CN117197395B

CN117197395B - Curve triangulation method and device, storage medium and computer equipment

Info

Publication number: CN117197395B
Application number: CN202311444042.XA
Authority: CN
Inventors: 史立松; 陈曦
Original assignee: Zwcad Software Co ltd
Current assignee: Zwcad Software Co ltd
Priority date: 2023-11-02
Filing date: 2023-11-02
Publication date: 2024-03-01
Anticipated expiration: 2043-11-02
Also published as: CN117197395A

Abstract

According to the curved surface triangulation method, the curved surface triangulation device, the storage medium and the computer equipment, when the curved surface to be subdivided is subjected to triangulation, the sampling point set and the auxiliary triangle of the curved surface to be subdivided can be determined first, triangular grids are triangulated by sequentially utilizing all sampling points in the sampling point set, the final triangulated grids are obtained, and finally, the final triangulated grids can be subjected to boundary adjustment according to the boundary line and the shape characteristics of the curved surface to be subdivided, so that the triangulated grids are obtained. And when each sampling point is inserted, the dividing direction of the triangle related to the grid and the sampling point can be adjusted according to the energy field of the sampling point in the corresponding area of the auxiliary triangle, and the auxiliary triangle is updated, and the energy field can measure the change trends of the curved surface to be split in different directions on the area of the sampling point, so that the local geometric characteristics of the curved surface to be split are reflected, and therefore, the triangular mesh can be more attached to the curved surface to be split.

Description

Curve triangulation method and device, storage medium and computer equipment

Technical Field

The present disclosure relates to the field of graphics technologies, and in particular, to a surface triangulation method, apparatus, storage medium, and computer device.

Background

Triangulation is a key technology in surface expression, and the triangulation takes a surface equation and a sampling point set of a surface in a parameter plane as a data basis, so that the purpose of obtaining a grid fitting surface is good, a displayed triangular grid is served, and the adopted triangular grid data has the advantages of simple structure, excellent geometric shape description capability on complex topology, mature related algorithm and the like, so that the triangulation plays an important role in the fields of computer aided design, computer vision, finite element analysis, geographic information systems, scientific visualization and the like.

For such triangle mesh data, the basic requirement is to attach the original curved surface as much as possible without changing the topological structure of the curved surface, and the higher the degree of attaching the original curved surface is, the better the triangle mesh quality is. For any point on the free-form surface, the change trend of the surface in different directions is different, namely, the free-form surface has the change trend in different areas and in different directions, however, the existing triangulation method ignores the geometric characteristics of the surface in the three-dimensional space, and the expression effect on the free-form surface is poor.

Disclosure of Invention

The purpose of the present application is to solve at least one of the above technical drawbacks, and in particular, the triangulation method in the prior art ignores the geometric feature of the curved surface in the three-dimensional space, and has a poor effect on expressing the free curved surface.

The application provides a surface triangulation method, which comprises the following steps:

determining a sampling point set of a curved surface to be split and an auxiliary triangle;

selecting any sampling point in the sampling point set as a starting point, inserting the starting point into the auxiliary triangle, triangulating the auxiliary triangle by using the starting point to form an initial triangulating grid, and deleting the starting point in the sampling point set;

selecting any sampling point in the sampling point set as a current sampling point, inserting the current sampling point into the initial triangularization grid, and adjusting the division direction of a triangle related to the current sampling point in the initial triangularization grid according to the energy field of the current sampling point in a corresponding area in the initial triangularization grid;

updating the initial triangulated mesh according to the adjustment result, deleting the current sampling points in the sampling point set, and returning to execute any sampling point in the sampling point set to be selected as the current sampling point and the subsequent steps until all sampling points in the sampling point set are inserted, so as to obtain a final triangulated mesh;

And carrying out boundary adjustment on the final triangulated mesh according to the boundary line and the shape characteristic of the curved surface to be split to obtain the triangulated mesh of the curved surface to be split.

Optionally, triangulating the auxiliary triangle with the starting point to form an initial triangulated mesh, including:

and determining three vertexes of the auxiliary triangle, and connecting the starting points with the vertexes respectively to form an initial triangularized grid.

Optionally, the adjusting the dividing direction of the triangle related to the current sampling point in the initial triangle mesh according to the energy field of the current sampling point in the initial triangle mesh includes:

selecting a triangle where the current sampling point is located from the initial triangle mesh as a triangle to which the current sampling point belongs;

connecting the current sampling point with each vertex of the triangle to which the current sampling point belongs respectively, and determining a quadrangle corresponding to the current sampling point according to a connection result;

and constructing a local energy field of the quadrangle, and adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulated mesh according to the local energy field.

Optionally, the determining, according to the connection result, the quadrilateral corresponding to the current sampling point includes:

regarding each side of the triangle to which the current sampling point belongs, taking the side as a suspected side of the current sampling point, and judging whether opposite vertexes exist on the other side of the suspected side of the current sampling point;

if yes, connecting the current sampling point, the opposite vertex and the two vertexes of the suspected side to obtain a quadrilateral corresponding to the sampling point, and judging whether the quadrilateral is a convex quadrilateral;

if yes, taking the quadrangle as the quadrangle corresponding to the suspected side;

if the current sampling point does not have an opposite vertex on the other side of the suspected edge or the quadrangle is not a convex quadrangle, the quadrangle of the suspected edge is not required to be determined.

