Abstract:
Method for modelling an individual dental prosthesis, which includes an abutment, wherein a first geometry is ascertained by a detection device, wherein an auxiliary element is affixed to at least one manipulation implant/implant, and a first data set is determined therefrom. A second data set describing a geometry having at least one manipulation implant/implant without an auxiliary element is ascertained. Using the second data set, which includes no data from auxiliary elements, or using the first and second data sets, a direction of insertion is determined by which a dental prosthesis part is to be pushed onto the abutment. A production method and a system for modelling an individual dental prosthesis and a computer-readable medium having instructions, which, when loaded into a computer, execute the methods A further method is provided for automatically determining a direction of insertion for a dental prosthesis part.

Description:
FIELD OF INVENTION 
       [0001]    The invention relates to methods for modelling an individual dental prosthesis, methods for producing an individual dental prosthesis and systems for modelling an individual dental prosthesis, as well as computer-readable media and a method for automatic determination of a direction of insertion for a dental prosthesis part. 
       BACKGROUND 
       [0002]    From the state of the art, it is known to measure a residual tooth area after the dental preparation by means of optical scanning directly in the patient&#39;s mouth or by means of optical scanning of a model that represents the situation in the mouth of the patient. It is furthermore known to model models of dental prosthesis parts digitally, whereby scanned data of the residual tooth area are taken into consideration. 
         [0003]    Furthermore, it is known, as given in EP 1 062 916 A2, to produce a working model of a jaw impression, in which, depending upon the dental prosthesis to be produced, one or more manipulation implants are worked in, whereby these manipulation implants describe the position of the implants in the jaw. Because the manipulation implants do not protrude or only barely protrude from the working model, an auxiliary element that protrudes from the working model is affixed to each manipulation implant. The auxiliary elements describe the deployment depth, longitudinal axis alignment and angular position of the manipulation implants in the working model. It should be possible to have additional data ascertained with the ascertained data of the geometry of the working model with affixed auxiliary bodies, whereby these data are required for the fully automatic production and for the determination of the direction of insertion of the additional elements of the individual dental prosthesis. 
       SUMMARY OF THE INVENTION 
       [0004]    The object of the present invention is to provide a method for modelling an individual dental prosthesis, a method for producing an individual dental prosthesis and a system for modelling an individual dental prosthesis, so that one or more improved data sets are available during the modelling of the dental prosthesis, which leads to a well-producible dental prosthesis. 
         [0005]    It is moreover the object of the present invention to provide a method for automatically determining a direction of insertion for a dental prosthesis part so that time savings result in the determination of the direction of insertion as compared to the determination of the direction of insertion by a user. 
         [0006]    This object is solved with various methods, systems and a computer readable medium according to the invention. 
         [0007]    In one method for modelling an individual dental prosthesis that comprises an abutment, at least one manipulation implant, which corresponds to an implant in the residual tooth area, is affixed in a model of a residual tooth area that is to be provided with the dental prosthesis. 
         [0008]    An auxiliary element can be affixed to each manipulation implant in the model, whereby the auxiliary element, together with the manipulation implant, describes the position of the implant in the residual tooth area. A first three-dimensional geometry of the model with the at least one auxiliary element can be ascertained by means of a detection device, and a first data set can be determined therefrom, whereby this first data set describes the first three-dimensional geometry. 
         [0009]    A second three-dimensional geometry of the model with the at least one manipulation implant but without, however, the auxiliary element, can be ascertained by means of a detection device, and a second data set can be determined therefrom, whereby this second data set describes the second three-dimensional geometry. The second geometry can also be ascertained before the ascertainment of the first geometry. 
         [0010]    If the model of a residual tooth area is ascertained without affixed auxiliary elements, possible shadowing effects due to the auxiliary bodies can be avoided. If an auxiliary body is affixed to a manipulation implant, it can happen, depending on the position of the auxiliary body, whose position is also determined by the position of the manipulation implant, that certain areas, for example, a gap between teeth, cannot be ascertained by the detection device. This can be detrimental if, e.g., an outer shape of the abutment is to be specified, because then the corresponding shape cannot be defined. Without the affixed auxiliary element, the entire area, for example, of the gap between teeth, can be ascertained and an outer shape of the abutment can be correspondingly defined. 
