CN112998888B - False tooth model undercut removing method based on grid projection - Google Patents
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Abstract
The invention relates to a false tooth model undercut removing method based on grid projection, and belongs to the field of computer aided design and graphics. The method comprises the following steps: s1: inputting a tooth mesh model, converting the tooth mesh model into an OFF format, and setting a projection direction; s2: adding a projection grid surface at the top of the bounding box perpendicular to the projection direction, and adding a base surface at the bottom; s3: inputting a grid and a base plane to a projection plane in the bounding box space to perform BVH space division; s4: and projecting the projection grid surface according to a given projection direction to intersect with the input grid or the base surface, and placing the projection point on the intersection point. S5: calculating a curvature field of a new grid formed by the projection grids; s6: and (4) carrying out self-adaptive subdivision on the new grid based on local grid operation and a Gaussian curvature field, and outputting the grid after iteration is stopped. The invention can use the computer aided design technology to replace the manual filling of the undercut part in the tooth preparation process, thereby reducing the error and the cost brought by manual operation.
Description
Technical Field
The invention belongs to the field of computer aided design and graphics, and relates to a false tooth model undercut removing method based on grid projection.
Background
With the development of relevant computer-aided technologies such as digitalization, three-dimensional scanning and the like and the continuous iterative update of various data acquisition devices and means, the innovation and the application of the digitalization technology in the oral cavity field continuously break through the limitation of the traditional medical technology. In the conventional oral medical technology, complex data needs to be processed in many cases, and high precision is required, which can be simulated only by a computer, but complex three-dimensional space data is difficult to be expressed visually by only using two-dimensional slices, so that it is very valuable to visualize and process some medical data by using a three-dimensional model.
The oral medicine is different from other medical fields, the treatment means is more similar to the mechanical processing, the dental technologist technology is derived to specially research the preparation processing technology in various oral medicines, and the development of the dental technologist technology greatly benefits from the progress of the 3D printing technology. The tooth shape has the irregular characteristic that individual deviation with a certain range exists on the basis of the same functional form. Injection molding is an important step in the formation of appliances in digital oral systems, and is directly related to the wearing and treatment effects of patients, wherein resin films are generally used for cooling and solidifying to form the shapes of teeth, and finally, the appliances worn by the patients are formed through demolding and cutting. As with the problems encountered with machined plastic parts in general, during the cold extraction of the appliance, areas of the model on which the appliance is difficult to remove from the model due to the depressions are known as undercuts (also called chamfers or undercuts) and also as irregular areas of the surface of the crown preparation that affect the seating of the crown restoration.
In the conventional dental technician process, a doctor needs to perform a large amount of manual operations in the preparation process of the artificial tooth, including copying the jaw shape, generating a plaster working model, measuring the tissue shape, carving the wax shape and the like. The core of the above process is that a technician manually designs the shape of the prosthesis and converts the designed shape into a prosthesis of a different material. Based on the above analysis of the process, the possibility of replacing with a CAD system can be clearly seen. Dental CAD technology has a great many practical values: for example, the treatment time is greatly saved, and diagnosis, tooth preparation, prosthesis manufacturing and wearing are completed by one-time diagnosis. Cooperation with hospitals and processing plants also saves costs: the tooth model is transferred by using a digital technology, so that the process of manufacturing the plaster model and the cost of mailing the model can be saved.
Disclosure of Invention
In view of the above, the present invention provides a method for removing undercut from a denture model based on mesh projection, which replaces the conventional manual undercut removing step with a computer aided design. The problems that the manual operation precision is limited by the technical level of a technician, the labor cost is high, the model transfer and preparation time is long and the like are solved.
In order to achieve the purpose, the invention provides the following technical scheme:
a false tooth model undercut removing method based on grid projection comprises the following steps:
s1: inputting a tooth mesh model, converting the tooth mesh model into an OFF (object File Format) format, and setting a projection direction;
s2: adding a projection grid surface at the top of the bounding box perpendicular to the projection direction, adding a base surface at the bottom, and performing BVH space division on the projection surface, the input grid and the base surface in the bounding box space;
s3: projecting the projection grid surface according to a given projection direction to intersect with the input grid or the base surface, and placing the projection point on the intersection point;
s4: calculating a Gaussian curvature field of a new grid formed by the projection grids, and generating corresponding target side length for each area according to the curvature field;
s5: and performing feature preserving re-division iteration on the new grid in a self-adaptive manner based on local grid operation and a Gaussian curvature field, and performing final tuning on the angle of the grid after the iteration is stopped and outputting the grid.
Further, in step S1, for input mesh models (STL, OFF, OBJ) of different formats, the input mesh models are all converted into an OFF file format, the projection direction can be adjusted, and if the specified projection direction is not input, the input mesh bounding box defaults to the negative x-axis direction.