Optionally, the adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulating grid according to the local energy field includes:

calculating energy coordinates of each vertex of the quadrangle according to the local energy field of the quadrangle, wherein the energy coordinates of each vertex of the quadrangle comprise the energy coordinates of the current sampling point, the opposite vertex and the two vertexes of the suspected side;

Constructing a corresponding circumscribed circle based on the current sampling point and the energy coordinates of the two vertexes of the suspected edge, and judging whether the energy coordinates of the opposite vertexes are in the circumscribed circle or not;

if yes, removing the suspected edges, connecting the current sampling point with the opposite vertex, taking a connecting line between the opposite vertex and the two vertexes of the removed suspected edges as a new suspected edge, taking the opposite vertex as the current sampling point, and returning to execute the step of judging whether the opposite vertex exists at the other side of the suspected edge or not by the current sampling point for each suspected edge;

if not, the dividing direction of the related triangle in the quadrangle is not adjusted.

Optionally, said constructing the quadrilateral local energy field includes:

acquiring curvature measurement and linear velocity measurement of each vertex in the quadrangle;

and determining the vertex energy of each vertex according to the curvature measure and the linear velocity measure of each vertex, and constructing the local energy field of the quadrangle by utilizing the vertex energy.

Optionally, the performing boundary adjustment on the final triangulated mesh according to the boundary line and the shape feature of the surface to be dissected to obtain the triangulated mesh of the surface to be dissected, including:

Determining a plurality of triangles which are intersected with the boundary line of the curved surface to be split in the final triangulated mesh to form a polygon corresponding to the boundary line;

dividing the polygon into two sub-polygons by utilizing the boundary line, re-triangulating the two sub-polygons respectively, and taking the final triangulated mesh after re-triangulating as an initial subdivision mesh of the curved surface to be triangulated;

and determining a feasible domain and a non-feasible domain in the initial mesh according to the shape characteristics of the surface to be split, and removing triangles in the non-feasible domain to obtain the triangular mesh of the surface to be split.

The application also provides a surface triangulation device, comprising:

the triangle construction module is used for determining a sampling point set of the curved surface to be split and an auxiliary triangle;

the grid dividing module is used for selecting any sampling point in the sampling point set as a starting point, inserting the starting point into the auxiliary triangle, triangulating the auxiliary triangle by using the starting point to form an initial triangulating grid, and deleting the starting point in the sampling point set;

the dividing direction adjusting module is used for selecting any sampling point in the sampling point set as a current sampling point, inserting the current sampling point into the initial triangularization grid, and adjusting the dividing direction of a triangle related to the current sampling point in the initial triangularization grid according to the energy field of the corresponding region of the current sampling point in the initial triangularization grid;

The sampling point inserting module is used for updating the initial triangulated mesh according to the adjustment result, deleting the current sampling point in the sampling point set, and returning to execute any sampling point in the sampling point set as the current sampling point and the subsequent steps until all sampling points in the sampling point set are inserted, so as to obtain a final triangulated mesh;

and the grid boundary adjusting module is used for carrying out boundary adjustment on the final triangulated grid according to the boundary line and the shape characteristic of the curved surface to be split to obtain the triangulated grid of the curved surface to be split.

The present application also provides a storage medium having stored therein computer readable instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of the surface triangulation method according to any of the embodiments above.

The present application also provides a computer device comprising: one or more processors, and memory;

the memory has stored therein computer readable instructions which, when executed by the one or more processors, perform the steps of the surface triangulation method as set forth in any of the above embodiments.

From the above technical solutions, the embodiments of the present application have the following advantages:

according to the curved surface triangulation method, the curved surface triangulation device, the storage medium and the computer equipment, when the curved surface to be subdivided is subjected to triangulation, a sampling point set and an auxiliary triangle of the curved surface to be subdivided can be determined firstly and used as triangular mesh data of the curved surface to be subdivided, any sampling point in the sampling point set can be selected as a starting point, triangular meshes are triangulated by using the starting point to form initial triangular meshes, sampling points except the starting point in the sampling point set are sequentially inserted into the initial triangular meshes to be triangulated until the last sampling point is inserted, and the final triangular meshes of the triangular meshes are obtained, so that the triangular meshes with different scales and shapes can be triangulated gradually, and the curved surface triangulation method has high expandability; and finally, carrying out boundary adjustment on the final triangulated mesh according to the boundary line and the shape characteristics of the curved surface to be split to obtain the triangulated mesh of the curved surface to be split. When each sampling point except the starting point is sequentially inserted into the initial triangular mesh, the method can adjust the dividing direction of triangles related to the sampling points in the initial triangular mesh according to the energy field of the corresponding area of the sampling point in the initial triangular mesh, update the initial triangular mesh according to the adjustment result, measure the changing trend of the to-be-split curved surface in different directions on the area of the sampling point by the energy field, and reflect the local geometric characteristics of the to-be-split curved surface.

Drawings

In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive faculty for a person skilled in the art.

