning force against the tooth or teeth that will reposition. In complex cases many or most of the teeth will be repositioned at a certain point during treatment. In these cases, the teeth that are going to move can also serve as a base or anchor region to keep the appliance P1737 / 99MX repositioning subject. Additionally, the gums and / or the palate can serve as anchoring regions, thus allowing all or practically all the teeth to be repositioned simultaneously. The polymeric apparatus 100 of Figure 1C is preferably formed of a thin sheet of a suitable elastomeric polymeric material, for example the 0.03 inch Tru-Tain thermoforming dental material, Tru-Tain Plastics, Rochester, Minnesota 55902. Normally no they will provide wires or other means to hold the apparatus in place for the teeth. However, in some cases it will be desirable or necessary to provide individual anchors on the teeth with corresponding receptacles or openings in the apparatus 100, so that the apparatus can apply an upward force on the tooth, which would not be possible in the absence of an anchor . The specific methods for producing the apparatuses 100 are described below. Referring to Figure 2, the general method of the present invention for producing incremental position adjustment apparatuses for subsequent use by a patient, in order to reposition the patient's teeth, will be described below. As a first step, a set of digital data representing an initial array of P1737 / 99MX tooth is obtained, and referred to as IDDS. The IDDS can be obtained in a variety of ways. For example, the patient's teeth can be scanned or their image can be obtained using well-known technology such as X-rays, three-dimensional X-rays, data sets or computer-assisted topographic images, magnetic resonance images, etc. Methods for digitizing these conventional images and producing the data sets useful in the present invention are well known and are described in the medical and patent literature. Normally, the present invention is based on first obtaining a plaster cast from the patient's teeth by well known techniques, such as those described by Graber, Orthodontics: Principle and Practice, Second Edition, Saunders, Philadelphia, 1969, pp. 401-415. After the tooth mold is obtained, it can be scanned by digital scanning using a conventional laser scanner or other range acquisition system to produce the IDDS (set of initial digital data.) The set of data produced by the acquisition system The range can, of course, be converted into other formats to be compatible with the software that will be used to manipulate images within the data set, as described in more detail below.

P1737 / 99MX tooth plaster and generate digital models using laser scanning techniques are described for example in U.S. Patent No. 5,605,459, the disclosure of which is hereby incorporated by reference. There is a variety of range acquisition systems, generally categorized because the acquisition process requires contact with the three-dimensional object. A contact type range acquisition system uses a probe, which has multiple degrees of translational and / or rotational freedom. By recording the physical displacement of the probe as it is passed through the surface of the sample, a computer-readable representation of the sample object is made. A range acquisition device that is not of the contact type can be either a reflective or transmissive type system. There is a variety of reflective systems in use. Some of these reflective systems use non-optical incident energy sources such as microwave radars or sonars. Others use optical energy. These systems, which are of the non-contact type, work by means of reflected optical energy and also contain special instrumentation configured to allow certain measurement techniques to be carried out (for example, image-forming radar, triangulation and interferometry).

P1737 / 99MX A preferred range acquisition system is an optical, reflective, non-contact type scanner. Scouts of the non-contact type are preferred because of their inherently non-destructive nature (ie, they do not damage the sample object, they are generally characterized by a higher capture resolution and they scan a sample in a relatively short period of time. These explorers are the Cyberware Model 15 model manufactured by Cyberware Inc., Monterey California. Contact-type and non-contact type scanners can also include a color camera, which when synchronized with the browser's abilities provides a means to capture, in a digital format, a color representation of the sample object The importance of this additional ability to capture not only the shape of the object shows but also its color, is discussed below In a preferred embodiment, a wax bite is also is obtained from the patient.The wax bite allows to explore the relative positions of the upper and lower dentition r in centric occlusion. This is usually achieved by first placing the lower mold in front of the scanner, with the teeth facing upwards, and then placing the wax bite on the upper part of the lower mold, and finally placing the upper mold on the part P1737 / 99MX upper mold, with the teeth facing down, resting on the wax bite. A cylindrical scan is then obtained from the upper and lower molds in their relative positions. The scanned data provides a digital model of medium resolution that represents an object that is the combination of the patient's arches placed in the relative configurations as they are in the mouth. The digital model acts as a mold that guides the placement of two individual digital models (one per arc). More precisely, using software, for example the CyberWre alignment software, each digital arc in turn is aligned with a paired scan. The individual models are then positioned one in relation to the other, corresponding to the arches in the patient's mouth. The methods of this invention will be based on the manipulation of the IDDS in a workstation or in a computer having a suitable graphical user interface (GUI) and software suitable for the observation and modification of the images. The specific aspects of the software will be described in detail below. While the methods are based on manipulation of the digital data in the computer, the systems of the present invention comprise multiple apparatuses P1737 / 99MX dental that have geometries that differ in increments and that can be produced by non-computer assisted techniques. For example, the plaster molds obtained as described above, can be cut using knives, saws or other cutting tools in order to allow repositioning of the individual teeth within the mold. The disconnected teeth can then be held in place by soft wax or any other malleable material, and a plurality of intermediate tooth arrangements can be prepared using this modified plaster mold of the patient's teeth. The different arrangements can be used to prepare sets of multiple apparatuses, generally as described below, using pressure and vacuum molding techniques. While this manual creation of the systems of the apparatuses of the invention in general is much less preferred, the systems produced in this manner are within the scope of this invention. Referring again to Figure 2, after the IDDS have been obtained, the digital information will be introduced to the computer or to another workstation for manipulation. In the preferred approach, individual teeth and other components will be "cut" to allow for individual repositioning or removal of digital data. After "releasing" the components in P1737 / 99MX this way, the user will normally follow a prescription or