Further, in step S2, a uniform and isotropic triangular mesh plane is added in the incident direction perpendicular to a projection direction, and a plane is added in the exit direction as a bottom surface for receiving projection; in order to accelerate subsequent grid projection and avoid unnecessary space search, an AABB (Axis Aligned Bounding Box) tree form is adopted to perform bvh (Bounding volume hierarchy) space division on the whole scene.
Further, in step S3, for each vertex on the projection mesh, performing a ray projection operation toward the projection direction according to the order of generation of the projection mesh points, where the first intersection point of the vertex and the intersection plane (which may be a model or a base plane) is a projected drop point, moving the projection point to the drop point, and keeping the connection relationship of the projection mesh unchanged until all mesh points are projected, so as to obtain a resampling based on mesh projection.
Further, in step S4, the vertex on the curved surface is mapped to the center of the unit sphere, the end point of the normal is mapped to the spherical surface, the point on the curved surface and the point on the spherical surface are mapped to each other, the geometric meaning of the gaussian curvature, that is, the limit of the area on the spherical surface/the local area of the curved surface, is specifically expressed as a gaussian curvature field on the discrete geometric model:
where A (v) represents the total area of the first-order neighborhood of the v-point, θiThe angle of the triangle corresponding to the v point (when the point is a two-dimensional plane, the sum of the angles of the first-order neighborhood triangles is 2 pi, so the curvature is 0) is represented, the geometric meaning of the formula is relatively intuitive, and the bending degree of the point is drawn immediately by subtracting the angle of the triangle corresponding to the neighborhood of the point from 2 pi and dividing the angle by the area of the corresponding area.
Further, in step S4, based on the obtained gaussian curvature field, the local region object side length is generated by the following formula:
for each vertex, its local target edge length L (x) is obtained, for each edge e (x) on the grid1,x2) And obtaining the side length of the local target corresponding to each side:
Local(e)＝min{L(x1),L(x2)}。
further, in step S5, local operations such as edge splitting, edge folding, edge flipping, and the like are performed on the mesh according to the target edge length corresponding to each edge to make each edge adapt to the target edge length, and meanwhile, in order to ensure the isotropy of the mesh, the positions of the vertices need to be adjusted as follows:
where v is a non-boundary point on the grid, N (v) is its first order neighborhood, and A (v) is viAnd vjMean area of two triangles in which p is locatedjIs point vjThe shape of the triangle can be effectively adjusted by placing the vertex at the position of the barycentric coordinate of the vertex.
Further, in step S5, in order to maintain the mesh characteristics as much as possible in the mesh local operation, it is necessary to project the vertex by tangential translation, and the position of the translated point is set to bepiTranslation amount is Δi＝gi-piThe tangential translation is then Δi'＝Δi-＜Δi,ni＞niWherein n isiIs viTo obtain the position p of the new pointi'＝pi+Δi', normal vector n of vertexiThe following formula is obtained:
projecting the point to the original grid along the normal direction, thereby completing the position adjustment of the point;
then, the grid local operations such as edge splitting, edge folding, edge turning and the like are used again for the anisotropy caused in the step S5 to eliminate sharp and obtuse angles, and finally, the grid is output.
The invention has the beneficial effects that: the false tooth model undercut removing method based on grid projection provided by the invention skillfully solves the undercut removing problem in the preparation of a tooth preparation body model by adopting the thinking of grid projection and resampling on the basis of a half-edge data structure based on graphics, and further researches the problem of low-quality triangular grid caused by the algorithm.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of the denture model undercut removal based on mesh projection according to the present invention;
FIG. 2 is a schematic diagram of the present invention with the addition of a projection grid and a base;
FIG. 3 is a flowchart of a local adaptive mesh re-segmentation algorithm based on Gaussian curvature according to the present invention;
FIG. 4 is a schematic diagram of a coarse mesh projected after the tooth mesh is input according to an embodiment of the present invention;
fig. 5 is an example of the inputs obtained after the coarse mesh is re-cut in accordance with the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
Referring to fig. 1 to 5, as shown in fig. 1, the method of the present invention provides a denture model undercut removing method based on mesh projection, the method includes the following steps:
s1: the tooth mesh model is input, converted to OFF format, and the projection direction is set. The method specifically comprises the following steps: firstly, inputting an original data grid, copying a part of the original data grid as a grid to be processed, setting a global precision parameter to be 0.10, and setting a default projection direction to be from the positive x-axis direction of a bounding box to the negative x-axis direction of the bounding box.