Fig. 1 is a schematic flow chart of a surface triangulation method according to an embodiment of the present application;

fig. 2 is a schematic structural diagram of an energy coordinate corresponding to a circumscribed circle according to an embodiment of the present application;

fig. 3 is a schematic structural diagram of a polygon corresponding to a boundary line according to an embodiment of the present application;

FIG. 4 is a schematic structural diagram of a feasible region and a non-feasible region in an initial subdivision grid according to an embodiment of the present application;

fig. 5 is a schematic structural diagram of a surface triangulation device according to an embodiment of the present application;

fig. 6 is a schematic diagram of an internal structure of a computer device according to an embodiment of the present application.

Detailed Description

The following description of the embodiments of the present application will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.

Based on this, the following technical solutions are proposed in the present application, see in particular below:

In one embodiment, as shown in fig. 1, fig. 1 is a schematic flow chart of a surface triangulation method provided in an embodiment of the present application; the application also provides a surface triangulation method, which specifically comprises the following steps:

s110: and determining a sampling point set of the curved surface to be split and an auxiliary triangle.

In this step, in order to facilitate calculation and analysis of the free-form surface, the free-form surface may be triangulated first, i.e., divided into a plurality of small triangles. The free-form surface to be triangulated can be used as the surface to be triangulated, and the sampling point set and the auxiliary triangle of the surface to be triangulated can be determined to be the triangulated data of the surface to be triangulated.

The sampling points are key points selected from the curved surface to be split and are used for discretizing the curved surface to be split so as to calculate the properties and characteristics of the curved surface to be split. The auxiliary triangle can ensure that all sampling points in the curved surface to be split are in the auxiliary triangle, so that the situation that some sampling points are not covered is avoided, and the triangulation accuracy of the curved surface to be split is lower.

Specifically, when determining the sampling points of the curved surface to be split, the sampling density of the curved surface to be split, that is, the number of the points sampled on the curved surface to be split, may be determined first, then a corresponding sampling method, such as a method of uniform sampling, adaptive sampling or curvature-based sampling, may be selected according to the shape and characteristics of the curved surface to be split, after determining the number of the sampling points and the sampling method, the sampling points may be generated by using a sampling tool, and the sampling points may be generated in a uniform sampling manner, thereby avoiding the sampling points from being too dense or too sparse, and ensuring the accuracy and efficiency of the subsequent triangulation.

It should be noted that, the determination of the sampling density needs to consider the balance between the accuracy and the efficiency of triangulation, and here, the application may determine the optimal sampling density in advance through experiments and adjustments. In addition, by selecting a proper sampling method, the accuracy and efficiency of the subsequent triangulation can be improved, for example, for a free-form surface with a regular shape, uniform sampling can be selected; for a free-form surface with a relatively complex shape, adaptive sampling can be selected, and the mode refers to adaptive adjustment of sampling density according to local curvature change of the surface; for curved surfaces with relatively severe curvature changes, a curvature-based sampling method can be selected, wherein the method is to determine the position and density of sampling points by calculating the curvature size and direction of each point on the curved surface. The application herein does not limit the sampling manner of the triangle to be split.

S120: selecting any sampling point in the sampling point set as a starting point, inserting the starting point into the auxiliary triangle, triangulating the auxiliary triangle by using the starting point to form an initial triangulating grid, and deleting the starting point in the sampling point set.

In this step, after determining the sampling point set and the auxiliary triangle of the curved surface to be split through step S110, any one sampling point may be selected from the sampling point set as a starting point, that is, the first sampling point to insert the auxiliary triangle for performing triangle division may be used to perform triangle division on the auxiliary triangle to obtain an initial triangle mesh, and after the insertion of the starting point is completed, the starting point in the sampling point set may be deleted.

It can be understood that the auxiliary triangle is an initial state before triangulating the surface to be triangulated, and is a basis for subsequent triangulating, so that after the auxiliary triangle of the surface to be triangulated is obtained, a starting point of triangulating can be determined first as a sampling point for triangulating the auxiliary triangle, and then the starting point can be used for triangulating the auxiliary triangle into a plurality of small triangles to form an initial triangulating grid, so that the initial triangulating grid is used as a basis for triangulating the next inserted sampling point.

S130: selecting any sampling point in the sampling point set as a current sampling point, inserting the current sampling point into the initial triangularization grid, and adjusting the division direction of triangles related to the current sampling point in the initial triangularization grid according to the energy field of the corresponding region of the current sampling point in the initial triangularization grid.

In this step, after the initial triangle mesh is obtained in step S120, any sampling point in the sampling point set may be selected as the current sampling point, and the current sampling point is inserted into the initial triangle mesh, then an energy field of a corresponding area of the current sampling point in the initial triangle mesh may be determined, and the dividing direction of the triangle related to the current sampling point in the initial triangle mesh may be adjusted according to the energy field.

It can be understood that the sampling points in the sampling point set can be inserted by adopting a random increment method, wherein the random increment method refers to that each sampling point in the sampling point set is randomly and randomly disturbed, then the sampling points are inserted one by one, and the relevant area is triangulated after each time one sampling point is inserted until all the points are inserted. Therefore, when the sampling point is inserted, any sampling point in the sampling point set can be selected as the current sampling point for insertion.

