CN107689253B - Method for generating parameterized inner surface of false tooth crown - Google Patents
Method for generating parameterized inner surface of false tooth crown Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 39
- 210000000332 tooth crown Anatomy 0.000 title claims abstract description 9
- 238000002360 preparation method Methods 0.000 claims abstract description 80
- 238000004364 calculation method Methods 0.000 claims abstract description 5
- 238000005070 sampling Methods 0.000 claims description 58
- 239000013598 vector Substances 0.000 claims description 41
- 230000007704 transition Effects 0.000 claims description 17
- 210000003464 cuspid Anatomy 0.000 claims description 4
- 210000004283 incisor Anatomy 0.000 claims description 4
- 238000012163 sequencing technique Methods 0.000 claims description 4
- 230000011218 segmentation Effects 0.000 abstract description 3
- 230000000694 effects Effects 0.000 description 13
- 238000010586 diagram Methods 0.000 description 12
- 239000000853 adhesive Substances 0.000 description 5
- 230000001070 adhesive effect Effects 0.000 description 5
- 210000000214 mouth Anatomy 0.000 description 2
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Abstract
The invention discloses a method for generating a parameterized inner surface of a denture crown, which comprises the following steps: s1, acquiring a preparation tissue surface of the denture crown, and acquiring preset generation parameters of the inner surface of the denture crown; s2, constructing a reference section of the tissue surface of the preparation body; s3, generating a plurality of ridge rings on the tissue surface of the preparation body according to the reference cross section, and simultaneously carrying out region division on the tissue surface of the preparation body according to preset generation parameters; s4, carrying out non-equidistant bias on the ridge line rings of the divided different regions according to preset generation parameters; s5, matching the deflected ridge line rings; and S6, generating the inner surface of the artificial tooth crown by the matched ridge line ring by adopting a skin subdivision algorithm. The method can be used for carrying out region segmentation on the tissue surface of the preparation body, then processing different regions of the top, the side and the bottom of the tissue surface of the preparation body, and finally generating the inner surface of the denture crown, can realize optimal fitting, has less calculation amount and high precision, and can be widely applied to the denture repair industry.
Description
Technical Field
The invention relates to the field of denture repair, in particular to a parameterized denture crown inner surface generation method.
Background
In recent years, the application of CAD/CAM technology in the field of oral restoration is rapidly developed, compared with the traditional manual restoration mode, the CAD/CAM technology in the oral cavity remarkably reduces the labor intensity of dental technicians, greatly improves the restoration efficiency, has better restoration quality, and meets the design requirement of personalized restoration. In the clinical restoration of the oral cavity, when the maxillofacial surface of a tooth has serious defects, the tooth needs to be restored by using a denture crown which is a restoration covering the whole tooth surface. The digital design of the artificial tooth crown comprises two parts: the design of the inner surface and the design of the outer surface. The inner surface of the dental crown is a retention contact surface of the dental crown and the preparation, and the dental crown and the preparation are generally connected by an adhesive. If the bonding clearance between the denture crown inner surface and the preparation tissue surface is unreasonable, the optimal fitting can not be realized, the comfort level of the denture crown worn by the patient can be influenced, and the important influence on the gum health can also be caused. Therefore, in the design of a dental crown, the design of the inner surface is a very important link. In the prior art, some methods for generating the inner surface of the denture crown take the preparation tissue surface as the inner surface of the denture crown, and the method does not consider the thickness of the adhesive, so that the inner surface of the denture crown and the preparation tissue surface can not be accurately attached. The inner surface of the denture crown is obtained through the preparation body tissue surfaces at equal intervals in some modes, the influence of the thickness of the adhesive is considered in the mode, the inner surface of the denture crown and the preparation body tissue surfaces can be accurately jointed, the inconsistency of different areas of the top, the side and the bottom of the preparation body tissue surfaces on the thickness of the adhesive is not considered, the thickness of the adhesive in different areas of the preparation body tissue surfaces cannot be controlled, and the optimal jointing cannot be realized. Thus, in the prior art, the inner surface of the generated denture crown cannot be optimally matched with the tissue surface of the denture preparation body.
Disclosure of Invention
In order to solve the above-mentioned problems, it is an object of the present invention to provide a method for generating a parameterized inner surface of a dental crown.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method of generating a parameterized inner surface of a dental crown, comprising the steps of:
s1, acquiring a preparation tissue surface of the denture crown, and acquiring preset generation parameters of the inner surface of the denture crown;
s2, constructing a reference section of the tissue surface of the preparation body;
s3, generating a plurality of ridge rings on the tissue surface of the preparation body according to the reference cross section, and simultaneously carrying out region division on the tissue surface of the preparation body according to preset generation parameters;
s4, carrying out non-equidistant bias on the ridge line rings of the divided different regions according to preset generation parameters;
s5, matching the deflected ridge line rings;
s6, generating the inner surface of the artificial tooth crown by the matched ridge line ring by adopting a skin subdivision algorithm;
the generation parameters comprise an occlusal surface bonding gap, a side surface bonding gap, a tooth neck bonding gap and a tooth neck bonding distance.
Further, in step S2, it specifically includes:
and taking the plane where the X axis and the Z axis of the tissue preparation surface are positioned as an initial section, taking the Z axis of the tissue preparation surface as a rotating axis, and rotating the initial section by theta degrees every time to obtain N sections as reference sections of the tissue preparation surface, wherein theta is 2 pi/N.