prescription or any other written specification provided by the professional in charge of the treatment. Alternatively, the user can reposition them based on the visual appearance or using rules and algorithms programmed into the computer. Once the user is satisfied with the final arrangement, the final arrangement of the tooth is incorporated into a final set of digital data (FDDS-final digital data set). Based on the IDDS (initial digital data set) and the FDDS (final digital data set) a plurality of intermediate sets of digital data (INTDDS-intermediate digital data sets) are generated to correspond to Figure 3 illustrates a representative technique for manipulate the IDDS in order to produce FDDS on the computer. Normally, the data from the digital browser is in a high resolution form. In order to reduce the computation time necessary to generate images, a parallel set of digital data set representing the IDDS and a lower resolution will be created. The user will manipulate the lower resolution images while the computer will update the high resolution data set, as needed. The user can also observe / manipulate the high resolution model if the P1737 / 99MX additional detail provided in that model is useful. The IDDS will also become a quadratic edge data structure, if it is not already present in that form. A quadratic edge data structure is a standard topological data structure defined in Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams, ACM Transactions of Graphics, Vol., 4, No. 2, April 1985 p. 74-123. Another structure of topological data, for example, the finned edge data structure, may also be used. As an initial stage, while the three-dimensional image of the patient's jaw, which includes the teeth, gingibas and other oral tissue, is being observed, the user will normally cancel the structure that is unnecessary for the manipulation of the image and / or the final production of an appliance. These unwanted sections of the model can be removed using a erasing tool to effect a solid subtraction in the model. The tool is represented by a graphics box. The volume to be erased (the dimensions, position and orientation of the box) is adjusted by the user using the GUI. Typically, unwanted sections will include foreign gum area and the base of the mold originally explored. Another application of this tool is to stimulate P1737 / 99MX extraction of teeth and "trimming" of tooth surfaces. This is necessary when additional space is needed in the jaw for the final positioning of a tooth that is to be moved. The professional in charge of the treatment can determine which teeth will be cut and / or which teeth will be extracted. Trimming allows the patient to retain their teeth when only a small space is needed. Typically, extraction and trimming, of course, will be used in planning the treatment only when the patient's actual teeth are to be extracted and / or trimmed before initiating repositioning according to the methods of the present invention. The removal of unwanted and / or unnecessary sections of the model increases the speed of data processing and improves visual display. Undesirable sections include those that are not needed for the creation of the tooth repositioning device. The removal of these unwanted sections reduces the complexity and size of the digital data set, thus accelerating the manipulations of the data set and other operations. After the user positions and dimensions the erasing tool and instructs the software to erase the unwanted section, all the triangles within the box P1737 / 99MX set by the user will be removed and the border triangles will be modified to leave a smooth linear border. The software cancels all the triangles inside the box and cuts all the triangles that cross the boundary of the box. This requires generating new vertices on the boundary of the box. The holes created in the model on the faces of the square are re-triangulated and closed using newly created vertices. The saw tool is used to define the individual teeth (or possibly groups of teeth) that will be moved. The tool separates the scanned image into individual graphics components that allow the software to move the tooth or other component images independent of the remaining portions of the model. In a "modality, the saw tool defines a cutting path of the graphic image using two cubic bevel curves in B that lie in space, possibly restricted to parallel planes, either open or closed. The user can edit the control points on the B-shaped cube flutes, the cut-off thickness and the number of erasures used, as described below. alternative and preferred modality, P1737 / 99MX the teeth are separated using the saw as a "sampler" device, cutting the tooth from above with vertical saw cuts. The crown of the tooth, as well as the gengibal tissue immediately below the crown, are separated from the rest of the geometry and treated as an individual unit, which is referred to as a tooth. When this model moves, the gengibal tissue moves relative to the crown, creating a first-order approximation of the way in which the gengibas will reform inside a patient's mouth. Each tooth can also be separated from the original trimmer model. Additionally, a base can be created from the original trimmer model by cutting the crowns of the teeth. The resulting model is used as a basis to move the teeth. This facilitates the eventual fabrication of a physical mold from the geometric model, as described below. Thickness: when a cut is used to separate a tooth, the user usually wishes that the cut be as thin as possible. However, the user may wish to make a thicker cut, for example, when the tooth is lowered in a surrounding manner, as already described. Graphically, the cut appears as a curve surrounded by the thickness of the cut on one side of the curve. Number of erasures: one cut is P1737 / 99MX comprised of several clearing boxes arranged one near the other, as a linear approximation piece by piece of the curve path of the saw tool. The user selects the number of drafts, which determines the sophistication of the created curve - the greater the number of segments the cut will follow the curve more exactly. The erasing number is graphically shown by the number of parallel lines connecting two cubic bevel curves in B. Once a saw cut is fully specified, the user applies the cut to the mold. The cut is made as a sequence of erasures. A preferred algorithm is set forth in Figure 4A. Figure 4B shows a single iteration of erasure in the cut as described in the algorithm for a curve of groove in B with open end. For a vertical cut, the curves are closed with PA (0) and PA (S) the same point, and PB (0) and PB (S) being the same point. In one embodiment, the software can automatically divide the saw tool into a set of drafts based on a smoothness measurement capture made by the user. The saw is subdivided adaptively until an error metric measures the deviation from the ideal representation to the approximate representation as less than the threshold specified by the data set for the smoothness. The preferred error metric used P1737 / 99MX compares the linear length of the subdivided curve with the arc length of the ideal groove curve. When the difference is greater than a threshold calculated for the data set for the smoothness, a subdivision point is added along the groove curve. A previously observed feature can also be provided in the software. The pre-observation feature visually exhibits a saw cut as two surfaces that represent opposite sides of the cut. This allows the user to consider the final cut