In addition, after the current sampling point is inserted into the initial triangular mesh, the energy field of the current sampling point in the initial triangular mesh can be calculated, so that the initial triangular mesh can be locally adjusted according to the energy field, namely, the dividing direction of triangles related to the current sampling point in the initial triangular mesh is adjusted, and the adjusted dividing direction can be more attached to the change trend of the curved surface to be split.

It should be noted that, the energy field in the present application may measure the magnitude of the trend of the change in the two parameter directions in the corresponding area of the curved surface to be split, so as to reflect the local geometric feature of the curved surface to be split. Because span in the direction that the trend of change is violent in the great parameter range, wait to split the curved surface and will accumulate great variation amplitude here for triangle-shaped "with flat bending" deviation degree greatly increased, lead to triangularization net unable and wait to split the curved surface fully laminating, consequently, this application can combine the energy field size to adjust the division direction of the triangle-shaped that is relevant to the current sampling point, thereby avoid the triangle-shaped net that relevant triangle-shaped is big in the parameter direction span to lead to not enough laminating wait to split the curved surface the condition that appears in the direction that the trend is violent.

S140: and updating the initial triangulated mesh according to the adjustment result, deleting the current sampling point in the sampling point set, and returning to execute any sampling point in the sampling point set as the current sampling point and the subsequent steps until all sampling points in the sampling point set are inserted, thereby obtaining the final triangulated mesh.

In this step, after the initial triangle mesh is locally adjusted in step S130, the initial triangle mesh may be updated according to the adjustment result, and the current sampling point in the sampling point set may be deleted, so as to complete the insertion of the current sampling point, then any sampling point may be continuously selected from the sampling point set as a new current sampling point, so as to complete the process of inserting the current sampling point, and after all sampling points in the sampling point set have been inserted, the initial triangle mesh that has been updated last time may be used as the final triangle mesh.

It can be understood that after the initial triangulated mesh is updated by using the current sampling point, the updated initial triangulated mesh is required to be used as the basis of triangulation of the next inserted sampling point, so that the method can be used for sampling, the initial triangulated mesh is enabled to continuously recalculate and update related triangles along with the insertion of the sampling point until all sampling points in the sampling point set are inserted, and the final triangulated mesh is obtained.

S150: and carrying out boundary adjustment on the final triangulated mesh according to the boundary line and the shape characteristic of the curved surface to be dissected to obtain the triangulated mesh of the curved surface to be dissected.

In this step, after the final triangulated mesh is obtained in step S140, boundary lines and shape features of the curved surface to be split can be obtained, wherein the final triangulated mesh is subjected to boundary adjustment according to the boundary lines of the curved surface to be split, so that triangles with partial range exceeding the curved surface to be split in the final triangulated mesh can be avoided, and the final triangulated mesh is subjected to boundary adjustment according to the shape features of the curved surface to be split, so that only triangles in the area range of the curved surface to be split in the final triangulated mesh can be reserved, and the triangulated mesh of the curved surface to be split is obtained.

It can be understood that the final triangulated mesh is obtained by triangulating the auxiliary triangle of the surface to be triangulated, and the coverage area of the final triangulated mesh is larger than the area of the surface to be triangulated, so that after the final triangulated mesh is obtained, the final triangulated mesh needs to be subjected to boundary adjustment according to the boundary line and the shape characteristic of the surface to be triangulated, and the triangulated mesh of the surface to be triangulated is obtained. The boundary line is an important feature of the surface to be split, and the accuracy of the boundary line is important for subsequent calculation and analysis of the surface to be split, so that the triangular mesh of the surface to be split can be obtained by readjusting the dividing regions of the unreasonable triangles of the final triangular mesh according to the boundary line of the surface to be split to ensure the accuracy of the boundary line of the surface to be split, and further retaining the triangles in the region range of the surface to be split in the final triangular mesh according to the boundary line and the shape feature of the surface to be split.

In the above embodiment, when the surface to be split is triangulated, the sampling point set and the auxiliary triangle of the surface to be split can be determined first, and then any one sampling point in the sampling point set can be selected as a starting point, and the triangle mesh is triangulated by using the starting point to form an initial triangulated mesh, and then sampling points except the starting point in the sampling point set are sequentially inserted into the initial triangulated mesh to triangulate until the last sampling point is inserted, so as to obtain the final triangulated mesh of the triangle mesh, thereby realizing the gradual triangulating of meshes with different scales and shapes, and having stronger expandability; and finally, carrying out boundary adjustment on the final triangulated mesh according to the boundary line and the shape characteristics of the curved surface to be split to obtain the triangulated mesh of the curved surface to be split. When each sampling point except the starting point is sequentially inserted into the initial triangular mesh, the method can adjust the dividing direction of triangles related to the sampling points in the initial triangular mesh according to the energy field of the corresponding area of the sampling point in the initial triangular mesh, update the initial triangular mesh according to the adjustment result, measure the changing trend of the to-be-split curved surface in different directions on the area of the sampling point by the energy field, and reflect the local geometric characteristics of the to-be-split curved surface.

In one embodiment, triangulating the auxiliary triangle with the starting point in step S120 to form an initial triangulated mesh may include:

s121: and determining three vertexes of the auxiliary triangle, and connecting the starting points with the vertexes respectively to form an initial triangularization grid.

