CN111317587A - Tooth basal crown digital design method based on Laplace deformation - Google Patents
Tooth basal crown digital design method based on Laplace deformation Download PDFInfo
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- CN111317587A CN111317587A CN202010101015.2A CN202010101015A CN111317587A CN 111317587 A CN111317587 A CN 111317587A CN 202010101015 A CN202010101015 A CN 202010101015A CN 111317587 A CN111317587 A CN 111317587A
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C13/00—Dental prostheses; Making same
- A61C13/01—Palates or other bases or supports for the artificial teeth; Making same
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C13/00—Dental prostheses; Making same
- A61C13/0003—Making bridge-work, inlays, implants or the like
- A61C13/0004—Computer-assisted sizing or machining of dental prostheses
Abstract
The invention discloses a tooth base crown digital design method based on Laplace deformation, which mainly comprises the following steps: generating a bonding layer, generating a base crown shoulder, equidistantly biasing a bonding layer replica model, and partially transiting and deforming a biased grid based on Laplace and merging the grid. The design algorithm of the invention has higher design speed and higher robustness, can ensure that the designed basal crown has uniform thickness, and obtains dental prosthesis data with high quality and natural transition. The algorithm has important application value in the field of computer oral cavity repair design.
Description
Technical Field
The invention belongs to the technical field of tooth design, and particularly relates to a tooth coping digital design method based on Laplace deformation.
Background
The digitization technology has wide application in the personalized medical field, especially the digitization dentistry. One of the most common forms of digital fixed denture restoration is the design of the dental coping. In the existing digital design process of the base crown, when the outer surface of the base crown is designed, the base crown and the shoulder of the base crown are seamlessly fused by methods such as cutting, sewing or implicit curved surface construction, however, the transition fusion result of the method is unnatural, the form of the method is poor, a mesh triangular patch needs to be processed in the transition process, and the problems in the aspects of non-popularity, distortion, self-crossing and the like are very likely to occur in the processing process, so that the problem is extremely unfavorable for the subsequent digital design, the algorithm is very likely to crash, and the higher requirement is provided for the robustness of the algorithm.
Disclosure of Invention
The invention aims to provide a tooth base crown digital design method based on Laplace deformation, which has higher robustness and adaptability.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a tooth base crown digital design method based on Laplace deformation comprises the following steps:
1) reading in a triangular mesh model after cutting of a preparation body;
2) biasing the cut triangular mesh model according to design parameters to generate a bonding layer;
3) the design parameters in step 2) include four parameters: the distance a from the cutting edge, the height b of the transition area, the distance c between the edge layer and the edge bonding layer, and the distance d between the center layer and the center bonding layer divide the triangular mesh model after the preparation body is cut into three areas according to the parameter a and the parameter b: an edge layer, a transition layer and a central layer;
4) according to the parameter c and the parameter d in the step 3), offsetting the vertexes of the edge layer and the central layer area along the external normal direction of the vertex of the mesh by utilizing a Laplace deformation technology, automatically transiting the vertex of the transition layer between the edge layer and the central layer between the two layers, wherein the triangular mesh model cut by the offset preparation body is the bonding layer, and the edge layer, the transition layer and the central layer respectively correspond to the edge bonding layer, the transition bonding layer and the central bonding layer on the bonding layer;
5) searching to obtain a boundary point set V1 of the bonding layer, offsetting each point in the boundary point set by a given height e along a given direction α to obtain an offset point set V2, wherein the index numbers of corresponding points in the point set V1 and the point set V2 are in one-to-one correspondence;
6) constructing a basal crown shoulder grid model by using the boundary point sets V1 and V2 in the step 5);
7) generating a bonding layer replica model, carrying out mesh simplification on the bonding layer replica model under the condition that the mesh boundary is not changed, carrying out equidistant bias on the bonding layer replica model after mesh simplification towards the external normal direction of the model, and recording a set V3 of mesh vertexes after the bias, wherein vertex sequence numbers of the set V3 correspond to vertex sequence numbers in boundary point sets V1 and V2 one by one;
8) dividing the bonding layer replica model subjected to equidistant offset into A, B, C regions, wherein the region A is a set of boundary points of the bonding layer replica model, namely V3 in the step 7), the region B is a vertex of an n-ring neighborhood which is away from the boundary points of the region A on the bonding layer replica model, and the rest is a region C;
9) performing transition deformation on the bonding layer replica model after the deviation obtained in the step 8 by using a Laplace deformation technology, and transitioning to the base crown shoulder grid model generated in the step 6);
10) combining the grid models respectively obtained in the step 4), the step 6) and the step 9) to obtain the tooth coping digital model.