         [0011]    For example, the outer shape of the abutment can be defined using an existing distance to adjacent teeth that lie in the same and/or opposite jaw (upper or lower jaw) and/or using the shape or the axes of the adjacent teeth. Furthermore, outer shapes of common abutments can also be available as suggestions, for example, parameterized, and, for example, such a suggestion can be used for a definition of an outer shape of the abutment (to be produced). The available outer shapes of common abutments can be altered and/or processed, so that the resulting outer shape can be used, for example, for the abutment (to be produced). The outer shapes of common abutments can be classified according to various tooth types and/or various connection geometries of the abutments at an implant, as a result of which a simple and/or rapid selection of an outer shape of a common abutment can result as a suggestion for an abutment (to be produced). 
         [0012]    Large auxiliary bodies are generally preferred for the auxiliary bodies, because with these, the geometric shape and position can be recognized with especially small errors. Such large auxiliary bodies in particular also generate large shadowing effects that are, however, particularly undesired. 
         [0013]    With the use of the second data set, a direction of insertion can be determined by which a dental prosthesis part should be pushed onto the abutment. The direction of insertion of the dental prosthesis part can, for example, be conditional upon the outer shape of the abutment and/or upon adjacent teeth, so that the dental prosthesis part can be satisfactorily pushed into the target position. To be understood here as the outer shape of the abutment is the surface of the abutment that faces toward the dental prosthesis part to be affixed. The determination of the direction of insertion from the second data set can even take place before the ascertainment of the first data set, because the second data set can preferably be used during the determination of the direction of insertion by which a dental prosthesis part should be pushed onto the abutment, but the first data set is not used. The order of the ascertainment of the two data sets is also optional. 
         [0014]    The outer shape of an abutment can, for example, be defined by including a previously ascertained direction of insertion, whereby it is not necessary for the abutment to be already partially or completely known or ascertained at the time of the determination of the direction of insertion. 
         [0015]    The determination of the direction of insertion can, for example, be based upon various axes that are implicitly or explicitly comprised by the ascertained data set. This can, for example, be the axes of the adjacent teeth and/or the perpendicular to a surface that is given by the U-shape of the upper or lower jaw and/or by the equatorial surface of the adjacent teeth, whereby the equatorial surface can be specified by the largest horizontal circumference of a tooth. A further criterion can be that a closed tooth line is obtained. 
         [0016]    The second data set is based upon the geometry of the model of the residual tooth area with at least one manipulation implant at which no auxiliary element is affixed. Shadowing effects due to the auxiliary elements can therefore be avoided and a direction of insertion of the dental prosthesis part can be determined, for example, with consideration given to the adjacent teeth. 
         [0017]    By using the first data set and the second data set for determining a direction of insertion by which a dental prosthesis part can be pushed onto the abutment, the advantages contained in the information in the two data sets can be combined. By using the first data set, the position of the manipulation implant in the model of the residual tooth area and consequently the position of the implant in the residual tooth area of a patient can be determined precisely by the affixed auxiliary body, and by using the second data set, it can be guaranteed that all areas of the model of the residual tooth area are described in the data set and that it is not the case that certain areas of the model of the residual tooth area are covered by an auxiliary element, as, for example, can occur in the first data set. 
         [0018]    The position of the manipulation implant can also influence the direction of insertion by which the dental prosthesis part can be pushed onto the abutment. The abutment that is comprised by the dental prosthesis part can be affixed onto the manipulation implant. It can moreover be provided that the abutment is connected to the manipulation implant, for example, by means of a screw. In order to guarantee this, a certain shape of the abutment can be provided that allows a screw channel to be provided in such a way that a screw can be connected to the manipulation implant through the abutment in a stable manner. For this purpose, the abutment can have a necessary material thickness in certain areas, whereby this material thickness guarantees such a stable connection, whereby the outer shape of the abutment, which can also determine the material thickness, can in turn be selected in such a way that the abutment can easily be introduced into the model of the residual tooth area, for example, a gap between teeth. The outer shape of the abutment and the surroundings of the residual tooth area around the abutment, i.e., for example, adjacent teeth of a gap between teeth, can be determining for the direction of insertion of the dental prosthesis part onto the abutment. 
         [0019]    By using the second data set, possible shadowing effects due to the auxiliary body can be avoided, as already described above. Without the affixed auxiliary element, the entire area of the, for example, gap between teeth, can be ascertained and accordingly to an outer shape of the abutment can be determined. 
         [0020]    The dental prosthesis part can be or comprise, for example, an overlay, an onlay, a cap, a crown, a primary crown, a secondary crown, a bridge or a framework. 