before applying it to the model data set. After the user has completed all the desired cutting operations with the saw tool, there are multiple graphic continuous lines. However, at this point, the software has to determine which triangles of the quadratic edge data structure belong to which components. The software selects a random start point in the data structure and traverses the data structure using adjacency information to find all the triangles that are linked together, identifying an individual component. This process is repeated starting with the component whose triangle is not yet determined. Once the entire data structure is traversed, all the components P1737 / 99 X have been identified. For the user, all the changes made in the high resolution model seem to occur simultaneously in the low resolution model, and vice versa. However, there is no one-to-one correlation between models of different resolution. Therefore, the computer "matches" the high and low resolution components as best as possible, subject to the defined limits. The algorithm is described in Figure 5. Tip detection: in a preferred embodiment, the software provides the ability to detect tips for a tooth. The tips are pointed projections of the bite surface of a tooth. The detection of tips can be made either before or after the cutting phase has been carried out. The algorithm used for tip detection is composed of two stages: (1) stage of "detection" during which a set of points of the teeth are determined as candidates for the tip locations; and (2) the "rejection" stage, during which the candidates from the set of points are rejected and do not meet a set of criteria associated with the points. A preferred algorithm for the "detection" step is that set forth in Figure 6A. In the detection stage, a possible tip is observed as an "island" on the surface of the tooth, and the tip P1737 / 99MX candidate at the highest point of the island. "The highest point" is measured with respect to the coordinate system of the model, but it could be easily measured with respect to the local coordinate system of each tooth if the detection is made after the cutting phase of the treatment. The set of all possible points is determined by looking for the local maxima in the tooth model that are within a specified distance from the top of the model's boundary box. First, the highest point in the model is designated as the first candidate tip. A plane is passed through this point, perpendicular to the direction along which the height of a point is measured. Then the plane is lowered by a small predetermined distance along the Z axis. Then, all the vertices connected to the tooth and that are above the plane and on some connected components, are associated with the candidate tip, as if they were points. . This step is also called the "flood-fill" step. For each candidate tip point, the "flood" outward is the one that is effected, making each vertex of the model observed in this way to be "part of" the corresponding candidate tip. After the flood fill step is completed, all vertices of the model are examined.

P1737 / 99MX Any vertex that is above the plane and that has not been visited by one of those filled by flood, is added to the list of candidate points. These steps are repeated until the plane travels a specified distance. While the interactive approach may be more laborious than a local maximum search, the approach described above leads to a shorter list of candidate tips. As the plane is lowered by a finite distance in each step, the very small local maxima that can occur due to noisy data are skipped. After the "detection" step, the tip detection algorithm proceeds to the "rejection" stage. A preferred algorithm for the "rejection" stage is that established in Figure 6B. At this stage the local geometries around each of the top candidates are analyzed to determine if they have "characteristics not corresponding to the tip". Top candidates who exhibit "characteristics not corresponding to the tip" are removed from the list of top candidates. Several criteria can be used to identify "non-tip characteristics". According to a test, the local curvature of the surface around the candidate candidate is used to determine if the candidate possesses a characteristic not corresponding to the tip. As P1737 / 99MX is illustrated in Figure 6b, the local curvature of the surface around the candidate candidate is approximate and then analyzed to determine if it is too large (very sharp surface) or too small (very flat surface), in which case the candidate is removed from the list of top candidates. Conservative values are used for minimum and maximum curvatures to ensure that genuine tips are not rejected by mistake. According to an alternative test, a measurement of smoothness is calculated based on the average normal in an area around the candidate tip. If the average normal deviates from the normal at the tip by more than a specified amount, the candidate tip is rejected. In a preferred embodiment, the deviation of a normal vector N from the normal of the CN tip is approximated by the formula: 1 - Abs (N * CN), where it is zero in the absence of deviation and is 1 when N and CN are perpendicular. Once the teeth have been separated, the FDDS can be created from the IDDS. The FDDS is created following the description of the orthodontist, moving the teeth towards its final prescription. In one modality, the prescription is entered into a computer that algorithmically computes the final position of the teeth. In alternative modalities, P1737 / 99MX A user can move the teeth towards their final positions by independently manipulating one or more teeth while the prescription restrictions are satisfied. It should be appreciated that various combinations of the techniques described above can also be used to achieve the final position of the teeth. The preferred method for creating the FDDS involves moving the teeth in a specified sequence. First, the centers of each of the teeth are aligned with a standard arch. Afterwards, the teeth are rotated until their roots are in the proper vertical position. Then, the teeth are rotated about their vertical axis towards the proper orientation. The teeth are then observed from the side and moved vertically to their proper vertical position. Finally, the two arcs are placed together and the teeth move slightly to ensure that the upper and lower arches mesh properly. The gear of the upper and lower arcs is displayed using the collision detection algorithm to highlight the points of contact of the teeth in red. After the teeth and other components have been placed or removed so that the final arrangement of the tooth has been produced, it is necessary to generate a treatment plan, as P1737 / 99MX illustrated in Figure 7, the treatment plan will eventually produce the INTDDS and FDDS series described above. To produce these data sets, it is necessary to define or map the movement of the individual teeth selected from the initial position to the final position over a series of successive steps. In addition, it may be necessary to add other features to the data sets in order to produce desired characteristics in the processing apparatuses. For example, it may be desirable to add wax patches on the image in order to define cavities or recesses for particular purposes. For example, it may be desired to maintain a space between the appliance and the particular regions of the teeth or jaw, in order to reduce gum injuries, avoid periodontal problems, allow the placement of a cure or hard cover, and the