In this embodiment, when the starting point is used to triangulate the auxiliary triangle, the three vertices of the auxiliary triangle may be determined, and since the starting point is inside the auxiliary triangle, the starting point may be directly connected to each vertex, so as to partition the auxiliary triangle into three small triangles, and form an initial triangulated mesh by using the triangles.

In one embodiment, in step S130, adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulated mesh according to the energy field of the corresponding region of the current sampling point in the initial triangulated mesh may include:

s131: and selecting the triangle where the current sampling point is located from the initial triangulated mesh as the triangle to which the current sampling point belongs.

S132: and respectively connecting the current sampling point with each vertex of the triangle to which the current sampling point belongs, and determining a quadrangle corresponding to the current sampling point according to the connection result.

S133: and constructing a quadrilateral local energy field, and adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulated mesh according to the local energy field.

In this embodiment, when adjusting the dividing direction of the triangle related to the current sampling point in the initial triangle mesh, firstly, the triangle where the current sampling point is located may be selected in the initial triangle mesh as the triangle to which the current sampling point belongs, then the current sampling point may be connected with each vertex of the triangle to which the current sampling point belongs, and the quadrangle corresponding to the current sampling point is determined according to the connection result, so as to construct a local energy field of the quadrangle, and adjust the dividing direction of the triangle related to the current sampling point in the initial triangle mesh according to the local energy field.

It can be understood that after other sampling points except the starting point are inserted into the sampling point set, local adjustment is needed to be performed on the initial triangulated mesh according to the inserted sampling points, and in order to improve the accuracy and efficiency of local adjustment of the initial triangulated mesh, the application can select the smallest triangle where the current sampling point is located as the triangle to which the current sampling point belongs, and further perform small-range adjustment on the initial triangulated mesh.

Specifically, after the triangle to which the current sampling point belongs is divided by using the current sampling point, the dividing direction of the relevant triangle of the current sampling point can be further adjusted, so that the dividing direction of the relevant triangle of the current sampling point can be more attached to the curvature change of the relevant position of the curved surface to be split. In the process, a quadrangle corresponding to the current sampling point can be determined according to the dividing result of the affiliated triangle, the quadrangle is mainly obtained by combining any one small triangle in the affiliated triangle with the small triangle adjacent to the small triangle outside the affiliated triangle, after the quadrangle corresponding to the current sampling point is obtained, a local energy field of the quadrangle can be constructed, and the local geometric characteristic of the quadrangle at the corresponding position in the curved surface to be divided can be represented through the local energy field.

Further, if the current sampling point is inserted into the initial triangle mesh, the insertion position of the current sampling point is just located on the edge of any triangle in the initial triangle mesh, at least one small triangle with the edge of the current sampling point as the bottom edge and the vertex of the small triangle in the initial triangle can be determined, and finally the current sampling point can be respectively connected with each vertex, so that the adjustment process of the current sampling point on the dividing direction of the triangle related to the current sampling point in the initial triangle mesh is realized. Still further, if the current sampling point overlaps with other already inserted sampling points, the step of adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulated mesh using the current sampling point may be skipped.

In one embodiment, determining, in step S132, the quadrangle corresponding to the current sampling point according to the connection result may include:

s321: regarding each side of the triangle, taking the side as a suspected side of the current sampling point, and judging whether the current sampling point has opposite vertexes on the other side of the suspected side; if yes, go to step S322, if no, go to step S324.

S322: connecting the current sampling point, the opposite vertex and the two vertexes of the suspected side to obtain a quadrangle corresponding to the sampling point, and judging whether the quadrangle is a convex quadrangle or not; if yes, go to step S323, otherwise, go to step S324.

S323: and taking the quadrangle as the quadrangle corresponding to the suspected side. S324: the quadrangle of the suspected edge need not be determined.

In this embodiment, when determining the quadrangle corresponding to the current sampling point, each side of the triangle may be used as a suspicious side, and for each suspicious side, if the opposite vertex of the current sampling point exists on the other side of the suspicious side, the current sampling point, the opposite vertex and the two vertices of the suspicious side are connected to obtain the quadrangle corresponding to the sampling point; then, it can be further determined whether the quadrangle is a convex quadrangle, if the quadrangle is not a convex quadrangle, or if no opposite vertex of the current sampling point exists on the other side of the suspected side, it is indicated that the suspected side does not have a convex quadrangle, so that the quadrangle of the current sampling point on the suspected side is not constructed.

Specifically, in the present application, the opposite vertex refers to a vertex of a triangle with the suspected side as a base outside the affiliated triangle, when judging whether the opposite vertex exists at the other side of the suspected side at the current sampling point, the triangle with the current sampling point as a vertex and the suspected side as a base in the affiliated triangle may be determined first, then whether the triangle with the suspected side as a base exists outside the affiliated triangle may be judged, if so, the vertex of the triangle outside the affiliated triangle is taken as the opposite vertex of the current sampling point, and further, two triangles with the suspected side as a base may be combined to obtain a quadrangle with the current sampling point on the suspected side; if not, then there is no need to construct a quadrilateral with the current sample point on the suspect edge.