         [0021]    The method can additionally comprise a step of determining the abutment data that define the abutment. The step of determining the abutment data can comprise the determination of a connection geometry of the abutment to the implant in the residual tooth area. In the event of a plurality of implants that are provided in order to attach, for example, a bridge, it is advantageous if the implant is rotationally symmetrical in its upper shape onto which the abutment is to be affixed, in order not to geometrically overdetermine the dental restoration. In addition or instead, the abutment can be rotationally symmetrical in its outer shape onto which the dental prosthesis part is to be affixed. 
         [0022]    If, however, an implant is provided onto which only a single dental prosthesis part, such as a crown or the like, is to be affixed, it is advantageous if the implant is not rotationally symmetrical in the corresponding area in order to prevent twisting of the dental prosthesis part. It is correspondingly then advantageous if the corresponding abutment in the corresponding part that comes into contact with the implant is also not rotationally symmetrical. It is furthermore also advantageous, however, if the abutment is not rotationally symmetrical in its outer shape that comes into contact with the dental prosthesis part. 
         [0023]    For specifying the connection geometry of the abutment to the implant, information previously stored in the computer and regarding the needed/desired geometry of the abutment in the connection area and/or regarding the geometry of the implant in the connection area can be used. Previously stored information can also be used for creating a screw channel (see below). 
         [0024]    Using the first and/or second data set, a direction can be determined by which the abutment can be affixed onto the implant. This direction can be specified by the adjacent teeth as well as by the position of the implant. The direction by which the abutment can be affixed onto the implant can be different than the direction of insertion of the dental prosthesis part onto the abutment, even for single-tooth restorations. Said direction and the direction of insertion can, however, also be the same. 
         [0025]    A screw channel can be modelled in the abutment, whereby the longitudinal axis of the screw channel corresponds to an axis of the implant in the residual tooth area, whereby preferably the first data set can be also or exclusively accessed for this. The second data set can optionally also be used. 
         [0026]    Furthermore, suitable software can be used to check whether or not a screw can be inserted into the screw channel of the abutment, if the abutment is affixed onto the implant in the residual tooth area or onto the manipulation implant in the model. The check can, for example, also be made by using the second data set. 
         [0027]    The check of the insertability of the screw into the screw channel can guarantee the use of the abutment, because, for example, the screw channel otherwise could be covered by an adjacent tooth, in which case it would therefore not be possible to attach the abutment to the implant by using the screw. A new abutment would have to be produced in this case. Where necessary, the check can allow a new abutment to be designed before it is produced. 
         [0028]    An outer shape of the abutment can be determined by means of the second data set. The second data set describes the geometry of the model with the at least one manipulation implant onto which there is no auxiliary element affixed. Due to the fact that no auxiliary element is used, there are no problems with shadowing effects during the ascertainment of, for example, an existing gap between teeth, in which the manipulation implant is located. The outer shape of the abutment can be correspondingly determined, so that, for example, a dental prosthesis part to be attached has sufficient room in the gap between teeth. 
         [0029]    The affixability of the abutment to the implant in the residual tooth area can be checked. As a result, it can be guaranteed that, for example, both the direction by which the abutment should be affixed onto the implant and also the outer shape of the abutment are in harmony with the conditions of the residual tooth area. The check of the affixability of the abutment can, for example, also be made in the model of the residual tooth area. 
         [0030]    An inner shape of the dental prosthesis part can be determined with consideration given to the outer shape of the abutment. To be understood here as the inner shape of the dental prosthesis part is the surface of the dental prosthesis part that faces toward the abutment. In determining the inner shape of the dental prosthesis part, areas can also be provided for the placement of cement or adhesive, whereby cement or adhesive can serve as a means of connecting the abutment and dental prosthesis part. 
         [0031]    In a method for producing an individual dental prosthesis that comprises an abutment, the production of the abutment and/or of the dental prosthesis part can take place by means of milling from a pre-manufactured blank, or from any shaped blank, such as a plate. During the milling, a steel or diamond milling cutter can, for example, be used. 
         [0032]    The blanks can be or can comprise sintered-through, pre-sintered, (already sintered, but not yet sintered through) and unsintered (green bodies) ceramics or one of the materials listed in the following. 
         [0033]    Metal, ceramic, glass or plastic can be used as materials for the abutment and/or the dental prosthesis part. Plastic or (glass-)fibre reinforced plastic, for example, can be used thereby, as well as metal or metal alloys, such as, for example, cobalt alloy, chrome-cobalt alloy, titanium or titanium alloy, gold or gold alloy. Moreover, ceramics, such as, for example, zirconium-oxide, yttrium-stabilized zirconium-oxide or aluminium-oxide can be used. 