like. Additionally, it will be necessary to provide a receptacle or opening adapted to adapt an anchor to be placed on a tooth, in order to allow the tooth to be manipulated in a way that requires anchoring, for example being elevated relative to the jaw. Some methods for manufacturing tooth repositioning devices require separate and repositioned teeth and other components to be unified into a single structure P1737 / 99MX continues in order to allow manufacturing. In these cases, "wax patches" are used to join the components that are disconnected from the INTDDS. These patches are added to the data set below the teeth and above the gums so that they do not affect the geometry of the tooth repositioning devices. The application software provides a variety of wax patches that will be added to the model, including boxes and spheres with adjustable dimensions. The wax patches that are added are treated by the software as pieces of additional geometry, identical to all the other geometries. Therefore, wax patches can be repositioned during the treatment route as well as teeth and other components. The preferred method of separating teeth using vertical sampling or segregation, as described above, avoids the need for most of these "wax patches" in the manufacturing process, which is based on the generation of positive models to produce the apparatus repositioner, the addition of a wax patch to a graphic model will generate a positive mold that has the same geometry added to the wax patch. Because the mold is a positive of the teeth and the apparatus is a negative of the teeth, when the apparatus is formed on the mold, the apparatus P1737 / 99MX will also form around the wax patch that has been added to the mold. When placed in the patient's mouth, the device will therefore allow a space to be left between the surface of the internal cavity of the appliance and the patient's teeth or gums. Additionally, the wax patch can be used to form a recess or opening within the apparatus, which engages with an anchor placed on the tooth in order to move the tooth in directions that would otherwise not be achieved. In addition to these wax patches, a single component, typically a tooth, can be scaled to a smaller or larger size that will result in a fabricated appliance having a tighter or looser fit, respectively. Treatment planning is extremely flexible in defining the movement of teeth and other components. The user can change the number of treatment stages as well as the individualized control of the route and the speed of the components. Number of stages of treatment: the user can change the number of desired treatment stages from the initial stages to the target states of the teeth. Any component that does not move is assumed to be stationary and therefore its final position is assumed to be the same as the initial position (the same happens for all P1737 / 99MX intermediate positions, unless one or more keyframes are defined for that component). Keyframes: the user can also specify "keyframes" by selecting an intermediate state and making changes to the position or positions of the component. Unless otherwise instructed, the software interpolates linearly and automatically between all the positions specified by the user (including the initial position, all keyframe positions and the white position). For example, if only one final position is defined for a particular component, each subsequent stage after the initial stage will simply display the component in a linear distance and rotation (specified by a quaternion) that is closest to the final position. If the user specifies two key frames for that component, he will "move" linearly from the initial position through different stages to the position defined by the first keyframe. It will then move possibly in a different direction, linearly to the position defined by the second keyframe. Finally, it will move perhaps in a still different direction, linearly to the objective position. The user can also specify the non-linear interpolation between the keyframes. A hard channel curve is used to specify the P1737 / 99MX interpolation function in a conventional way. These operations can be done independently of each component, so that a keyframe for one component will not affect another component, unless the other component is also moved by the user in that keyframe. A component can be accelerated along a curve between steps 3 and 8, while others move linearly from steps 1 to 5 and then change the direction suddenly and move slower along a linear path towards the stage 10 This flexibility allows a great degree of freedom in the planning of a patient's treatment. In one modality, the software automatically determines the route of the treatment based on the IDDS and the FDDS. This is normally achieved using a route programming algorithm that determines the speed at which each component, ie a tooth, moves along a straight route from the initial position to the final position. The route programmer algorithm used by this invention determines the route of treatment while avoiding "round trips" which is the term used by orthodontists to refer to the movement of a tooth over a distance greater than absolutely necessary. to straighten the tooth. This movement is very undesirable and has side effects P1737 / 99 X potentially negative in the patient. In order to avoid "round trip" the programmer algorithm of route program or stages the movements of all the teeth restricting them to a shorter straight line route between the initial and final position, while avoiding all interferences between the gap-toothed . The route programmer algorithm uses a randomized search technique to find an unobstructed route through a configuration space that descripossible treatment plans. A preferred embodiment of the algorithm for scheduling movement between two global and defined user keyframes is described below. The programming over the course of time that includes intermediate keyframes is achieved by dividing the time interval into subintervals, which do not include intermediate keyframes, programming each of these intervals independently and then co-programming the resulting schedules. The flow chart 120 of Figure 8A illustrates a simplified algorithm for scheduling routes according to an embodiment of this invention. As shown in Figure 8, the first step 122 involves the construction of the description "configuration space". A "configuration" refers in this context to a P1737 / 99MX set given positions of all the teeth that are being considered for movement. Each of these positions can be described in multiple ways. In a preferred embodiment of the present invention, the positions are described by a transformation to specify the change in location and a rotational transformation to specify the change in orientation of a tooth from its initial position to its final position. The intermediate arrangements of each tooth is described by a pair of numbers that specify how far the location and orientation are interpolated between two endpoints. A "configuration" therefore consists of two numbers of each tooth that is moving and the "configuration spaces" refer to the space of all pairs of numbers. Therefore, the configuration space is a Cartesian space, any location where it could be interpreted that positions of all the teeth are specified. The affine transformation that descrithe movement of each tooth from its starting position towards its termination position decomposes a translational and rotational component, these transformations are independently interpolated with scalar