Further, step S3 specifically includes:
s31, calculating all intersecting lines of the tissue surface of the preparation body and the reference section;
s32, uniformly sampling all the obtained intersecting lines in sequence, and further forming a ridge ring by sampling points of different intersecting lines in the same sequence;
and S33, marking four key ridge rings in the obtained ridge rings according to preset conditions, and dividing all the ridge rings into five regions.
Further, step S31 specifically includes:
s311, randomly acquiring a triangular plate from the triangular plate set of the preparation tissue surface until the acquired triangular plate is intersected with the reference section;
s312, sequentially transferring and searching the next triangular plate intersected with the reference section according to the topological structure of the grid from the triangular plate intersected with the reference section, calculating the intersection point of the triangular plate and the reference section until the boundary of the grid is reached, and finally obtaining N groups of intersection point sequences with sequence and normal vectors corresponding to the intersection point sequences;
and S313, dividing each group of the obtained ordered intersection point sequences into two groups of intersection point sets, sequencing, and obtaining all intersection lines of the preparation tissue surface and the reference section according to each group of the intersection point sets.
Further, in step S312, the step of sequentially transferring and searching the next triangle intersecting the reference cross section according to the topological structure of the mesh, and calculating an intersection point of the next triangle and the reference cross section includes:
sequentially transferring and searching a next triangular plate intersected with the reference section according to the topological structure of the grid, when the intersection point of the previous triangular plate and the reference section is on the vertex of the triangular plate, acquiring a ring of neighborhood triangular plates of the intersection point through the topological structure, and calculating to obtain the next intersection point of the reference section and the grid after detecting the position relation between the acquired triangular plate and the reference section;
or
When the intersection point of the previous triangular plate and the reference section is on the side of the triangular plate, the other triangular plate containing the side where the intersection point is located is obtained through the topological structure, the position relation between the other two line segments of the triangular plate except the side where the intersection point is located and the reference section is detected, and the next intersection point of the reference section and the grid is obtained through calculation.
Further, step S32 specifically includes:
s321, obtaining the number of preset sampling points for each intersection point set, and dividing the total length of all line segments formed by the intersection point sets by the number of the sampling points to obtain sampling length;
s322, from the first point of the intersection line, inserting sampling points on the intersection line in sequence according to the sampling length, and then obtaining the sampling point sequences of all the intersection lines and the corresponding normal vectors thereof;
s323, forming a ridge line ring by the sampling points with the same sequence of different intersection lines.
Further, step S33 specifically includes:
s331, taking the intersection points among all the intersecting lines as the starting points of the intersecting lines, and taking the first ridge line ring after the starting points as a first key ridge line ring;
s332, taking the intersection line with the maximum Z-axis coordinate as a reference intersection line, taking a ridge line ring where the point with the maximum Z-axis coordinate on the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is molar, and taking a ridge line ring where the Mth sampling point from the starting point of the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is cuspid or incisor, wherein M is a given integer;
s333, acquiring a ridge line ring where a point on the reference intersection line, which is away from the starting point of the reference intersection line by a distance equal to a preset tooth neck bonding distance, is located as a third key ridge line ring;
s334, taking the last ridge line ring as a fourth key ridge line ring;
s335, dividing the second key ridge line ring and the adjacent j ridge line rings on two sides into a second area, dividing the third key ridge line ring and the adjacent j ridge line rings on two sides into a fourth area, dividing the first key ridge line ring and the ridge line ring between the first key ridge line ring and the second area into a first area, dividing the ridge line ring between the second area and the fourth area into a third area, and dividing the fourth key ridge line ring and the ridge line ring between the fourth key ridge line ring and the fourth area into a fifth area.
Further, step S4 specifically includes:
s41, offsetting the point on the ridgeline ring of the first region by the preset distance of the occlusal surface bonding gap along the normal vector of the point, offsetting the point on the ridgeline ring of the third region by the preset distance of the lateral surface bonding gap along the normal vector of the point, and offsetting the point on the ridgeline ring of the fifth region by the preset distance of the tooth neck bonding gap along the normal vector of the point;
and S42, offsetting the point on the ridge line ring of the second area by a first uniform transition distance along the normal vector thereof, wherein the first uniform transition distance is uniformly transited between the occlusal bonding gap and the lateral bonding gap, and offsetting the point on the ridge line ring of the fourth area by a second uniform transition distance along the normal vector thereof, wherein the second uniform transition distance is uniformly transited between the lateral bonding gap and the tooth neck bonding gap.
Further, step S5 specifically includes:
s51, uniformly sampling the first key ridge ring;
s52, calculating matching points corresponding to the sampling points on the other ridge rings and the uniformly sampled first key ridge by adopting a plane intersection method;
and S53, forming a corresponding matched ridgeline ring according to the uniform sampling points or the matching points.
Further, step S6 specifically includes:
s61, respectively taking the discrete points on each ridge line ring as a group of interpolation points, and interpolating to generate a B spline curve as a ridge line;
s62, after the ridge lines are subjected to uniform discretization, all discrete points in the same sequence on the ridge lines are used as a group of interpolation points, and a B spline curve is generated by interpolation and used as a section line;
and S63, converting the discrete points into a mesh model represented by triangular plates through triangulation.