         [0034]    In a system for modelling an individual dental prosthesis that comprises an abutment, means are provided in order to ascertain a first data set that describes a first three-dimensional geometry, whereby this geometry comprises a model of a residual tooth area that is to be provided with a dental prosthesis as well as at least one manipulation implant onto which an auxiliary element is affixed, and in order to ascertain a second data set that describes a second three-dimensional geometry, whereby this geometry comprises the model of the residual tooth area that is to be provided with a dental prosthesis as well as at least one manipulation implant onto which no auxiliary element is affixed. By using the second data set, however preferably without using the first data set, or by using the first data set and the second data set, a direction of insertion can be determined by which a dental prosthesis part can be pushed onto the abutment. The device can consequently be formed in such a way that a direction of insertion can even be determined from a data set that comprises no data regarding the auxiliary bodies. 
         [0035]    The ascertained data sets can additionally be stored, further processed and/or sent by means of remote data transmission. 
         [0036]    The invention also relates to a computer-readable data medium that comprises instructions that, when loaded into a computer, execute one of the methods described above or further below. 
         [0037]    In a method for modelling an individual dental prosthesis that comprises an abutment, an auxiliary element is affixed to one, several or all implants that are located in a residual tooth area of a patient who is to be provided with a dental prosthesis, whereby this auxiliary element, together with the implant, describes the position of the implant in the residual tooth area. A first three-dimensional geometry of the residual tooth area with the at least one auxiliary element can be ascertained by means of a detection device, and a first data set can be determined therefrom, whereby this first data set describes the first three-dimensional geometry. 
         [0038]    A second three-dimensional geometry of the residual tooth area with the at least one implant but without, however, the auxiliary element, can be ascertained by means of a detection device, and a second data set can be determined therefrom, whereby this second data set describes the second three-dimensional geometry. The second geometry can also be ascertained before the ascertainment of the first geometry. 
         [0039]    The method steps described above or below can correspondingly be performed with these ascertained data sets, whereby it must be observed that instead of the model of the residual tooth area and manipulation implants, the residual tooth area itself and implants are used. 
         [0040]    The invention relates moreover to a method for automatically determining a direction of insertion for a dental prosthesis part. 
         [0041]    Three points that stand out the farthest from the jaw can be selected from teeth or from gum elevations that are located in the dental arch in which a residual tooth area is located that is to be provided with a dental prosthesis. A plane can be laid through these three points, whose perpendicular can specify the direction of insertion. A dental arch here is understood to be the upper jaw or the lower jaw of a patient. 
         [0042]    A dental arch can be divided into a incisor area and into the two molar areas, whereby a point standing out the farthest from the jaw can be selected in each of the three areas and a plane can be laid through these three points, whereby the perpendicular of this plane can specify the direction of insertion. A division into the three areas can also be made if not all teeth are still present, or if no teeth are still present, whereby then the areas in which incisors and/or molars should be present can be used for the division. 
         [0043]    The areas of the canine teeth can be included in the area of the incisors and/or in the respective area of the molars. It is, however, also possible to provide separate areas for the area of the canine teeth and/or not to take into consideration the canine teeth or the areas of the canine teeth. 
         [0044]    Three points standing out from the jaw can be selected from the teeth and from gum elevations that are located in a dental arch, whereby:
       a) the point standing out the farthest from the jaw is selected as a first point;   b) the point standing out the next farthest from the jaw is selected as a second point, if the second point has a minimum distance to the first point, whereby the minimum distance amounts to 1 cm, 1.5 cm, 2 cm, 2.5 cm or more;   c) if the distance between the first and the second point is less than the minimum distance, the second point is rejected and steps b) and c) are repeated until a second point has been selected, whereby in each of the steps b) and c) the point is used that stands out a smaller distance from the jaw than the previously used points;   d) if a second point has been selected according to b), a third point is selected if the third point is a minimum distance apart from both the first point and the second point, whereby a point that stands out a smaller distance from the jaw than the previously used points is used as the third point;   e) if the distance between the third and the first and/or the third and the second point is less than the minimum distance, the third point is rejected and steps d) and e) are repeated until a third point has been selected, whereby in each of the steps d) and e) the point is used that stands out a smaller distance from the jaw than the previously used points;   f) when three points have been selected, a plane is laid through these three points, whereby the perpendicular to this plane specifies the direction of insertion.       