parameters that are considered two dimensions of the space of the configuration space. The entire configuration space consists of P1737 / 99MX both of two dimensions per moved tooth, all of which are treated in an equivalent manner during the subsequent investigation. The configuration space is made of "free space" and "clogged space". The "free" configurations are those that represent valid and physically realizable positions of the teeth, while the "obstructed" configurations are those that do not. To determine whether a determination is free or obstructed, a model is created for the positions of the teeth whose configuration it descri A collision detection algorithm is then applied to determine if any of the geometries that describe the surfaces of the teeth intersect. If there is no obstruction, the space would be considered free, otherwise it is considered obstructed. The collision detection algorithm is discussed below in more detail. In step 124, a function of "visibility" V (YES, s2) that takes two vectors in the configuration space, "yes" and "s2", as input and returns to a Boolean value of false or true. The visibility function returns to a true value if and only if a straight line path connecting yes and s2 passes completely through a free and unobstructed region of the configuration space. A preferred algorithm for function Visibility P1737 / 99MX is established in Figure 8b. The visibility function is roughly calculated with the model test of the teeth with respect to interference at discretely sampled points along the line S? -s2. Techniques, for example early termination due to faults or the choice of the order of the sample points by recursive subdivision of the interval to be tested, may be used to increase the effectiveness of the visibility function. In step 126 of Figure 8A, a "children" function C (s) is defined as the input parameter, "s" is a vector in the configuration space and returns a set of vectors, "sc" in the space Of configuration. Figure 8C illustrates a simplified flow chart illustrating the steps followed for the calculation of the children function C (s). Each vector within sc satisfies the property that V (s, sc) is true and that each of its components are greater than or equal to the corresponding component of "s". This implies that any state represented by this vector can be reached from "s" without encountering any interference and without making any movement other than the direction prescribed by the treatment. Each vector of the set "sc" is created by disturbing each component of "s" by a random and positive amount. The visibility function V (s, sc) is then calculated and P1737 / 99MX "s" is added alk set "sc" if the visibility function returns to a true boolean value. Additionally, for each of these generated vectors, a pointer to its related "s" is recorded for later use. After the configured space has been defined, in step 128, route programming takes place between an initial state "sint" and a final stage "Sfina?". Figure 8 illustrates a preferred flow chart for performing step 128 illustrated in Figure 8A. As illustrated in Figure 8D, in step 128a, a set of states "W" is defined to initially contain only the initial state s? N? T. Then, in step 128b, the visibility function is invoked in order to determine whether V (s, Sfina?) Is true for at least one state S in W. If the visibility function returns to a false Boolean value, in step 128c, the set of states "W" is replaced with the junction of C (Si) for all Si in W. Steps 128b and 128c are repeated until V (s17 Sfina?) returns to a true boolean value for any s ± belonging to W. In step 128d, for every s ± for which V (S ?, Sf nai) is true, an unobstructed path P is constructed from Si to s n? T by following the pointers related back to s? Nit. In step 128e, the route from s? N? T to final s is then constructed by concatenating the Pj routes. with the final step P1737 / 99MX from sx to Sfina? . If there are multiple routes from init to Sfina ?, the total length of each route is calculated in step 128f. Finally, in step 128g the route with the shortest length is then selected as the final route. The length of the selected route corresponds to the total time and the total stages required for a treatment plan. The resulting final path consists of a series of vectors, each of which represents a group of values of the interpolation parameters of the transverse and rotational components of the transformations of the teeth in motion. Taken together, these constitute a programming of tooth movement that avoids tooth-to-tooth interference. Collision detection algorithm: the collision or interference detection algorithm employed by this invention is based on the algorithm described in the SIGGRAPH article, Stepan Gottschalk et al. (1996): "OBBTree: A Hierarchical Structure for Rapid Interference Detection." The content of this article is incorporated as a reference. The algorithm is centered around a recursive subdivision of the space occupied by an object, which is organized in a similar way to a binary tree. The triangles are used to represent the teeth in the DDS. Each node of P1737 / 99 X tooth refers to a bounding box (OBB-orient bounding box) and contains a subset of triangles that appear in the node's relative. The children of a relative node contain among them all the triangle data stored in the relative node. The boundary box of a node is oriented so that it fits snugly around the triangles of that node. The leaf nodes in the tree ideally contain a simple triangle, but possibly contain more than one triangle. The detection of collisions between two objects involves determining if the OBB trees of the objects intersect. Figure 9A establishes a flow chart illustrating a simplified version of a recursive collision test to verify whether a "Ni" node of a first object intersects a node "N2" of a second object. If the OBBs of the root nodes of the trees overlap, the children of the roots are checked for overlap. The algorithm proceeds in a recursive manner until the leaf nodes are reached. At this point, a robust triangle intersection routine is used to determine if the triangles in the leaves are involved in a collision. The present invention provides various reinforcements of the collision detection algorithm P1737 / 99MX described in the SIGGRAPH article. In one embodiment, the present invention provides a unique method for building OBB trees in an idle manner, to save memory and time. This approach arises from the observation that there are parts of the model that will never be involved in a collision and, consequently, in mind the OBB tree for these parts of the model does not need to be computed. The OBB trees are expanded by dividing the internal nodes of the tree as necessary during the recursive collision determination algorithm, as illustrated in Figure 9B. In another embodiment of the invention, model triangles that are not required for collision data can also be specifically excluded from consideration when constructing an OBB tree. As illustrated in Figure 9C, additional information is provided to the collision algorithm to specify moving objects. The movement can be observed in two levels. Objects can be conceptualized as "moving" in a global sense, or they can be conceptualized as "moving" in relation to other objects. The additional information improves the time required for collision detection to avoid recalculation of collision information between objects that are at rest relative to each other, since the state of the collision between these objects does not change.