Further, the areas in the step 3) are divided, and different offset thicknesses are set in different areas.
Further, setting a matrix for Laplace deformation in the step 4) according to the layering and the offset thickness in the step 3), wherein the matrix equation is as follows:
AV' ═ b, wherein
In the formula, V' is the vertex of the deformed grid model to be calculated, B and C are constraint conditions of the equation, namely the positions finally determined by the grid vertices in the edge layer and the central layer in the step 3), delta is a coordinate vector formed by Laplacian coordinates of the grid model before deformation, L is a Laplacian matrix operator, and the expression is as follows:
wherein L isijThe ith row and jth column values in the matrix operator, i, j, k are the index numbers of the vertexes in the grid model, (i, j) is the edge composed of the vertex i and the vertex j, wijAnd (3) taking the weight of the edge (i, j) as 1, namely the weight of each edge is equal, E is a set of edges at the midpoint of the mesh model, and solving the matrix equation to obtain a set V' of deformed mesh vertexes, wherein the positions of the mesh vertexes in the edge layer and the central layer region of the triangular mesh model after the preparation body cutting are the positions of the mesh vertexes expected after the deviation, and the model transition layer can be in uniform transition between the edge layer and the central layer.
Further, in step 5), in determining α, the positioning direction of the adhesive layer is first calculated, the positioning direction is the processing direction when the base crown is processed, which is defined as a direction in which a beam parallel to the positioning direction is irradiated onto the adhesive layer, all triangular patches on the adhesive layer can be irradiated, and the positioning direction is calculated, the gravity center point of the adhesive layer passes through the gravity center point, and the axis of the positioning direction is defined as the axis of the adhesive layer, and the direction α of each boundary point is defined as a direction having an acute angle with the normal vector outside the boundary point in two directions in which the included angle between the axis and the direction of the projection line of the boundary point and the axis is α in the plane defined by the axis and the boundary point.
Further, area division is carried out on the bonding layer copy model after the distance deviation in the step 8), only the area A and the area B are subjected to transitional deformation during transitional deformation, and the thickness of the base crown is ensured, and meanwhile, the continuity of the transitional area is ensured.
Further, in step 9), performing transient deformation on the biased bonding layer replica model by using a Laplace deformation technology, and performing transient deformation by using a matrix equation (1), wherein in the equation, the constraint is as follows: the final position of each point in the V3 point set of the area A in the step 8) is the position of the point corresponding to the V2 point set in the step 5), each point in the area C in the step 8) keeps the original position unchanged, and the area B in the step 8) is naturally transited to the base crown shoulder grid model by solving the matrix equation (1), so that the natural form of the base crown is ensured.
Further, n in the step 8) is in the range of 5-8.
Compared with the prior art, the invention has the remarkable advantages that:
(1) under the condition of parameter setting, the method can automatically generate the basal crown by one key without any manual interaction, thereby improving the design efficiency of the basal crown;
(2) when the bonding layer is designed, the personalized design can be carried out according to the shape of the tooth, different areas of the bonding layer are offset by different thicknesses, and the triangular mesh model cut by the preparation body is offset by utilizing the Laplace deformation technology, so that the better bonding and fitting of the basal crown and the tooth preparation body are ensured, and the repair quality is ensured;
(3) before the adhesive layer replica model is biased outwards, grid simplification is carried out on the adhesive layer replica model, and during biasing, grid selfing after biasing can be effectively reduced, so that subsequent processing is facilitated;
(4) when the outer surface of the base crown is designed, the Laplace deformation technology is used for carrying out transition deformation on the biased bonding layer replica model, the natural form of a transition region and the fused base crown are ensured to be a closed model, and meanwhile, the algorithm has higher robustness and adaptability;
(5) the method has important practical value for localization of digital repair of the fixed denture.