The invention has the beneficial effects that: the invention relates to a method for generating a parameterized inner surface of a denture crown, which comprises the following steps: s1, acquiring a preparation tissue surface of the denture crown, and acquiring preset generation parameters of the inner surface of the denture crown; s2, constructing a reference section of the tissue surface of the preparation body; s3, generating a plurality of ridge rings on the tissue surface of the preparation body according to the reference cross section, and simultaneously carrying out region division on the tissue surface of the preparation body according to preset generation parameters; s4, carrying out non-equidistant bias on the ridge line rings of the divided different regions according to preset generation parameters; s5, matching the deflected ridge line rings; s6, generating the inner surface of the artificial tooth crown by the matched ridge line ring by adopting a skin subdivision algorithm; the generation parameters comprise an occlusal surface bonding gap, a side surface bonding gap, a tooth neck bonding gap and a tooth neck bonding distance. The method can perform region segmentation on the tissue surface of the preparation body, then process different regions of the top, the side and the bottom of the tissue surface of the preparation body, and finally generate the inner surface of the denture crown, and can realize optimal fitting.
Drawings
The invention is further illustrated by the following figures and examples.
FIG. 1 is a flow chart of a method of generating a parameterized inner surface of a dental crown according to the present invention;
FIG. 2 is a schematic diagram of parameter meanings of the generated parameters obtained in the second embodiment of the present invention;
FIG. 3 is a schematic illustration of an initial cross-section of a preparation tissue surface in a second embodiment of the invention;
FIG. 4 is a schematic illustration of a reference cross-section of a preparation tissue surface in a second embodiment of the invention;
FIG. 5 is a schematic view of the triangular plate of the second embodiment of the present invention, in which the intersection point of the triangular plate with the reference cross section is at the apex of the triangular plate;
FIG. 6 is a schematic view of the intersection of the triangular plate with the reference cross-section on the sides of the triangular plate in a second embodiment of the present invention;
FIG. 7 is a schematic view of all the intersections of the calculated prepared tissue plane with the reference cross-section in the second embodiment of the present invention;
FIG. 8 is a graph of the effect of uniformly sampling all the intersections of FIG. 7;
fig. 9 is a schematic diagram illustrating the effect of area division on the tissue surface of the preparation according to the second embodiment of the present invention;
FIG. 10 is a schematic diagram of a plane section method according to a second embodiment of the present invention;
FIG. 11 is an effect diagram of a ridge ring without interpolation according to the second embodiment of the present invention;
FIG. 12 is a diagram illustrating the interpolation of the ridge line ring of FIG. 11 according to a second embodiment of the present invention;
FIG. 13 is a schematic diagram of a sequence of adding discrete points during triangulation according to a second embodiment of the present invention;
FIG. 14 is a schematic diagram showing the effect of the surface form obtained after triangulation in the second embodiment of the present invention;
fig. 15 is a schematic diagram showing an effect of a wire frame form obtained after triangulation is performed in the second embodiment of the present invention;
FIG. 16 is a graph illustrating the effect of the inner surface of a dental crown generated using a first set of generation parameters according to a second embodiment of the present invention;
FIG. 17 is a graph illustrating the effect of the inner surface of a dental crown generated using a second set of generation parameters according to a second embodiment of the present invention;
fig. 18 is a graph illustrating the effect of the inner surface of the dental crown generated using the third set of generation parameters according to the second embodiment of the present invention.
Detailed Description
Embodiment one of the invention
Referring to fig. 1, the present invention provides a method for generating a parameterized inner surface of a dental crown, comprising the steps of:
s1, acquiring a preparation tissue surface of the denture crown, and acquiring preset generation parameters of the inner surface of the denture crown;
s2, constructing a reference section of the tissue surface of the preparation body;
s3, generating a plurality of ridge rings on the tissue surface of the preparation body according to the reference cross section, and simultaneously carrying out region division on the tissue surface of the preparation body according to preset generation parameters;
s4, carrying out non-equidistant bias on the ridge line rings of the divided different regions according to preset generation parameters;
s5, matching the deflected ridge line rings;
s6, generating the inner surface of the artificial tooth crown by the matched ridge line ring by adopting a skin subdivision algorithm;
the generation parameters comprise an occlusal surface bonding gap, a side surface bonding gap, a tooth neck bonding gap and a tooth neck bonding distance.
Further, as a preferred embodiment, in step S2, it is specifically:
and taking the plane where the X axis and the Z axis of the tissue preparation surface are positioned as an initial section, taking the Z axis of the tissue preparation surface as a rotating axis, and rotating the initial section by theta degrees every time to obtain N sections as reference sections of the tissue preparation surface, wherein theta is 2 pi/N.
Further as a preferred embodiment, the step S3 specifically includes:
s31, calculating all intersecting lines of the tissue surface of the preparation body and the reference section;
s32, uniformly sampling all the obtained intersecting lines in sequence, and further forming a ridge ring by sampling points of different intersecting lines in the same sequence;
and S33, marking four key ridge rings in the obtained ridge rings according to preset conditions, and dividing all the ridge rings into five regions.