P1737 / 99MX The software of the present invention can also incorporate a "cinema" feature and the user can use it at any time to automatically animate the movement from the initial state to the target state. This is very useful to visualize the general movement of the component through the treatment process. It was previously described that the preferred user interface for component identification is a three-dimensional interactive GUI. A three-dimensional GUI is also preferred for the manipulation of components. This interface provides the person in charge of the treatment or the user with instant and visual interaction with the components of the digital model. It is preferred over interfaces that allow only simple low level commands to direct the computer and manipulate a particular segment. In other words, a GUI adapted for manipulation is preferred over an interface that accepts guidelines, for example, only from the class: "move this component by 0.1 mm to the right." These commands or low-level commands are useful for the fine tuning but, if they were the only interface, the component manipulation processes would become a tedious and laborious interaction. Before or during the handling process, one or more tooth components may be increased with P1737 / 99MX template models of tooth roots. The manipulation of an enlarged tooth model with a root template is useful, for example, in situations where the impact of the teeth below the gum line is a concern. These template models could, for example, comprise a digitized representation of the X-rays of the patient's teeth. The software also allows annotations to be added to data sets that may comprise text and / or the sequence number of the device. The annotation is added as reduced text, (that is to say in a three-dimensional geometry) so that it will be evident on the printed positive model. If the annotation can be placed on a part of the mouth that will be covered by a repositioning device, but is not important for tooth movement, the annotation may appear on the delivered repositioning apparatus or apparatus. The identification of the component described above and the component handling software are designed to operate with a sophistication commensurate with the level of operator training. For example, the component manipulation software can help a computer operator that lacks orthodontic training, providing feedback regarding P1737 / 99MX allowed and prohibited manipulations of the teeth. On the other hand, an orthodontist who has great expertise in intraoral physiology and in the dynamics of tooth movement, can simply use component identification and manipulation software as a tool and incapacitate or ignore any other advice in another aspect. While the intermediate and final data sets have been created, the apparatuses can be manufactured as illustrated in Figure 10. Preferably, the manufacturing methods will employ a rapid prototype device 200, for example a stereolithography machine. A particularly suitable prototype therapy machine is the SLA-250/50 model obtained from 3D System, Valencia, California. The rapid prototype machine 200 will selectively harden a liquid or any other non-hardened resin in a three-dimensional structure, which can be separated from the rest of the uncured resin, washed and used either directly as the apparatus or indirectly as a mold to produce the apparatus. The prototype machine 200 will receive the set of individual digital data and produce a structure corresponding to each of the desired devices. In general, as the rapid prototype machine 200 can use a resin that has non-optimal mechanical properties and that may not be generally acceptable P1737 / 99MX for patient use, it will be preferred to use the prototype machine to produce molds that, in effect, are positive models of the tooth of each successive stage of the treatment. After the positive models are prepared, a conventional vacuum or pressure molding machine can be used to produce the apparatus from a more suitable material, for example a 0.03 inch thermoformable dental material, which is obtained from Tru-Tain. Plastics, Rochester. Minessota 55902. The appropriate pressure molding equipment is obtained under the BIOSTAR brand of Great Lakes Orthodintics, Ltd., Tonawanda New York 14150. The molding machine 250 produces each of the appliances directly from the positive model of the tooth and the desired material . Suitable vacuum molding machines are obtained from Raintree Essix, Inc. After production, the plurality of apparatuses comprising the system of the present invention are preferably supplied to the professional in charge of the treatment, all at once. The devices will frame a certain way, typically with a sequential number directly on the device or on labels, bags or other items that can be attached or attached to each device, to indicate their order of use. Optionally, written instructions for the system that will establish that the P1737 / 99MX patient must use the individual device in the order marked on the devices elsewhere on the package. The use of the devices in this way will gradually reposition the patient's teeth towards the final tooth arrangement. Figure 11 is a simplified block diagram of the data processor system 300 embodying the present invention. The data processor system 300 typically includes at least one processor 302 that communicates with various peripheral devices via a bus subsystem 304. These peripheral devices typically include a storage subsystem 306 (memory subsystem 308 and file storage subsystem 314) a set of user interface input and output devices 318 and an interface to the output networks 316, which includes the public switched telephone network. This interface is shown schematically in block 316 as "modem and network interface" and is coupled to the corresponding interface device in other data processing systems via the communication network interface 324. The data processing system 300 could be a personal end-point computer or a terminal or a high-end personal computer, a workstation or a mainframe. The interface input devices of P1737 / 99MX user typically include a keyboard and may also include a pointing device and a digitizer or scanner. The pointer device can be an indirect pointer device for example a mouse, a trackball, a touch-sensitive tapetil or graphics boards or a direct pointer device such as a touch screen incorporated into the screen. Other types of user interface devices, for example speech recognition systems, are also possible, they are also available. The interface output devices typically include a printer and a screen subsystem, which includes a display driver and a display device coupled to the display controller. The display device may be a cathode ray tube (CRT), a flat screen device, such as a liquid crystal display (LCD) or a projection device. The screen subsystem may also provide a non-visual display, for example audio output. The storage subsystem 306 maintains the basic programming and data constructions that provide the functionality of the present invention. The software modules discussed above are typically stored in the storage subsystem 306. The storage subsystem 306 P1737 / 99 X typically comprises the memory subsystem 308 and the file storage subsystem 314. The memory subsystem 308 typically includes several