 
         [0051]    Three or more tangents can be laid on the edges of a ground tooth and/or the edges of an abutment that is located in a residual tooth area that is to be provided with a dental prosthesis, whereby a cone envelope can be specified by these tangents around the ground tooth and/or the abutment, whereby the aperture angle of the cone can define an angular range for the direction of insertion. 
         [0052]    An additional ground tooth and/or an additional abutment can be located in the residual tooth area, whereby the additional ground tooth and/or the additional abutment is to be provided with an additional or the same dental prosthesis, whereby three or more additional tangents can be laid on the additional ground tooth and/or the additional abutment, by means of which tangents an additional cone envelope can be specified around the additional ground tooth and/or the additional abutment, whereby an angular range can result for the direction of insertion from an intersection of the two aperture angles of the two cones. 
         [0053]    A direction of an axis of a ground tooth and/or of an abutment, together with an implant, which ground tooth and/or abutment is located in a residual tooth area and which is to be provided with the dental prosthesis, can define the direction of insertion. 
         [0054]    The direction of the axis of the ground tooth and/or of the abutment together with the implant can be determined from the volume data of the ground tooth and/or of the abutment together with the implant. 
         [0055]    The direction of the axis can correspond to the direction of the longest line within the ground tooth and/or the abutment together with the implant, and/or the direction of the axis can correspond to a projection direction in which the volume of the ground tooth and/or the abutment together with the implant has a smallest possible area when projected onto a plane. 
         [0056]    The direction of the axis of the ground tooth can correspond to a perpendicular through an equatorial surface of the ground tooth, whereby the equatorial surface can be defined by a largest horizontal circumference of the ground tooth. 
         [0057]    An equatorial line of the ground tooth can be fit with a circle, an ellipse and/or a polygon, and the direction of the axis can correspond to the perpendicular to the circular, elliptical and/or polygonal plane, whereby the equatorial line can be given by a largest horizontal circumference of the ground tooth. 
         [0058]    The direction of the axis of the ground tooth can be defined by a perpendicular through an area that is given by a preparation line of the ground tooth. 
         [0059]    A preparation line of a ground tooth can be fit with a circle, an ellipse and/or a polygon, and the direction of the axis of the ground tooth can correspond to the perpendicular to the circular, elliptical and/or polygonal plane. 
         [0060]    The direction of insertion of the dental prosthesis part can be defined with consideration of side surfaces of adjacent teeth that join to a residual tooth area that is to be provided with the dental prosthesis, whereby only those side surfaces are considered that face the dental prosthesis. 
         [0061]    A user can select, modify and/or save the automatically determined direction of insertion, and/or select and/or save the modified direction of insertion. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0062]    Embodiments of the invention will be explained using the accompanying figures. Shown are: 
           [0063]      FIG. 1 : Model of a residual tooth area with manipulation implant and with auxiliary element; 
           [0064]      FIG. 2 : Model of a residual tooth area with manipulation implant without auxiliary element; 
           [0065]      FIG. 3 : Residual tooth area of the patient, with implant and auxiliary element; 
           [0066]      FIG. 4 : Residual tooth area of the patient, with implant without auxiliary element; 
           [0067]      FIG. 5 : Model of a residual tooth area with manipulation implant and affixed abutment; 
           [0068]      FIG. 6 : Model of a residual tooth area with two manipulation implants, two abutments and one dental prosthesis part; 
           [0069]      FIG. 7 : System for modelling an individual dental prosthesis; 
           [0070]      FIG. 8 : Schematic representation of a dental arch with a gap between teeth; 
           [0071]      FIG. 9 : Flowchart for the selection of points standing out from the jaw; 
           [0072]      FIG. 10 : Determination of the direction of insertion from the intersection of aperture angles of cones; 
           [0073]      FIG. 11 : Schematic representation of an equatorial line of a tooth with fitted circle. 
       
    
    
     DETAILED DESCRIPTION 
       [0074]      FIG. 1  shows a model of a residual tooth area  1  that comprises a plurality of teeth along with a manipulation implant  2  with an affixed auxiliary element  3 . The manipulation implant  2  can take on the position relative to model  1  that corresponds to the position of a corresponding implant  10  in the jaw of a patient. The longitudinal axis  4  of the manipulation implant can correspond to the orientation of the longitudinal axis  11  of the implant in the patient&#39;s mouth. The auxiliary element  3  can, together with the manipulation implant  2 , describe the position of the implant  10  in the jaw area. 