Further as a preferred embodiment, the step S31 specifically includes:
s311, randomly acquiring a triangular plate from the triangular plate set of the preparation tissue surface until the acquired triangular plate is intersected with the reference section;
s312, sequentially transferring and searching the next triangular plate intersected with the reference section according to the topological structure of the grid from the triangular plate intersected with the reference section, calculating the intersection point of the triangular plate and the reference section until the boundary of the grid is reached, and finally obtaining N groups of intersection point sequences with sequence and normal vectors corresponding to the intersection point sequences;
and S313, dividing each group of the obtained ordered intersection point sequences into two groups of intersection point sets, sequencing, and obtaining all intersection lines of the preparation tissue surface and the reference section according to each group of the intersection point sets.
Further as a preferred embodiment, in step S312, the step of sequentially searching for the next triangle intersecting with the reference cross section according to the topological structure of the mesh and calculating the intersection point of the next triangle and the reference cross section includes:
sequentially transferring and searching a next triangular plate intersected with the reference section according to the topological structure of the grid, when the intersection point of the previous triangular plate and the reference section is on the vertex of the triangular plate, acquiring a ring of neighborhood triangular plates of the intersection point through the topological structure, and calculating to obtain the next intersection point of the reference section and the grid after detecting the position relation between the acquired triangular plate and the reference section;
or
When the intersection point of the previous triangular plate and the reference section is on the side of the triangular plate, the other triangular plate containing the side where the intersection point is located is obtained through the topological structure, the position relation between the other two line segments of the triangular plate except the side where the intersection point is located and the reference section is detected, and the next intersection point of the reference section and the grid is obtained through calculation.
Further as a preferred embodiment, the step S32 specifically includes:
s321, obtaining the number of preset sampling points for each intersection point set, and dividing the total length of all line segments formed by the intersection point sets by the number of the sampling points to obtain sampling length;
s322, from the first point of the intersection line, inserting sampling points on the intersection line in sequence according to the sampling length, and then obtaining the sampling point sequences of all the intersection lines and the corresponding normal vectors thereof;
s323, forming a ridge line ring by the sampling points with the same sequence of different intersection lines.
Further as a preferred embodiment, the step S33 specifically includes:
s331, taking the intersection points among all the intersecting lines as the starting points of the intersecting lines, and taking the first ridge line ring after the starting points as a first key ridge line ring;
s332, taking the intersection line with the maximum Z-axis coordinate as a reference intersection line, taking a ridge line ring where the point with the maximum Z-axis coordinate on the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is molar, and taking a ridge line ring where the Mth sampling point from the starting point of the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is cuspid or incisor, wherein M is a given integer;
s333, acquiring a ridge line ring where a point on the reference intersection line, which is away from the starting point of the reference intersection line by a distance equal to a preset tooth neck bonding distance, is located as a third key ridge line ring;
s334, taking the last ridge line ring as a fourth key ridge line ring;
s335, dividing the second key ridge line ring and the adjacent j ridge line rings on two sides into a second area, dividing the third key ridge line ring and the adjacent j ridge line rings on two sides into a fourth area, dividing the first key ridge line ring and the ridge line ring between the first key ridge line ring and the second area into a first area, dividing the ridge line ring between the second area and the fourth area into a third area, and dividing the fourth key ridge line ring and the ridge line ring between the fourth key ridge line ring and the fourth area into a fifth area. i is a predetermined integer, and in this embodiment i is 2.
Further as a preferred embodiment, the step S4 specifically includes:
s41, offsetting the point on the ridgeline ring of the first region by the preset distance of the occlusal surface bonding gap along the normal vector of the point, offsetting the point on the ridgeline ring of the third region by the preset distance of the lateral surface bonding gap along the normal vector of the point, and offsetting the point on the ridgeline ring of the fifth region by the preset distance of the tooth neck bonding gap along the normal vector of the point;
and S42, offsetting the point on the ridge line ring of the second area by a first uniform transition distance along the normal vector thereof, wherein the first uniform transition distance is uniformly transited between the occlusal bonding gap and the lateral bonding gap, and offsetting the point on the ridge line ring of the fourth area by a second uniform transition distance along the normal vector thereof, wherein the second uniform transition distance is uniformly transited between the lateral bonding gap and the tooth neck bonding gap.
Further as a preferred embodiment, the step S5 specifically includes:
s51, uniformly sampling the first key ridge ring;
s52, calculating matching points corresponding to the sampling points on the other ridge rings and the uniformly sampled first key ridge by adopting a plane intersection method;
and S53, forming a corresponding matched ridgeline ring according to the uniform sampling points or the matching points.
Further as a preferred embodiment, the step S6 specifically includes:
s61, respectively taking the discrete points on each ridge line ring as a group of interpolation points, and interpolating to generate a B spline curve as a ridge line;
s62, after the ridge lines are subjected to uniform discretization, all discrete points in the same sequence on the ridge lines are used as a group of interpolation points, and a B spline curve is generated by interpolation and used as a section line;
and S63, converting the discrete points into a mesh model represented by triangular plates through triangulation.
Embodiment two of the invention
The invention is a detailed example of the first embodiment, which specifically comprises the following steps:
the method comprises the steps of firstly, obtaining a preparation body tissue surface of the denture crown, and simultaneously obtaining preset generation parameters of the inner surface of the denture crown. The acquired tissue surface of the preparation body is a triangular mesh model, and the triangular mesh model can be obtained by adopting a triangulation method in the prior art. As shown in fig. 2, the generation parameters include the occlusal bonding gap top _ offset, the lateral bonding gap side _ offset, the tooth neck bonding gap bottom _ offset, and the tooth neck bonding distance bottom _ length.