memories including a master random access memory (RAM) 310 for the storage of instructions and data during the execution of the program and a read-only memory (ROM-312) in which fixed instructions are stored. In the case of personal computers compatible with Macintosh, the ROM could include portions of the operating system, in the case of personal computers compatible with IBM this could include the BIOS (basic input / output system). The file storage subsystem 314 provides persistent (non-volatile) storage for the program and data files and typically includes at least one hard disk drive and at least one floppy disk drive (with associated removable media). There may also be other devices such as CD-ROM drives and optical drives (all with their associated removable media). Additionally, the system may include disk drives of the type that are used with removable media cartridges. Removable media cartridges can, for example, be hard drive cartridges, such as those marketed by Syquest and others, and floppy disk cartridges, such as those from Iomega. One or more of the disk drives can P1737 / 99MX be placed at a remote location, for example on a server or on a local area network or on a World Wide Web site on the Internet. In this context the term "bus subsystem" is used in a generic way to include any mechanism to let the different components and subsystems communicate with each other, in the intended manner. With the exception of the capture or entry devices and the screen, the other components do not need to be in the same physical location. For example, portions of the file storage system that could be connected by various means of local area or wide area network including telephone lines. Similarly, the capture or entry devices and the screen need not be in the same location as the processor, although it is anticipated that the present invention will be very commonly implemented in the context of the PCs and workstations. The bus subsystems 304 are shown schematically as a single bus, but a typical system has a number of buses, for example a local bus and one or more expansion buses (i.e. ADB, SCSI, ISA, EISA, MCA, NuBus, or PCI), as serial and parallel ports. Network connections are usually established through a device, for example the network adapter in one of these expansion buses or a modem in a serial port. The P1737 / 99MX client computer can be a desktop system or a portable system. The digitizer or scanner (Scanner) 320 is responsible for making the scan of the patient's tooth molds obtained either from the patient or from an orthodontist and providing the digitized information from the digital data set to the data processing system 300 for further processing. In a distributed environment, the browser 320 can be located at a remote location and communicate the scanned information of the digital data sets to the data processing system 300 via the network interface 324. The manufacturing machine 322 manufactures dental apparatus with a base in intermediate and final information of the data set, received from the data processing system 300. In a distributed environment, the manufacturing machine 322 can be located at a remote location and receive information from the data set from the processing system of data 300 via the network interface 324. While the foregoing is a complete description of the preferred embodiments of the invention, various alternatives, modifications and equivalents may be employed. Therefore, the above description should not be taken as limiting P1737 / 99MX of the scope that is defined by the appended claims. P1737 / 99MX

Claims (44)

1. NOVELTY OF THE INVENTION Having described the present invention, it is considered as a novelty and, therefore, the content of the following CLAIMS is claimed as property: 1. A system for repositioning the teeth from an initial tooth arrangement to a final arrangement of tooth, the system comprises a plurality of incremental position adjustment dental apparatuses including: a first apparatus having a selected geometry for repositioning the teeth from an initial tooth array to a first intermediate array; one or more intermediate apparatuses having selected geometries to progressively reposition the teeth from the first intermediate array to successive intermediate arrangements; and a final apparatus having a selected geometry to progressively reposition the teeth from the last intermediate array toward the final tooth arrangement. A system according to claim 1, wherein the apparatus comprises polymeric shells having cavities shaped to resiliently receive and reposition the teeth from an array toward a successive array. 3. A system according to claim 2, in P1737 / 99MX where the tooth positions defined by the cavities in each successive apparatus differ from those defined by the previous apparatus by not more than 2 mm. 4. A system according to claim 1, comprising at least two intermediate apparatuses. 5. A system according to claim 4, comprising at least ten intermediate apparatuses. 6. A system according to claim 5, comprising at least twenty-five intermediate apparatuses. 7. A method for repositioning the teeth from an initial tooth arrangement to a final tooth arrangement, the method comprising: placing a first position adjustment apparatus in increments in the patient's mouth, wherein the first apparatus has a selected geometry to reposition the teeth from the initial tooth arrangement to a first intermediate arrangement; successively replacing one or more additional apparatuses, wherein the additional apparatuses have selected geometries to progressively reposition the teeth from the first intermediate array to successive intermediate arrangements; and placing a final device in the patient's mouth, where the final apparatus has a selected geometry to reposition P1737 / 99MX Progressively the teeth from the last intermediate arrangement towards the final arrangement of teeth. A system according to claim 7, wherein the apparatus comprises polymeric shells having cavities shaped to receive and resiliently reposition the teeth from an array to a successive array. 9. A system according to claim 8, wherein the tooth positions defined by the cavities in each successive apparatus differ from those defined by the previous apparatus by not more than 2 mm. 10. A system according to claim 7, wherein the step of successively placing comprises placing at least two intermediate apparatuses. 11. A system according to claim 10, wherein the step of successively placing comprises placing at least ten intermediate apparatuses. 12. A system according to claim 11, wherein the step of successively placing comprises placing at least twenty-five intermediate apparatuses. A system according to claim 7, wherein the apparatus is placed successively at a range within the range of 2 days to 20 days. 14. An improved method for repositioning the teeth using apparatuses, comprising polymeric shells having shaped cavities for P1737 / 99 X Resiliently receiving and repositioning the teeth, in order to produce a final tooth arrangement, wherein the improvement comprises determining at the beginning of the treatment, geometries for at least three apparatuses that are going to be used successively by a patient to reposition teeth from an initial tooth arrangement to the final tooth arrangement. 