S2: and adding a projection grid surface at the top of the bounding box perpendicular to the projection direction, adding a base surface at the bottom, and carrying out BVH space division on the projection surface, the input grid and the base surface in the bounding box space.
Fig. 2 is a schematic diagram of adding a projection grid and a base plane, as shown in the left diagram of fig. 2, an isotropic grid having a complete connection relationship is added at the top of a bounding box in the projection incident direction, and then a simple surface element is added at the bottom of the bounding box in the projection emergent direction as the base plane; and finally, carrying out space division of aligning coordinate axes on the whole space so as to accelerate the search efficiency of subsequent intersection operation.
S3: and projecting the projection grid surface according to a given projection direction to intersect with the input grid or the base surface, and placing the projection point on the intersection point.
As shown in fig. 2, each vertex on the projection grid surface is subjected to ray projection operation towards the projection direction exactly according to the generation sequence of the projection grid points, the first intersection point of the vertex and the intersection plane (which may be a model or a base plane) is a projection drop point, the projection point is moved to the drop point, the connection relation of the projection grid is kept unchanged until all grid points are projected, and resampling based on grid projection is obtained. A specific example can be seen in fig. 4.
S4: and calculating a Gaussian curvature field of a new grid formed by the projection grids, and generating corresponding target side length for each area according to the curvature field.
A gaussian curvature field embodied on a discrete geometric model can be expressed as:
where A (v) represents the total area of the first-order neighborhood of the v-point, θiThe angle of the triangle corresponding to the v point (when the point is a two-dimensional plane, the sum of the angles of the first-order neighborhood triangles is 2 pi, so the curvature is 0) is represented, the geometric meaning of the formula is relatively intuitive, and the bending degree of the point is drawn immediately by subtracting the angle of the triangle corresponding to the neighborhood of the point from 2 pi and dividing the angle by the area of the corresponding area.
According to the obtained Gaussian curvature field, the length of the side of the target in the local area can be generated by the following method:
for each vertex, its local target edge length L (x) is obtained, so for each edge e (x) on the mesh1,x2) And obtaining the side length of the local target corresponding to each side:
Local(e)＝min{L(x1),L(x2)}
s5: performing feature preserving re-partition iteration on the new mesh in a self-adaptive manner based on local mesh operation and a Gaussian curvature field, and respectively processing a sharp angle and an obtuse angle caused by the step after iteration is stopped: aiming at obtuse angles larger than 86 degrees, triangles adjacent to opposite sides L of the obtuse angles are taken to form a quadrangle Q together, the midpoint of the triangle L is taken to split the sides, a new point V is inserted, and the position of the V is adjusted to enable the sum of the included angle between each vertex and the line of the V and the root mean square error of the optimal angle of 60 degrees to be minimum. And then adopting a conservative edge folding strategy for acute angles less than 35 degrees, namely eliminating the minimum angle and checking whether the grid is effective or not by performing edge folding on the grid copy each time under the condition of ensuring the connectivity of the edge and the effectiveness of the grid, and skipping the angle if the grid is not effective.
Fig. 3 is a flowchart of a local adaptive mesh re-segmentation algorithm based on gaussian curvature, and as shown in fig. 3, the mesh re-division includes the following steps: the method comprises the steps of firstly calculating the side length of a local target corresponding to each side through a Gaussian curvature field, then enabling the side length of each side to adapt to the side length of the local target through side-related operation, optimizing a topological structure of a grid through tangential translation of a vertex position and projection of the tangential translation and projection of the vertex position back to an original model, and ensuring that the shape of the grid is not seriously distorted and jittered to the greatest extent. And finally, continuously iterating the process until the number proportion of the overall long and narrow triangles is converged, namely the change rate is less than 1%, stopping iteration and outputting the mesh model.
In the denture model undercut removing method based on grid projection, theoretical knowledge is based on computer graphics and grid re-dissection, and a part of oral cavity model data to be processed obtained by scanning is shown in figure 4. Fig. 5 shows the latter half processing effect of the present invention, the upper diagram is a rough mesh model obtained after mesh projection, and it can be seen from a wire frame diagram that although the mesh structure is overall regular, there are many long and narrow triangles in the feature region, and through adaptive mesh repartitioning, it can be seen that the mesh structure is greatly improved, and an effect of practical use is achieved.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.