And step two, constructing a reference section of the tissue plane of the preparation body, specifically, as shown in fig. 3, taking a plane where an X axis and a Z axis of the tissue plane of the preparation body are located as an initial section, taking the Z axis of the tissue plane of the preparation body as a rotating axis, and rotating the initial section by theta degrees each time to obtain N sections as the reference section of the tissue plane of the preparation body, as shown in fig. 4, wherein theta is 2 pi/N, and N is a natural number, the reference section can be represented by a section normal vector Nor (sin α, cos α,0) and a point P (0,0,0) of a cross section, and P (0,0,0) is a common zero point of all the sections, and the section equation is as follows:
where i denotes the i-th reference section and α denotes the angle of the reference section.
Step three, generating a plurality of ridge rings on the tissue preparation surface according to the reference cross section, and simultaneously performing area division on the tissue preparation surface according to preset generation parameters, wherein the method specifically comprises the following steps of S31-S33:
s31, calculating all intersecting lines of the tissue surface of the preparation body and the reference section;
s32, uniformly sampling all the obtained intersecting lines in sequence, and further forming a ridge ring by sampling points of different intersecting lines in the same sequence;
and S33, marking four key ridge rings in the obtained ridge rings according to preset conditions, and dividing all the ridge rings into five regions.
Step S31 specifically includes steps S311 to S313:
s311, randomly acquiring a triangular plate from the triangular plate set of the preparation tissue surface until the acquired triangular plate is intersected with the reference section;
s312, sequentially transferring and searching the next triangular plate intersected with the reference section according to the topological structure of the grid from the triangular plate intersected with the reference section, calculating the intersection point of the triangular plate and the reference section until the boundary of the grid is reached, and finally obtaining N groups of intersection point sequences with sequence and normal vectors corresponding to the intersection point sequences;
and S313, dividing each group of the obtained ordered intersection point sequences into two groups of intersection point sets, sequencing, and obtaining all intersection lines of the preparation tissue surface and the reference section according to each group of the intersection point sets. Here, the division point is a common point pt _ same of all intersecting lines. Although each group of intersection point sets is sequential, the order of the intersection point sets among different groups is not necessarily the same, so the intersection point sets need to be reordered, wherein the intersection point sets are ordered by taking the distance from the starting point and the last point in the intersection point sets to the Z axis as a reference: if the distance from the starting point to the Z axis is greater than the distance from the tail point to the Z axis, reversely ordering the intersection point set; otherwise, no reordering is required. Aiming at the normal vector of the intersection point, when the intersection point is at the vertex of the triangular plate, the normal vector of the intersection point is the normal vector of the corresponding vertex of the triangular plate; when the intersection point is on the side of the triangular plate, the normal vector of the intersection point is the average of the plane normal vectors of the two triangular plates sharing the side of the intersection point.
In detail, whether the triangular plate intersects with the reference section is detected, and whether three sides of the triangular plate intersect with the plane is actually calculated. The end points of the line segment are v1 and v2, the normal vector of the plane is Nor, and the position relationship between the line segment and the plane is judged by the following method:
(1) if it is
There are two cases: the line segment is parallel to the plane or in the plane, and the position relation of the line segment and the plane can be determined by substituting the coordinate of the end point into the plane equation to determine whether the test result is 0. When the result is 0, the line segment is in the plane, and the line segment and the plane have numerous intersection points; when the result is not 0, the line segment is parallel to the plane, and there are two cases where the line segment does not intersect the plane: the line segment is parallel to the plane or in the plane, and the position relation of the line segment and the plane can be determined by substituting the coordinate of the end point into the plane equation to determine whether the test result is 0.
(2) If it is
Order:
the results of solving for t expressed in different ranges are as follows
(2.1) if t is greater than 1 or t is less than 0, the intersection point is outside the line segment, and the plane and the line segment do not have an intersection point;
(2.2) if t is 0, the intersection coincides with v 1; if t is 1, the intersection coincides with v 2;
(2.3) if 0< t <1, the intersection point is inside the line segment, and the intersection point coordinate pt is:
fig. 5 is a schematic diagram of the intersection point of the triangular plate and the reference cross section at the apex of the triangular plate, and fig. 6 is a schematic diagram of the intersection point of the triangular plate and the reference cross section at the side of the triangular plate. Sequentially transferring and searching the next triangular plate intersected with the reference section according to the topological structure of the grid, and aiming at the condition that the intersection point of the last triangular plate and the reference section is at the vertex of the triangular plate in the graph 5, acquiring a ring of neighborhood triangular plates of the intersection point through the topological structure, detecting the position relation between the acquired triangular plate and the reference section, and calculating to obtain the next intersection point of the reference section and the grid;
for the case that the intersection point of the previous triangle and the reference cross section is on the side of the triangle in fig. 6, another triangle including the side where the intersection point is located is obtained through the topological structure, the position relationship between the other two line segments of the triangle except the side where the intersection point is located and the reference cross section is detected, and the next intersection point of the reference cross section and the grid is obtained through calculation.