In general, when the suspicious edge of the current sampling point is the side length of the auxiliary triangle of the surface to be split, the current sampling point does not have a corresponding quadrangle at the suspicious edge, whereas when the suspicious edge of the current sampling point is not the side of the auxiliary triangle of the surface to be split, the current sampling point has a corresponding quadrangle at the suspicious edge.

In one embodiment, the adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulating mesh according to the local energy field in step S133 may include:

S331: and calculating the energy coordinates of each vertex of the quadrangle according to the local energy field of the quadrangle.

S332: constructing a corresponding circumscribed circle based on the current sampling point and the energy coordinates of the two vertexes of the suspected edge, and judging whether the energy coordinates of the opposite vertexes are in the circumscribed circle or not; if yes, step S333 is executed, and if no, step S334 is executed.

S333: removing the suspected edges, connecting the current sampling point and the opposite vertex, taking the connecting line between the opposite vertex and the two vertexes of the removed suspected edges as a new suspected edge, taking the opposite vertex as the current sampling point, and for each suspected edge, returning to execute the step of judging whether the opposite vertex exists at the current sampling point on the other side of the suspected edge.

S334: the dividing direction of the relevant triangle in the quadrangle is not adjusted.

In this embodiment, when adjusting the dividing direction of the triangle related to the current sampling point in the initial triangle mesh, the energy coordinates of each vertex of the quadrilateral may be obtained by calculating according to the local energy field of the quadrilateral, where each vertex of the quadrilateral includes the current sampling point, the opposite vertex and two vertices of the suspicious edge; the method and the device can construct a corresponding circumcircle based on the current sampling point and the energy coordinates of the two vertexes of the suspected edge, if the energy coordinates of the opposite vertexes are in the circumcircle, the dividing direction of the triangle related to the quadrangle needs to be adjusted, and if the energy coordinates of the opposite vertexes are not in the circumcircle, the dividing direction of the triangle related to the current sampling point does not need to be adjusted.

Specifically, in the process of adjusting the dividing direction of the triangle related to the quadrangle, the suspicious edge corresponding to the quadrangle may be removed, the current sampling point and the opposite vertex may be connected, then a connecting line between the opposite vertex and the two vertexes of the removed suspicious edge may be used as a new suspicious edge, the opposite vertex may be used as the current sampling point, and the dividing direction of the triangle related to the quadrangle corresponding to the current sampling point may be continuously adjusted for each suspicious edge until the dividing directions of the triangles related to the quadrangle corresponding to all suspicious edges are adjusted.

Schematically, as shown in fig. 2, fig. 2 is a schematic structural diagram of an energy coordinate corresponding to a circumscribed circle according to an embodiment of the present application; in FIG. 2, a quadrilateralIs to->For suspicious edges, in->For the current sampling point, in +.>The two directions of the local energy field of the quadrangle are v and u respectively, and the energy coordinates of four vertexes of the quadrangle can be calculated under the local energy field, which are respectively +.>、/>、/>、/>. The energy coordinates of the quadrangle are calculated>、/>、/>And->After that, can be based on +.>、/>And->Constructing a corresponding circumscribed circle and determining the energy coordinates of opposite vertices of the quadrangle +. >Whether the square is in the circumscribed circle, if so, the current quadrangle is described as +.>The direction change trend is smaller in the internal connection mode, and the change trend of the other direction needs to be more focused at the moment, so that the quadrangle needs to be changed>The internal connection mode; if, as shown in FIG. 2, the energy coordinates of the opposite vertices are +.>Is not in the circumscribing circle, the quadrilateral ++is not required to be changed>Internal connection mode.

Further, in FIG. 2, in calculating the quadrangleFour of (4)When the energy coordinates of the vertices are defined, the energy coordinates can be defined by utilizing the local energy field of the quadrangle, and the specific definition is as follows:

；

in the method, in the process of the invention,represents the energy coordinates, wherein ∈>Representing vertex at +.>Value in direction, +_>Representing vertex at +.>Values in the direction; />Representing the local energy field of the quadrilateral.

Quadrangle calculated from the aboveEnergy coordinate of>、/>、/>、/>The method can be used for measuring the geometric variation amplitude of the corresponding area of the curved surface to be split in the three-dimensional space instead of the variation on the parameter plane, so that the method can utilize the quadrilateral local energy fieldThe connection mode inside the quadrangle is adjusted, so that the adjusted quadrangle is more attached to the curved surface to be split.

In one embodiment, constructing the quadrilateral local energy field in step S133 may include:

S335: and obtaining the curvature measure and the linear velocity measure of each vertex in the quadrangle.

S336: and determining the vertex energy of each vertex according to the curvature measure and the linear velocity measure of each vertex, and constructing a quadrilateral local energy field by utilizing the vertex energy.

In this embodiment, when constructing the local energy field of the quadrangle, the curvature measure and the linear velocity measure of each vertex in the quadrangle may be obtained first, so that the vertex energy of each vertex may be obtained by calculation according to the curvature measure and the linear velocity measure of each vertex, and finally, the local energy field of the quadrangle may be constructed by using each vertex energy.

It is to be understood that the vertex energy of the present application includes the vertex at、/>Energy in two parameter directionsAnd->Here, the energy characterizes the magnitude of the curvature change trend of the apex in the direction of the parameter.