Claims (7)
1. A false tooth model undercut removing method based on grid projection is characterized in that: the method comprises the following steps:
s1: inputting a tooth mesh model, converting the tooth mesh model into an OFF format, and setting a projection direction;
s2: adding a projection grid surface at the top of the bounding box and a base surface at the bottom of the bounding box perpendicular to the projection direction, and performing BVH space division on the projection surface, the input grid and the base surface in the bounding box space;
s3: projecting the projection grid surface according to a given projection direction to intersect with the input grid or the base surface, and placing the projection point on the intersection point; for each vertex on the projection grid, performing ray projection operation towards the projection direction according to the sequence generated by the projection grid points, wherein the first intersection point of the projection grid point and the intersection plane is a projection drop point, moving the projection point to the drop point, and keeping the connection relation of the projection grid unchanged until all grid points are projected, so as to obtain resampling based on grid projection;
s4: calculating a Gaussian curvature field of a new grid formed by the projection grids, and generating corresponding target side length for each area according to the curvature field;
s5: and performing feature preserving re-division iteration on the new grid in a self-adaptive manner based on local grid operation and a Gaussian curvature field, and performing final tuning on the angle of the grid after the iteration is stopped and outputting the grid.
2. The denture model undercut removing method based on grid projection according to claim 1, wherein: in step S1, the input mesh models with different formats are all converted into an OFF file format, the projection direction can be adjusted, and if the designated projection direction is not input, the default is the negative x-axis direction of the input mesh bounding box.
3. The denture model undercut removing method based on grid projection according to claim 1, wherein: in step S2, a uniform and isotropic triangular mesh plane is added in the incident direction perpendicular to a projection direction, and a plane is added in the exit direction as the bottom surface to receive projection; and adopting an AABB tree form to perform BVH space division on the whole scene.
4. The denture model undercut removing method based on grid projection according to claim 1, wherein: in step S4, the vertex on the curved surface is mapped to the center of the unit sphere, the end point of the normal is mapped to the spherical surface, and a correspondence is established between the point on the curved surface and the point on the spherical surface, specifically, a gaussian curvature field on the discrete geometric model is represented as:
where A (v) represents the total area of the first-order neighborhood of the v-point, θiRepresenting the angle of the v-point corresponding to the triangle.
5. The denture model undercut removing method based on grid projection according to claim 4, wherein: in step S4, the local region object side length is generated according to the obtained gaussian curvature field by the following formula:
for each vertex, its local target edge length L (x) is obtained, for each edge e (x) on the grid1,x2) And obtaining the side length of the local target corresponding to each side:
Local(e)＝min{L(x1),L(x2)}。
6. the denture model undercut removing method based on grid projection according to claim 1, wherein: in step S5, edge splitting, edge folding, edge flipping and edge transferring are performed on the mesh according to the target edge length corresponding to each edge to adapt to the target edge length, and the positions of the vertices are adjusted as follows:
where v is a non-boundary point on the grid, N (v) is its first order neighborhood, and A (v) is viAnd vjMean area of two triangles in which p is locatedjIs point vjThe coordinates of (a).
7. The denture model undercut removing method based on grid projection according to claim 6, wherein: in step S5, the vertex is tangentially translated and projected, and the position of the translated point is piTranslation amount is Δi＝gi-piAnd then tangential translation is Δ'i＝Δi-＜Δi,ni＞niWherein n isiIs viTo obtain the position p 'of the new point'i＝pi+Δ'iNormal vector n of vertexiThe following formula is obtained:
projecting the point to the original grid along the normal direction, thereby completing the position adjustment of the point;
then edge splitting, edge folding, and edge flipping are again used to eliminate sharp and obtuse angles for the anisotropy caused in step S5, and finally the grid is output.
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| CN102930091A (en) * | 2012-10-24 | 2013-02-13 | 浙江大学 | Tooth-and-gum-oriented high-efficiency mesh repairing method |
| CN108024841A (en) * | 2015-10-07 | 2018-05-11 | 友莱博系统公司 | Tooth modeling |
| CN112155762A (en) * | 2020-09-30 | 2021-01-01 | 深圳云甲科技有限公司 | Novel computer-assisted removal method for undercut of dental crown preparation |
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| WO2003034288A2 (en) * | 2001-10-16 | 2003-04-24 | Koninklijke Philips Electronics N.V. | Method for designing a template that removably fits to an object's surface |
| EP3777756A1 (en) * | 2012-02-14 | 2021-02-17 | 3Shape A/S | Modeling a digital design of a denture |
| US20210137640A1 (en) * | 2018-02-07 | 2021-05-13 | 3M Innovative Properties Company | Standard orthodontic appliances with semi-custom bases |
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| CN102930091A (en) * | 2012-10-24 | 2013-02-13 | 浙江大学 | Tooth-and-gum-oriented high-efficiency mesh repairing method |
| CN108024841A (en) * | 2015-10-07 | 2018-05-11 | 友莱博系统公司 | Tooth modeling |
| CN112155762A (en) * | 2020-09-30 | 2021-01-01 | 深圳云甲科技有限公司 | Novel computer-assisted removal method for undercut of dental crown preparation |
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