In the transmission searching process, if the first searched triangular plate is not positioned at the grid boundary, when the next intersection point is explored for the first time, two intersection points can be obtained and are evolved into the exploration in two directions, and finally, the grid boundary can be explored and stopped; if the triangular plate is at the grid boundary, when an intersection point is explored for the first time, the intersection point is obtained, the exploration in one direction is carried out, and finally the grid boundary is explored and stopped.
In step S32, after all intersecting lines are obtained, because the intersecting points in the intersecting lines are extremely unevenly distributed, in order to make the finally generated grid form uniform, the intersecting lines need to be uniformly sampled, the number of sampling points of each intersecting line is the same, the starting points of all intersecting lines are the common point pt _ same of all intersecting lines, and the end points are the points on the boundary of the tissue surface of the preparation body. Step S32 specifically includes:
s321, obtaining the number of preset sampling points for each intersection set, and then dividing the total length of all line segments formed by the intersection sets by the number of the sampling points to obtain a sampling length, i.e. obtaining a sampling length len according to the following formula:
Pithe intersection point is shown.
S322, from the first point of the intersection line, inserting sampling points on the intersection line in sequence according to the sampling length, and then obtaining the sampling point sequences of all the intersection lines and the corresponding normal vectors thereof; FIG. 7 is a schematic diagram of all the intersections calculated by the method, and FIG. 8 is a schematic diagram of the intersections of FIG. 7 after uniform sampling;
s323, forming a ridge line ring by the sampling points with the same sequence of different intersection lines.
In order to realize the setting of the parameters of the bonding gaps of different areas, the ridge line ring needs to be divided into areas, specifically, the division is performed through steps S331 to S335:
s331, taking the intersection points among all the intersecting lines as the starting points of the intersecting lines, and taking the first ridge line ring after the starting points as a first key ridge line ring;
s332, taking the intersection line with the maximum Z-axis coordinate as a reference intersection line, taking a ridge line ring where the point with the maximum Z-axis coordinate on the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is molar, and taking a ridge line ring where the Mth sampling point from the starting point of the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is cuspid or incisor, wherein M is a given integer;
s333, acquiring a ridge line ring where a point on the reference intersection line, which is away from the starting point of the reference intersection line by a distance equal to a preset tooth neck bonding distance, is located as a third key ridge line ring;
s334, taking the last ridge line ring as a fourth key ridge line ring;
s335, dividing the second key ridge line ring and the adjacent j ridge line rings on two sides into a second area, dividing the third key ridge line ring and the adjacent j ridge line rings on two sides into a fourth area, dividing the first key ridge line ring and the ridge line ring between the first key ridge line ring and the second area into a first area, dividing the ridge line ring between the second area and the fourth area into a third area, and dividing the fourth key ridge line ring and the ridge line ring between the fourth key ridge line ring and the fourth area into a fifth area. The effect graph of each separated region after dividing the region is shown in fig. 9.
S4, carrying out non-equidistant bias on the ridge line rings of the divided different regions according to preset generation parameters; the method specifically comprises the following steps of S41 and S42:
s41, offsetting the point on the ridge line ring of the first region by the preset distance top _ offset of the occlusal bonding gap along the normal vector, offsetting the point on the ridge line ring of the third region by the preset distance side _ offset of the lateral bonding gap along the normal vector, offsetting the point on the ridge line ring of the fifth region by the preset distance bottom _ offset of the tooth neck bonding gap along the normal vector, and for any point v in the ridge line rings of the three regionsiPoint v 'after biasing'iComprises the following steps:
Nithe normal vector is shown.
S42, offsetting the point on the ridge line ring of the second area by a first uniform transition distance along the normal vector, wherein the first uniform transition distance is uniformly transited between the occlusal bonding gap and the lateral bonding gapThe points on the ridgeline ring of the fourth region are offset along their normal vector by a second uniform transition distance that is a uniform transition between the flank bond gap and the neck bond gap. In order to make the final inner surface of the denture crown transition uniformly at the key ridge ring, the offset distance of the points in the second area along the normal vector is uniformly transited between the occlusal bonding gap top _ offset and the lateral bonding gap side _ offset, and the second area has 5 ridge rings in total, so that the offset distance offset of the ith (i ═ 1,2, …,5) ridge ring and any point v in the ridge ringiPoint v 'after biasing'iComprises the following steps:
similarly, any point v in the ridge line ring of the fourth area can be solvediPoint v 'after biasing'i。
S5, matching the deflected ridge line rings; the method specifically comprises the following steps of S51-S53:
s51, uniformly sampling the first key ridge ring;
s52, calculating matching points corresponding to the sampling points on the other ridge rings and the uniformly sampled first key ridge by adopting a plane intersection method; referring to fig. 10, the plane intersection method is as follows:
calculating the center c of the first critical ridge ring and some remaining ridge ringt、co(ii) a Then calculate point vt i、ct、coThe formed section plane S; and finally, calculating the intersection point of the section plane S and one of the other ridge rings. Since the loops of the spinal wire are closed and regular in shape, there are and only two points of intersection vi1And vi2If, if
Is greater than
V is theni1Is vt iCorresponding matching point, otherwise vi2Is the matching point.
And S53, forming a corresponding matched ridgeline ring according to the uniform sampling points or the matching points.