In a specific embodiment, the vertex energy of each vertex of the quadrilateral is defined specifically as follows:

；

in the method, in the process of the invention,representing the curve to be splitVertex in face +.>Curvature measure in direction; />Representing that the vertex in the surface to be split is +.>Curvature measure in direction; />Representing that the vertex in the surface to be split is +.>Measuring linear velocity in the direction; / >Representing that the vertex in the surface to be split is +.>Linear velocity in direction.

After the vertex energy of each vertex of the quadrangle is obtained through the calculation, the local energy field of the quadrangle can be constructed by utilizing the vertex energyThe specific process is as follows:

；

in the method, in the process of the invention,representing local energy fieldsAt->The energy magnitude of the direction; />Representing the local energy field at +.>The energy magnitude of the direction; />Representation->Direction variable->Representation->A variable of direction; />Representation->Coordinate mean of direction,/->Representation->A coordinate mean value of the direction; />、/>、/>And->Respectively represent that the energy of four vertexes is +.>The energy magnitude of the direction; />、/>、/>And->Respectively represent that the energy of four vertexes is +.>The energy magnitude in the direction.

It should be noted that the number of the substrates,and->The +.A. in the area corresponding to the curved surface to be split in the quadrangle is measured>、/>The intensity of the direction change trend of the two parameters. The smaller the value, the smaller the geometric variation trend in the corresponding direction, whereas the larger the value, the larger the geometric variation trend in the corresponding direction. That is, even if the deviation in the parameter plane is +.>Larger, but ifExtremely small, at this point +.>Energy accumulated in the direction and +.>Is still small, i.e. in three dimensions in this +.>The geometric variation in direction is small in magnitude. In practice, to avoid directional energy +. >Or->If the problem is 0, a minimum threshold value greater than zero can be set>If->，/>Less than->Then put it as +.>：

；

；/>

In one embodiment, in step S150, performing boundary adjustment on the final triangulated mesh according to the boundary line and the shape feature of the surface to be dissected to obtain the triangulated mesh of the surface to be dissected may include:

s151: and determining a plurality of triangles which are intersected with the boundary line of the curved surface to be split in the final triangulated mesh to form a polygon corresponding to the boundary line.

S152: dividing the polygon into two sub-polygons by utilizing the boundary line, re-triangulating the two sub-polygons respectively, and taking the final triangulated mesh after re-triangulating as an initial triangulated mesh of the curved surface to be triangulated.

S153: and determining a feasible domain and a non-feasible domain in the initial mesh according to the shape characteristics of the surface to be split, and removing triangles in the non-feasible domain to obtain the triangular mesh of the surface to be split.

In this embodiment, when the final triangulated mesh is subjected to boundary adjustment, each boundary line in the curved surface to be split may be determined first, a plurality of triangles intersecting with the boundary line of the curved surface to be split in the final triangulated mesh may be determined for each boundary line, polygons corresponding to the boundary lines may be formed according to the triangles, then the polygons may be divided into two sub-polygons by using the boundary lines, triangulating may be performed on the two sub-polygons respectively, until the triangulating is completed again for the polygons corresponding to each boundary line, the final triangulated mesh after the re-triangulating is used as the initial triangulated mesh of the curved surface to be split, finally, a feasible region and an infeasible region in the initial triangulated mesh may be determined according to the shape characteristics of the curved surface to be split, and the triangles in the infeasible region may be removed, thereby obtaining the triangulated mesh of the curved surface to be split.

It is to be understood that the feasible region herein refers to the area range of the initial subdivision grid that belongs to the surface to be subdivided, and the non-feasible region refers to the area range of the initial subdivision grid that does not belong to the surface to be subdivided. According to the method and the device, the feasible region and the infeasible region in the initial subdivision grid can be divided according to the shape characteristics of the curved surface to be subdivided, and then triangles in the infeasible region inside the initial subdivision grid can be removed, so that the triangulated grid of the curved surface to be subdivided is obtained.

Schematically, as shown in fig. 3 and fig. 4, fig. 3 is a schematic structural diagram of a polygon corresponding to a boundary line according to an embodiment of the present application; FIG. 4 is a schematic structural diagram of a feasible region and a non-feasible region in an initial subdivision grid according to an embodiment of the present application; in FIG. 3, for any one boundary of the surface to be splitWire (C)All triangles intersecting it can be found from the initial subdivision grid +.>The peripheries of these triangles can then be connected to form a polygon for which +.>It can be divided into two sub-polygons +.>And->Local triangulation can be performed on QL and QR, respectively, to obtain a mesh of mesh with boundary lines preserved. After the re-subdivision of the polygons corresponding to all the boundary lines is finished, an initial subdivision grid of the curved surface to be subdivided can be obtained, then the feasible region and the non-feasible region in the initial subdivision grid can be determined according to the shape characteristics of the curved surface to be subdivided, as shown in fig. 4, the peripheral triangle represents the initial subdivision grid, the black region represents the feasible region in the initial subdivision grid, the white region represents the non-feasible region in the initial subdivision grid, when the boundary adjustment is carried out on the initial subdivision grid, the non-feasible region of the white region in the initial subdivision grid can be removed, and only the feasible region in the black region is reserved, so that the triangular subdivision grid of the curved surface to be subdivided is output after the triangular subdivision grid of the curved surface to be subdivided is generated.