Drawings
FIG. 1 is a flow chart of a tooth coping digital design method based on Laplace deformation.
FIG. 2 is a grid diagram after the preparation is cut.
FIG. 3 is a parameter layout of an adhesive layer.
Fig. 4 is a diagram of the formation of the adhesive layer.
Fig. 5 is a view of the basal crown shoulder.
FIG. 6 is a design drawing of equidistant offset related parameters.
FIG. 7 is a graph of results of equidistant bias of a bond layer replica model.
FIG. 8 is a graph of biased bond layer replica model transition results.
FIG. 9 is a two-dimensional cross-sectional view of a mesh, a bond layer, a substrate crown shoulder, a bond layer replica model equidistant offset result and an offset bond layer replica model transition result mesh model after preparation cutting.
Fig. 10 is a graph of the results of a digital design of a dental coping based on Laplace deformation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The following describes the implementation of the present invention in detail with reference to specific embodiments.
As shown in fig. 1, the digital design method of a tooth coping based on Laplace deformation of the present invention mainly comprises the following steps:
1) reading in a triangular mesh model after cutting of the preparation body, as shown in FIG. 2;
2) carrying out offset of the grid model according to the design parameters to generate a bonding layer, wherein a bonding layer parameter design drawing is shown in FIG. 3, and a designed bonding layer is shown in FIG. 4;
when designing the adhesive layer, mainly contain 4 parameters, be respectively: the distance a from the cutting edge, the height b of the transition area, the distance c between the edge layer and the edge bonding layer, and the distance d between the center layer and the center bonding layer divide the triangular mesh model after the preparation body is cut into three areas according to the parameter a and the parameter b: an edge layer, a transition layer and a central layer;
when the triangular mesh model is divided into three parts, according to the parameter a, the topological structure of the triangular mesh model is utilized to search vertexes from the edge of the triangular mesh model ring by ring, in the searched vertexes, an area formed by vertexes which are less than a from the edge of the triangular mesh model is an edge bonding layer, an area formed by vertexes which are more than a from the edge of the triangular mesh model and less than b is a transition layer, and the rest areas except the edge bonding layer and the transition layer in the triangular mesh model are center bonding layers.
And offsetting vertexes of the edge layer and the central layer area along the external normal direction of the vertex of the mesh by utilizing a Laplace deformation technology according to the thickness parameter c and the parameter d, wherein the vertex of a transition layer between the edge layer and the central layer can automatically transit between the two layers, the triangular mesh model cut by the offset preparation body is the bonding layer, and the edge layer, the transition layer and the central layer respectively correspond to the edge bonding layer, the transition bonding layer and the central bonding layer on the bonding layer. And when grid biasing is carried out, utilizing a grid deformation technology based on Laplace to realize biasing of the grid model. The key of Laplace grid deformation lies in the setting of a deformation matrix, and the matrix equation is as follows:
AV' ═ b, wherein
In the formula, V' is the position of the vertex of the deformed grid model to be calculated, B and C are constraint conditions of the equation, namely the positions finally determined by the grid vertices in the edge layer and the central layer regions in the step 3), Δ is a coordinate vector formed by Laplacian coordinates of the grid model before deformation, L is a Laplacian operator, and the expression is as follows:
wherein L isijThe ith row and jth column values in the matrix operator, i, j, k are the index numbers of the vertexes in the grid model, (i, j) is the edge composed of the vertex i and the vertex j, wijThe weight of the edge (i, j) is 1, that is, the weight of each edge is equal, and E is the set of edges at the midpoint of the mesh model.
And obtaining a set V' of the deformed grid vertexes by solving the matrix equation, wherein the positions of the grid vertexes in the edge layer and the central layer region of the triangular grid model after the preparation body cutting are the positions of the expected grid vertexes after the deviation, and the model transition layer can be uniformly transited between the edge layer and the central layer. The Laplace deformed model is the bonding layer, and the edge layer, the transition layer and the center layer of the model become the edge bonding layer, the transition bonding layer and the center bonding layer of the bonding layer.