S6, generating the inner surface of the artificial tooth crown by the matched ridge line ring by adopting a skin subdivision algorithm; the method specifically comprises the following steps of S61-S63:
s61, respectively taking the discrete points on each ridge line ring as a group of interpolation points, and interpolating to generate a B spline curve as a ridge line; the effect graphs before and after interpolation of the ridge line ring are shown in fig. 11 and 12, so that the ridge line and the section line obtained after interpolation can keep a certain degree of smoothness, the inner surface of the subsequently generated crown prosthesis can be ensured to keep a certain smoothness, and the condition that the inner surface model is processed by using a smoothness algorithm at a later stage is avoided.
S62, after the ridge lines are subjected to uniform discretization, all discrete points in the same sequence on the ridge lines are used as a group of interpolation points, and a B spline curve is generated by interpolation and used as a section line;
and S63, converting the discrete points into a mesh model represented by triangular plates through triangulation. S63 which is specifically: and connecting discrete points between the same two section lines according to a certain sequence to form a triangular plate, obtaining a triangulated mesh curved surface, and filling the area surrounded by the first key ridge line ring. The distribution of discrete points on each section line has the same rule, and the discrete points can be connected between two adjacent section lines in a certain sequence to form a triangular patch, so that a triangulated mesh curved surface is obtained. The normal vector of the triangular surface patch in the mesh curved surface faces outwards and is consistent with the normal vector of the triangular surface patch in the preparation tissue surface. Finally, the area surrounded by the first critical ridge loop needs to be filled. This area is very small and the boundary is obtained after uniform sampling, which is very regular and can be handled as follows: and adjacent sampling points on the first key ridge line ring sequentially generate a triangular patch with a common point pt _ same of all intersecting lines, and the outward orientation of the normal vector of the triangular patch is consistent with the orientation of the normal vector of the triangular patch in the preparation tissue surface. FIG. 13 shows the order in which discrete points are added during triangulation. The effect graph in the form of a surface obtained after triangulation is shown in fig. 14, and the effect graph in the form of a wire frame obtained is shown in fig. 15.
Fig. 16, 17 and 18 show the generating effect of the inner surface of the dental prosthesis crown when the generating parameters top _ off, side _ off and bottom _ off are set to different values respectively and bottom _ length is set to 1. The corresponding generation parameters of fig. 16 are: top _ off is 0.06, side _ off t is 0.06, bottom _ off is 0, and bottom _ length is 1. The corresponding generation parameters of fig. 17 are: top _ offset is 0.06, side _ offset is 0, bottom _ offset is 0.06, and bottom _ length is 1. The corresponding generation parameters of fig. 16 are: top _ off is 0, side _ off t is 0.06, bottom _ off is 0.06, and bottom _ length is 1. Fig. 16 to 18 show the attachment of the preparation tissue surface to the inner surface of the dental crown and the attachment of the entire preparation to the inner surface of the dental crown, respectively. The preparation and the tissue surface of the preparation are displayed in a surface form, the inner surface of the denture crown is displayed in a wire frame form, and the overlapping area of the wire frame model and the surface model is the area with the bonding gap value of 0.
The method can perform region segmentation on the tissue surface of the preparation body, then process different regions of the top, the side and the bottom of the tissue surface of the preparation body, and finally generate the inner surface of the denture crown, and can realize optimal fitting.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A method of generating a parameterized inner surface of a dental crown, comprising the steps of:
s1, acquiring a preparation tissue surface of the denture crown, and acquiring preset generation parameters of the inner surface of the denture crown;
s2, taking the plane where the X axis and the Z axis of the preparation tissue surface are located as an initial cross section, taking the Z axis of the preparation tissue surface as a rotation axis, and rotating the initial cross section by θ degrees each time to obtain N cross sections as reference cross sections of the preparation tissue surface, where θ is 2 pi/N;
s31, calculating all intersecting lines of the tissue surface of the preparation body and the reference section;
s32, uniformly sampling all the obtained intersecting lines in sequence, and further forming a ridge ring by sampling points of different intersecting lines in the same sequence;
s33, marking four key ridge rings in the obtained ridge rings according to preset conditions, and dividing all the ridge rings into five regions;
s4, carrying out non-equidistant bias on the ridge line rings of the divided different regions according to preset generation parameters;
s5, matching the deflected ridge line rings;
s6, generating the inner surface of the artificial tooth crown by the matched ridge line ring by adopting a skin subdivision algorithm;
the generation parameters comprise an occlusal surface bonding gap, a side surface bonding gap, a tooth neck bonding gap and a tooth neck bonding distance.
2. The method according to claim 1, wherein the step S31 specifically comprises:
s311, randomly acquiring a triangular plate from the triangular plate set of the preparation tissue surface until the acquired triangular plate is intersected with the reference section;
s312, sequentially transferring and searching the next triangular plate intersected with the reference section according to the topological structure of the grid from the triangular plate intersected with the reference section, calculating the intersection point of the triangular plate and the reference section until the boundary of the grid is reached, and finally obtaining N groups of intersection point sequences with sequence and normal vectors corresponding to the intersection point sequences;
and S313, dividing each group of the obtained ordered intersection point sequences into two groups of intersection point sets, sequencing, and obtaining all intersection lines of the preparation tissue surface and the reference section according to each group of the intersection point sets.