15. An improved method according to claim 14, where at least four geometries are determined at the beginning. 16. An improved method according to claim 15, wherein at least ten geometries are determined at the beginning. 17. An improved method according to claim 16, wherein at least twenty-five geometries are determined at the beginning. 18. An improved method according to claim 14, wherein the tooth positions defined by the cavities in each successive geometry differ from those defined by the geometry by no more than 2 mm. 19. A method for producing a digital data set representing a final tooth array, the method comprising: providing an initial set of digital data representing an initial tooth array; P1737 / 99MX present a visual image based on the initial data set; manipulate the visual image to reposition the individual teeth in the visual image; and produce a final set of digital data representing the final tooth arrangement with the teeth repositioned as seen in the image. 20. A method according to claim 19, wherein the step of providing a set of digital data representing an initial array of teeth comprises a scanning of a three-dimensional model of a patient's teeth. 21. A method according to claim 20, wherein the manipulation step comprises: defining boundaries around at least some of the individual teeth; and moving at least some of the tooth boundaries relative to other teeth in an image based on the digital data set. 22. A method for producing a plurality of digital data sets that represent a series of discrete tooth arrays that progress from an initial array to a final array, the method comprises. provide a set of digital data representing an initial tooth array; provide a set of digital data P1737 / 99MX representing a final tooth array, producing a plurality of successive sets of digital data based on the digital data sets provided, wherein the plurality of digital data sets represent a series of successive tooth arrangements that progress from the initial tooth arrangement towards the final tooth arrangement. 23. A method according to claim 22, wherein the step of providing a set of digital data representing an initial array of teeth comprises scanning a three-dimensional model of the teeth of a patient. 24. A method according to claim 22, wherein the step of providing a set of digital data representing a final tooth arrangement comprises: defining boundaries around at least some of the individual teeth, and moving at least some of the tooth boundaries relative to the other teeth in an image based on the digital data set to produce the final data set. 25. A method according to claim 22, wherein the step of providing a plurality of successive digital data sets comprises determining the positional differences between the initial data set and the data set. P1737 / 99MX and interpolate those differences. 26. A method according to claim 25, wherein the interpolation step comprises linear interpolation. 27. A method according to claim 25, wherein the interpolation step comprises non-linear interpolation. 28. A method according to claim 25, further comprising defining one or more key frames between the initial tooth array and the final tooth array and interpolating them between the key frames. 29. A method for manufacturing a plurality of dental incremental position adjustment apparatuses, the method comprising: providing a digital data set representing an initial tooth array; providing a digital data set representing a final tooth array, producing a plurality of successive digital data sets based on the digital data sets provided, wherein the plurality of digital data sets respect a series of successive tooth arrangements which progress from the initial tooth arrangement to the final arrangement, and manufacture apparatus based on at least some of the digital data sets produced. P1737 / 99 X 30. A method according to claim 29, wherein the step of providing a digital data set representing an initial tooth array comprises scanning the three-dimensional model of a patient's teeth. 31. A method according to claim 29, wherein the step of providing a digital data set representing a final tooth arrangement comprises: defining boundaries around at least some of the individual teeth, and move at least some of the tooth boundaries relative to the other teeth in an image based on the digital data set to produce the final data set. 32. A method according to claim 29, wherein the step of producing a plurality of successive digital data sets comprises determining the position differences between the initial data set and the final data set and interpolating those differences. 33. A method according to claim 32, wherein the interpolation step comprises linear interpolation. 34. A method according to claim 32, wherein the interpolation step comprises the non-linear interpolation. 35. A method according to claim 32, P1737 / 99MX which further comprises defining one or more key frames between the initial tooth arrangement and the final tooth arrangement and interpolating them between the key frames. 36. A method according to claim 29, wherein the manufacturing step comprises: controlling a manufacturing machine based on the successive sets of digital data to produce successive positive models of the successive tooth arrangements; and produce the dental apparatus as a negative of the positive model. 37. A method according to claim 36, wherein the control step comprises: providing a volume of unhardened polyhedral resin; and laser scanning to selectively harden the resin in a conformation that is based on the digital data set, in order to produce the positive model. 38. A method according to claim 36, wherein the step of producing comprises modeling the apparatus on the positive model. 39. A method for manufacturing a dental appliance, the method comprises: providing a digital data set representing a modified tooth arrangement for a patient, controlling a manufacturing machine with P1737 / 99MX base in the digital data set to produce a positive model of the modified tooth array; And produce the dental apparatus as a negative of the positive model. 40. A method according to claim 39, wherein the control step comprises: providing a volume of uncured polyhedral resin; make a laser scan to selectively harden the resin in a way that is based on the digital data set to produce the positive model. 41. A method according to claim 39, wherein the production step comprises molding the apparatus on the positive model. 42. A method for manufacturing a dental appliance, the method comprises: providing a first set of digital data representing a modified tooth array for a patient; producing a second set of digital data from the first data set, wherein the second data set represents a negative model of the modified tooth array; and controlling a manufacturing machine based on the second set of digital data to produce the dental appliance. P1737 / 99MX 43. A method according to claim 42, wherein the control step comprises selectively hardening a non-hardened resin to produce the apparatus and separating the apparatus from the remaining liquid resin. 44. A method according to claim 42, wherein the apparatus comprises a polyhedral shell having a cavity shaped to receive and reposition the teeth recently from an initial tooth array to a modified tooth arrangement. P1737 / 99MX