3) Generating basal crown shoulders
And searching to obtain a boundary point set V1 of the bonding layer, offsetting each point in the boundary point set by a given height e along a given direction α to obtain an offset point set V2, wherein the index numbers of corresponding points in the point set V1 and the point set V2 are in one-to-one correspondence.
Using the boundary point sets V1 and V2, a base crown shoulder grid model is constructed as shown in fig. 5, with orientation α and height e as shown in fig. 6.
4) Bond layer replica model equidistant bias
Generating a bonding layer replica model, carrying out grid simplification on the bonding layer replica model under the condition that the grid boundary is not changed, carrying out equidistant bias on the bonding layer replica model after grid simplification towards the external normal direction of the model, wherein the related design parameters of the equidistant bias are shown in figure 6, and f in the figure is the thickness of the equidistant bias. The offset result is shown in fig. 7, and the set V3 of mesh vertices after offset is recorded, and the vertex numbers thereof correspond to the vertex numbers in V1 and V2 one by one.
In determining direction α, the orientation of the bond is first calculated, which is the machine direction of the base crown, and is defined as the direction in which a beam parallel to this direction is incident on the bond, and all triangular facets on the bond can be incident, and this direction is the orientation, the center of gravity point of the bond is calculated, and the axis of the orientation is defined as the axis of the bond, and the direction α of each boundary point is defined as the direction that makes an acute angle with the normal vector outside the boundary point, among the two directions α within the plane defined by the axis and the boundary point, and the direction that makes a line connecting the boundary point and its projected point to the axis.
5) Local transition deformation of offset mesh
Carrying out region division on the bonding layer copy model after equidistant offset to divide the bonding layer copy model into three regions A, B and C; the region a is a set of boundary points of the adhesive layer replica model, namely V3 in step 4), the region B is a vertex of an n-ring neighborhood on the adhesive layer replica model, which is away from the boundary points of the region a (the value of n is usually 5-8 as required), and the rest is a region C.
The biased adhesive layer sub-model is subjected to transition deformation by using a Laplace deformation technology, and is transited to a base crown shoulder grid model, and the result is shown in FIG. 8.
Performing transition deformation on the biased bonding layer replica model by using a Laplace deformation technology, and performing transition deformation by using a matrix equation (1), wherein in the equation, the constraint is as follows: the final position of each point in the V3 point set in the area a is the position of the point corresponding to the point set V2 in the step 4), and each point in the area C remains unchanged.
FIG. 9 is a two-dimensional cross-sectional view of a mesh, a bond layer, a substrate crown shoulder, a bond layer replica model equidistant offset result and an offset bond layer replica model transition result mesh model after preparation cutting;
6) mesh merging
The bond layer, the base crown shoulder model, and the offset and post-transition mesh models were combined to generate the base crown mesh, with the results shown in fig. 10.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. A tooth base crown digital design method based on Laplace deformation is characterized by comprising the following steps:
1) reading in a triangular mesh model after cutting of a preparation body;
2) biasing the cut triangular mesh model according to design parameters to generate a bonding layer;
3) the design parameters in step 2) include four parameters: the distance a from the cutting edge, the height b of the transition area, the distance c between the edge layer and the edge bonding layer, and the distance d between the center layer and the center bonding layer divide the triangular mesh model after the preparation body is cut into three areas according to the parameter a and the parameter b: an edge layer, a transition layer and a central layer;
4) according to the parameter c and the parameter d in the step 3), offsetting the vertexes of the edge layer and the central layer area along the external normal direction of the vertex of the mesh by utilizing a Laplace deformation technology, automatically transiting the vertex of the transition layer between the edge layer and the central layer between the two layers, wherein the triangular mesh model cut by the offset preparation body is the bonding layer, and the edge layer, the transition layer and the central layer respectively correspond to the edge bonding layer, the transition bonding layer and the central bonding layer on the bonding layer;
5) searching to obtain a boundary point set V1 of the bonding layer, offsetting each point in the boundary point set by a given height e along a given direction α to obtain an offset point set V2, wherein the index numbers of corresponding points in the point set V1 and the point set V2 are in one-to-one correspondence;
6) constructing a basal crown shoulder grid model by using the boundary point sets V1 and V2 in the step 5);
7) generating a bonding layer replica model, carrying out mesh simplification on the bonding layer replica model under the condition that the mesh boundary is not changed, carrying out equidistant bias on the bonding layer replica model after mesh simplification towards the external normal direction of the model, and recording a set V3 of mesh vertexes after the bias, wherein vertex sequence numbers of the set V3 correspond to vertex sequence numbers in boundary point sets V1 and V2 one by one;
8) dividing the bonding layer replica model subjected to equidistant offset into A, B, C regions, wherein the region A is a set of boundary points of the bonding layer replica model, namely V3 in the step 7), the region B is a vertex of an n-ring neighborhood which is away from the boundary points of the region A on the bonding layer replica model, and the rest is a region C;
9) performing transition deformation on the bonding layer replica model after the deviation obtained in the step 8 by using a Laplace deformation technology, and transitioning to the base crown shoulder grid model generated in the step 6);
10) combining the grid models respectively obtained in the step 4), the step 6) and the step 9) to obtain the tooth coping digital model.