         [0075]    A geometry of this model of the residual tooth area  1  can be ascertained with a detection device  5 , for example, with a scanner. A data set  6  of this geometry can additionally be passed on, processed or stored. 
         [0076]    The auxiliary element  3  can have a characteristic shape that can be recognized well in the data set  6 , so that it is possible to determine the position of the manipulation implant  2  and/or the implant  10  from the recognized position of the auxiliary element  3 . 
         [0077]      FIG. 2  shows a model of the residual tooth area  7 , whereby no auxiliary element is, however, affixed onto the manipulation implant  2 . Here again a data set  8  that describes the geometry of this model  7  can be ascertained with the detection device  5 , whereby the data set  8  can be passed on, processed or stored. The position of the upper end of a manipulation implant can be roughly determined from this data set  8 . As a rule, the information is not sufficient for exactly determining the precise position of the manipulation implant  2 , but the position of the upper end can be determined with sufficient precision. With, for example, this information, as well as, for example, with the data on the shape of the residual tooth area, such as arrangement, and/or size of the adjacent teeth, the direction of insertion, for example, can be defined by which a dental prosthesis part can be pushed onto an abutment, whereby the abutment can be affixed onto the implant. 
         [0078]      FIG. 3  shows the residual tooth area  9  of a patient, whereby the area in the case shown comprises a plurality of teeth as well as an implant  10  onto which an auxiliary element  3  is affixed. The residual tooth area  9  can be ascertained by means of a detection unit  5 , whereby this detection unit can be the same as the detection unit for ascertaining the models; the two detection units can also be different, however. The determined data set  12  can be passed on, processed and/or stored. The implant  10  in the jaw of the patient can have a longitudinal axis  11 . The position of the implant can be roughly determined from the upper end of the implant. 
         [0079]      FIG. 4  shows a residual tooth area  13  of the patient, whereby no auxiliary element is affixed onto the implant  10 . The geometry of this residual tooth area  13  can be ascertained with a detection unit  5 , and the data set  14  obtained in this way can be passed on, processed and/or stored. 
         [0080]      FIG. 5  shows a model of a residual tooth area  15  onto the manipulation implant  2  of which an abutment  16  is affixed. The abutment  16  can have a screw channel  18  in order to connect the abutment  16  and (manipulation) implant  2 ,  10 , for example, by means of a screw. The longitudinal axis of the screw channel can correspond to the axis of the manipulation implant  4  and the axis of the implant  11 , so that the abutment  16  and the manipulation implant  2  and/or the abutment  16  and implant  10  can be connected to each other without tensions that can, for example, be caused by a twisted screw. The longitudinal axis of the screw channel and the axis of the implant  11  can also, however, be slanted with respect to each other or can be skewed with respect to each other. Adapters can be inserted between the implant and abutment for this purpose. 
         [0081]    An outer shape of an abutment  16  can be determined by using the data set  8 , which describes the geometry of the corresponding model without affixed auxiliary elements (see  FIG. 2 ). The possible outer shape of an abutment  16  can be restricted by the arrangement of adjacent teeth, a direction by which the abutment  16  is to be affixed onto the manipulation implant  2  and/or implant  10  or the possibility of the insertion of a screw into the screw channel  18  and/or its attachment in the manipulation implant  2  and/or implant  10 . The outer shape of an abutment  16  can also be necessitated by one or more characteristics of a dental prosthesis part that is to be pushed on. Such characteristics can, for example, be the direction of insertion of the dental prosthesis part, minimal thickness of the material of the dental prosthesis part or existing undercuts of the dental prosthesis part. 
         [0082]    Manipulation implant  2  and implant  10  as well as the abutment  16  can have connection geometries  7  at their ends that guarantee that the parts can be positioned appropriately against one another and, for example, a twisting of the abutment  16  on the manipulation implant  2  and/or implant  10  can be prevented. 
         [0083]      FIG. 6  shows a model of a residual tooth area  20  with two manipulation implants  2   a,    2   b  and with affixed abutments  16   a,    16   b.  A three-section bridge  21  with a pontic is affixed onto the abutments  16   a,    16   b.  The manipulation implants  2   a,    2   b  have different alignments. The outer shape of the abutments  16   a,    16   b  can be defined with consideration given to the alignment and position of the manipulation implants  2   a,    2   b  and/or the corresponding implants in such a way that the two directions R 1 , R 2  that are given by the longitudinal axes of the manipulation implants and/or of the implants are transformed into a single direction of insertion. As a result, it is possible to push a multi-sectional dental prosthesis part  21  onto the corresponding abutments  16   a,    16   b  by a single direction of insertion E. The dental prosthesis part  21  can, for example, also be given a facing in order to correspond, in terms of the colour and shape, to the teeth in the mouth of a patient. 