3. The method for generating a parameterized denture crown inner surface according to claim 2, wherein the step S312 of sequentially searching the next triangle intersecting the reference cross section according to the topological structure of the mesh and calculating the intersection point of the triangle and the reference cross section is specifically:
sequentially transferring and searching a next triangular plate intersected with the reference section according to the topological structure of the grid, when the intersection point of the previous triangular plate and the reference section is on the vertex of the triangular plate, acquiring a ring of neighborhood triangular plates of the intersection point through the topological structure, and calculating to obtain the next intersection point of the reference section and the grid after detecting the position relation between the acquired triangular plate and the reference section; or
When the intersection point of the previous triangular plate and the reference section is on the side of the triangular plate, the other triangular plate containing the side where the intersection point is located is obtained through the topological structure, the position relation between the other two line segments of the triangular plate except the side where the intersection point is located and the reference section is detected, and the next intersection point of the reference section and the grid is obtained through calculation.
4. The method for generating a parameterized denture crown inner surface according to claim 3, wherein the step S32 specifically includes:
s321, obtaining the number of preset sampling points for each intersection point set, and dividing the total length of all line segments formed by the intersection point sets by the number of the sampling points to obtain sampling length;
s322, from the first point of the intersection line, inserting sampling points on the intersection line in sequence according to the sampling length, and then obtaining the sampling point sequences of all the intersection lines and the corresponding normal vectors thereof;
s323, forming a ridge line ring by the sampling points with the same sequence of different intersection lines.
5. The method for generating a parameterized denture crown inner surface according to claim 4, wherein the step S33 specifically includes:
s331, taking the intersection points among all the intersecting lines as the starting points of the intersecting lines, and taking the first ridge line ring after the starting points as a first key ridge line ring;
s332, taking the intersection line with the maximum Z-axis coordinate as a reference intersection line, taking a ridge line ring where the point with the maximum Z-axis coordinate on the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is molar, and taking a ridge line ring where the Mth sampling point from the starting point of the reference intersection line is located as a second key ridge line ring when the preparation tissue surface is cuspid or incisor, wherein M is a given integer;
s333, acquiring a ridge line ring where a point on the reference intersection line, which is away from the starting point of the reference intersection line by a distance equal to a preset tooth neck bonding distance, is located as a third key ridge line ring;
s334, taking the last ridge line ring as a fourth key ridge line ring;
s335, dividing the second key ridge line ring and the adjacent j ridge line rings on two sides into a second area, dividing the third key ridge line ring and the adjacent j ridge line rings on two sides into a fourth area, dividing the first key ridge line ring and the ridge line ring between the first key ridge line ring and the second area into a first area, dividing the ridge line ring between the second area and the fourth area into a third area, and dividing the fourth key ridge line ring and the ridge line ring between the fourth key ridge line ring and the fourth area into a fifth area.
6. The method for generating a parameterized denture crown inner surface according to claim 5, wherein the step S4 specifically includes:
s41, offsetting the point on the ridgeline ring of the first region by the preset distance of the occlusal surface bonding gap along the normal vector of the point, offsetting the point on the ridgeline ring of the third region by the preset distance of the lateral surface bonding gap along the normal vector of the point, and offsetting the point on the ridgeline ring of the fifth region by the preset distance of the tooth neck bonding gap along the normal vector of the point;
and S42, offsetting the point on the ridge line ring of the second area by a first uniform transition distance along the normal vector thereof, wherein the first uniform transition distance is uniformly transited between the occlusal bonding gap and the lateral bonding gap, and offsetting the point on the ridge line ring of the fourth area by a second uniform transition distance along the normal vector thereof, wherein the second uniform transition distance is uniformly transited between the lateral bonding gap and the tooth neck bonding gap.
7. The method for generating a parameterized denture crown inner surface according to claim 1, wherein the step S5 specifically includes:
s51, uniformly sampling the first key ridge ring;
s52, calculating matching points corresponding to the sampling points on the other ridge rings and the uniformly sampled first key ridge by adopting a plane intersection method;
and S53, forming a corresponding matched ridgeline ring according to the uniform sampling points or the matching points.
8. The method for generating a parameterized denture crown inner surface according to claim 1, wherein the step S6 specifically includes:
s61, respectively taking the discrete points on each ridge line ring as a group of interpolation points, and interpolating to generate a B spline curve as a ridge line;
s62, after the ridge lines are subjected to uniform discretization, all discrete points in the same sequence on the ridge lines are used as a group of interpolation points, and a B spline curve is generated by interpolation and used as a section line;
and S63, converting the discrete points into a mesh model represented by triangular plates through triangulation.
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| CN104504759A (en) * | 2014-12-29 | 2015-04-08 | 佛山市诺威科技有限公司 | Quick transitional mending method based on triangular mesh of denture base crown |
| CN104504758A (en) * | 2014-12-16 | 2015-04-08 | 佛山市诺威科技有限公司 | Method for generating curved surface on surface of denture crown |
| CN105118093A (en) * | 2015-09-02 | 2015-12-02 | 宁波工程学院 | Parametric surface reconstruction method for false tooth discrete data |
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| CN104504759A (en) * | 2014-12-29 | 2015-04-08 | 佛山市诺威科技有限公司 | Quick transitional mending method based on triangular mesh of denture base crown |
| CN105118093A (en) * | 2015-09-02 | 2015-12-02 | 宁波工程学院 | Parametric surface reconstruction method for false tooth discrete data |
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