2. The method for digital design of a tooth coping based on Laplace deformation as claimed in claim 1, wherein the regions in step 3) are divided, and different regions are provided with different offset thicknesses.
3. The method for digitally designing a Laplace deformation-based dental coping according to claim 2, wherein the matrix for Laplace deformation in step 4) is set according to the layering and offset thickness in step 3), and the matrix equation is as follows:
AV' ═ b, wherein
In the formula, V' is the vertex of the deformed grid model to be calculated, B and C are constraint conditions of the equation, namely the positions finally determined by the grid vertices in the edge layer and the central layer in the step 3), delta is a coordinate vector formed by Laplacian coordinates of the grid model before deformation, L is a Laplacian matrix operator, and the expression is as follows:
wherein L isijThe ith row and jth column values in the matrix operator, i, j, k are the index numbers of the vertexes in the grid model, (i, j) is the edge composed of the vertex i and the vertex j, wijAnd (3) taking the weight of the edge (i, j) as 1, namely the weight of each edge is equal, E is a set of edges at the midpoint of the mesh model, and solving the matrix equation to obtain a set V' of deformed mesh vertexes, wherein the positions of the mesh vertexes in the edge layer and the central layer region of the triangular mesh model after the preparation body cutting are the positions of the mesh vertexes expected after the deviation, and the model transition layer can be in uniform transition between the edge layer and the central layer.
4. The method of claim 3, wherein in step 5), when determining α, the orientation of the bonding layer is first calculated, the orientation of the bonding layer in place is the processing direction of the base crown, which is defined as a direction parallel to the direction in which a light beam is irradiated onto the bonding layer, all triangular facets on the bonding layer can be irradiated, and the orientation is the orientation of the orientation, the centroid point of the bonding layer passes through the centroid point, and the axis of the orientation is the orientation of the bonding layer, and the orientation α of each boundary point is defined as an acute angle with respect to the normal vector outside the boundary point in the two directions whose included angles with the direction of the connecting line between the boundary point and the projected point of the axis is α in the plane defined by the boundary point.
5. The method for digitally designing a dental coping based on Laplace deformation according to claim 4, wherein the bonding layer replica model after being subjected to the distance offset in the step 8) is subjected to region division, and only the region A and the region B are subjected to transition deformation during the transition deformation, so that the thickness of the coping is ensured, and meanwhile, the continuity of the transition region is ensured.
6. The Laplace deformation-based tooth coping digital design method according to claim 5, wherein in step 9), the biased bond layer replica model is subjected to transient deformation by using a Laplace deformation technique, and the transient deformation is performed by using a matrix equation (1), wherein the constraint is as follows: the final position of each point in the V3 point set of the area A in the step 8) is the position of the point corresponding to the V2 point set in the step 5), each point in the area C in the step 8) keeps the original position unchanged, and the area B in the step 8) is naturally transited to the base crown shoulder grid model by solving the matrix equation (1), so that the natural form of the base crown is ensured.
7. The Laplace deformation based digital design method for dental coping according to any of the claims 1 to 6, wherein n in step 8) ranges from 5 to 8.
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