         [0084]      FIG. 7  shows a system  22  for modelling an individual dental prosthesis. Using a computer, one or more data sets  6 ,  8 ,  12 ,  14 ,  19  can be loaded in, such as, for example, the data sets that describe the geometry of the models of a residual tooth area with and without auxiliary elements. The data set that describes the residual tooth area of the patient can moreover be loaded in. The data sets can be processed, and corresponding views of a model and/or of a residual tooth area can, for example, be depicted on a monitor  23 . It is possible to edit the data. At the same time, editing steps can be selected and/or carried out by a user by means of a keyboard, a mouse or also by audio signals. The editing steps can also be carried out automatically by using predefined characteristics, such as, for example, materials to be used or specified geometries. The edited data sets can be stored and/or sent, so that the production of an abutment and/or a dental prosthesis part can take place at the location of the editing or the production can, for example, take place in a manufacturing centre. 
         [0085]    A method for modelling an abutment  16  can consequently proceed as follows: The model  1 ,  7  is scanned once with and once without auxiliary elements  3  (see  FIGS. 1 and 2 ), whereby the order is optional. The direction of insertion E can be determined from the data set  8 ,  14  without auxiliary elements  3 , for example, as described above. For this purpose, the data can, for example, be depicted simply, together with a possible direction of insertion E that is, for example, depicted as a line. The data can also be depicted as a surface from the point of view of the direction of insertion E, or consequently with a view onto the model surface along the direction of insertion. The direction of insertion E or the view onto the data is then modified by means of operator inputs, until the operator agrees with the selected direction of insertion E. 
         [0086]    The method for modelling an abutment  16  can, however, also be carried out with the use of the data sets  12 ,  14 , which comprise the three-dimensional geometry of the residual tooth area with implant and with affixed auxiliary element or the three-dimensional geometry of the residual tooth area with implant but without auxiliary element. The direction of insertion E can also be determined with the use of these data sets  12 ,  14 . 
         [0087]    Then the outer area of the abutment  16  can be modelled with or without the help of this direction of insertion E. A cone envelope stub around the direction of the direction of insertion E, for example, is suggested for this. Such a suggestion can still be modified with suitable means in the data model by the user. The model of the abutment  16  can here be modelled in such a way, with consideration of the data set without auxiliary bodies, that the abutment matches the other adjacent teeth or generally matches the residual tooth area. In this connection, the approximate information regarding the position of the upper end of the (manipulation) implant  2 ,  10  that was acquired from the data set  8 ,  14  without auxiliary body  3  is used in order to form the abutment  16  in such a way that it is possible also to attach it to the (manipulation) implant  2 ,  10 . 
         [0088]    To complete the data set that describes the abutment  16 , the underside and the screw channel  18  are now still to be modelled. For this purpose, for example, the already generated data set of the abutment  16  can be superimposed into a representation of the dataset with auxiliary bodies  3 . For example, the relative position of the planned abutment  16  compared to the adjacent teeth or to the residual tooth area can be used for this, because these data are equally available in both data sets  6 ,  8 ,  12 ,  14  (with and without auxiliary bodies). The exact positions of the (manipulation) implants  2 ,  10  are known from the data set  6 ,  12  with auxiliary bodies  3 , so that the screw channel  18  is preferably formed along the implant axes and the information about the exact position of the (manipulation) implant  2 ,  10  is used in order to form the underside of the abutment  16  correspondingly. This allows an abutment  16  to be created whose outer shape can be optimally formed, because no disrupting auxiliary bodies cause shadowing effects in the corresponding data set  8 ,  14 , and with which on the other hand the underside can be modelled with the necessary precision, because a data set with auxiliary bodies is available. 
         [0089]    The data set of an abutment modelled in this way can then be sent to a production station or a production centre, for example, via remote data transmission, for the production of the abutment. 
         [0090]      FIG. 8  shows a schematic representation of a dental arch with a gap between teeth  29 . The dental arch  24  can be divided into three areas, for example, as shown here, into two areas of molars  25 ,  26  and one incisor area  27 . The canine teeth  28  here are not assigned to any of the three areas, but can, for example, be assigned to the incisor area or to the corresponding areas of the molars. It is also possible to assign separate areas to the canine teeth. An implant and an abutment can be placed or can have been placed in the gap between teeth, whereby a dental prosthesis part can then be affixed onto them. A possible direction of insertion for the dental prosthesis part can be determined in that three points standing out from the jaw are selected, and then a plane is laid through these points, whereby the perpendicular to the plane can define the possible direction of insertion. 
         [0091]    For a selection of the points, it can be provided that:
       One point from each one of the three shown areas can be selected, whereby the respective point can be the one that stands out the farthest from the jaw. The points that stand out the farthest from the jaw can be given by the tip of the tooth or also by gum elevations if there are no more teeth in the jaw or in a jaw area.   There is a minimum distance between all pairs of the three points.       
 
         [0094]      FIG. 9  shows a flowchart for the selection of points standing out from the jaw. A database (not shown) can be available that contains the coordinates of such points that stand out from the jaw. For example, the points can be sorted in such a way that the points C i  with a higher index i stand out less from the jaw than such points C i  with a higher index value i. In step  100 , the point C i=1  that stands out the farthest from the jaw is selected as the first point P 1 . 
         [0095]    In step  101 , the distance d between the first point P 1  and the point C i=2  is determined for the next point C i=2 . In step  102 , a check is made to see whether or not the distance d between the first point P 1  and the point C i=2  is greater than or equal to a minimum distance m. The minimum distance can, for example, be 1 cm, 1.5 cm, 2 cm, 2.5 cm or more. The minimum distance can, however, also be smaller. 
         [0096]    If d is greater than or equal to m, in step  103  the point C i=2  is selected as the second point P 2 . If the distance d is less than the minimum distance m, steps  101  and  102  are repeated until a point C i  is found for which the distance d is greater than or equal to the minimum distance m. In the event that no such point is found, an automatic remark can be made. The remark can, for example, include that no second point could be selected and correspondingly the selection of points had to be ended. 
         [0097]    If a point C i  was assigned to the second point P 2  in step  103 , in step  104  the distance d′ to the first point P 1  and the distance d″ to the second point P 2  is calculated for the next point C j=i+1 . In step  105 , a check is made of whether or not the distances d′ and d″ are greater than or equal to the minimum distance m. 
         [0098]    If they are, in step  106  the point C j  is selected as the third point P 3 . If the distances d′ and/or d″ are less than the minimum distance m, steps  104  and  105  are repeated until a point C j  is found for which the distances d′ and d″ are greater than or equal to the minimum distance m. In the event that no such point is found, an automatic remark can be made. The remark can, for example, include that no third point could be selected and correspondingly the selection of points had to be ended. 
         [0099]      FIG. 10  schematically shows the determination of a direction of insertion for a dental prosthesis part on two ground teeth  32 ,  33 , whereby the intersection  36  of two aperture angles of cones  34 ,  34 ′,  35 ,  35 ′ is taken into consideration for the direction of insertion. In order to specify a cone around a ground tooth  32 ,  33 , three or more tangents can be laid on edges of the ground tooth in order to define a cone envelope that surrounds the ground tooth. If there are two ground teeth, there can correspondingly result two cone envelopes with different aperture angles and/or different directions of the cone axes. A direction of insertion for the dental prosthesis part can then result from the intersection  36  of the two aperture angles  34 ,  34 ′,  35 ,  35 ′. 
         [0100]    A cone envelope can, for example, also be laid around an abutment, whereby the aperture angle of the cone can specify a direction of insertion for a dental prosthesis part. If there is a plurality of abutments and/or if there is a combination of one and/or more abutments and/or of one and/or more ground teeth, the direction of insertion of the dental prosthesis part can be determined from the intersection of the corresponding aperture angles of the cones. 
         [0101]    A direction of insertion of a dental prosthesis part can, for example, be defined by the direction of an axis of a ground tooth. The direction of the axis of the ground tooth thereby can be given by the perpendicular to an equatorial surface of the ground tooth, whereby the equatorial surface is defined by the line of the largest, approximately horizontal circumference of the ground tooth. The equatorial line and correspondingly the equatorial surface will generally not run in a plane, but will instead, for example, have a wavy shape that describes the outer structure of the ground tooth. 
         [0102]      FIG. 11  shows an equatorial line  37  of a tooth together with a circular curve  38  fit onto the equatorial line. The fit of the circular curve results in a circular plane that approximately describes the course of the equatorial line and that runs in a plane. The perpendicular  39  to the circular plane can then be used as a possible direction of insertion for a dental prosthesis part.