The surface triangulation device provided in the embodiment of the present application is described below, and the surface triangulation device described below and the surface triangulation method described above may be referred to correspondingly.

In one embodiment, as shown in fig. 5, fig. 5 is a schematic structural diagram of a curved surface triangulation device according to an embodiment of the present application; the application provides a surface triangulation device, which comprises a triangle construction module 210, a grid division module 220, a division direction adjustment module 230, a sampling point insertion module 240 and a grid boundary adjustment module 250, and specifically comprises the following steps:

the triangle construction module 210 is configured to determine a set of sampling points of the surface to be split and an auxiliary triangle.

The grid dividing module 220 is configured to select any one of the sampling points in the sampling point set as a starting point, insert the starting point into the auxiliary triangle, triangulate the auxiliary triangle with the starting point to form an initial triangulated grid, and delete the starting point in the sampling point set.

The partition direction adjustment module 230 is configured to select any one of the sampling points in the sampling point set as a current sampling point, insert the current sampling point into the initial triangle mesh, and adjust a partition direction of a triangle related to the current sampling point in the initial triangle mesh according to an energy field of a corresponding region of the current sampling point in the initial triangle mesh.

The sampling point inserting module 240 is configured to update the initial triangulated mesh according to the adjustment result, delete the current sampling point in the sampling point set, and then return to perform any sampling point in the sampling point set as the current sampling point and the subsequent steps until all sampling points in the sampling point set are completely inserted, thereby obtaining the final triangulated mesh.

And the grid boundary adjustment module 250 is used for carrying out boundary adjustment on the final triangulated grid according to the boundary line and the shape characteristic of the curved surface to be split to obtain the triangulated grid of the curved surface to be split.

In one embodiment, the meshing module 220 may include:

and the vertex connection sub-module is used for determining three vertices of the auxiliary triangle, and connecting the starting points with the vertices respectively to form an initial triangle mesh.

In one embodiment, the division direction adjustment module 230 may include:

the triangle selecting sub-module is used for selecting the triangle where the current sampling point is located from the initial triangle mesh as the triangle where the current sampling point belongs.

And the quadrangle determining submodule is used for respectively connecting the current sampling point with each vertex of the triangle to which the current sampling point belongs and determining the quadrangle corresponding to the current sampling point according to the connection result.

The dividing direction adjusting sub-module is used for constructing a quadrilateral local energy field and adjusting the dividing direction of the triangle related to the current sampling point in the initial triangulated grid according to the local energy field.

In one embodiment, the quadrilateral determination submodule may include:

and the opposite vertex judging unit is used for regarding each side of the triangle to which the opposite vertex judging unit belongs as the suspicious side of the current sampling point and judging whether the opposite vertex exists at the other side of the suspicious side of the current sampling point.

And the quadrilateral judging unit is used for connecting the current sampling point, the opposite vertex and the two vertexes of the suspected side to obtain a quadrilateral corresponding to the sampling point and judging whether the quadrilateral is a convex quadrilateral or not.

In one embodiment, the partition direction adjustment sub-module may include:

and the energy coordinate calculation unit is used for calculating the energy coordinates of each vertex of the quadrangle according to the local energy field of the quadrangle.

And the circumscribed circle construction unit is used for constructing a corresponding circumscribed circle based on the current sampling point and the energy coordinates of the two vertexes of the suspected edge and judging whether the energy coordinates of the opposite vertexes are in the circumscribed circle or not.

And a suspicious edge adjusting unit for removing the suspicious edge, connecting the current sampling point and the opposite vertex, taking the connecting line between the opposite vertex and the two vertexes of the removed suspicious edge as a new suspicious edge, taking the opposite vertex as the current sampling point, and for each suspicious edge, returning to execute the step of judging whether the opposite vertex exists at the current sampling point at the other side of the suspicious edge.

In one embodiment, the division direction adjustment sub-module may further include:

and the vertex data acquisition unit is used for acquiring the curvature measure and the linear velocity measure of each vertex in the quadrangle.

And the energy field construction unit is used for determining the vertex energy of each vertex according to the curvature measure and the linear velocity measure of each vertex and constructing a quadrilateral local energy field by utilizing the vertex energy.

In one embodiment, the grid boundary adjustment module 250 may include:

and the polygon determination submodule is used for determining a plurality of triangles which are intersected with the boundary line of the curved surface to be split in the final triangulated mesh to form a polygon corresponding to the boundary line.

And the polygon subdivision sub-module is used for dividing the polygon into two sub-polygons by utilizing the boundary line, re-triangulating the two sub-polygons respectively, and taking the final triangulated mesh after re-triangulating as an initial subdivision mesh of the curved surface to be subdivided.

And the non-feasible domain removing sub-module is used for determining a feasible domain and a non-feasible domain in the initial subdivision grid according to the shape characteristics of the curved surface to be subdivided, and removing triangles in the non-feasible domain to obtain the triangular subdivision grid of the curved surface to be subdivided.

In one embodiment, the present application also provides a storage medium having stored therein computer readable instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of the surface triangulation method according to any of the above embodiments.

In one embodiment, the present application also provides a computer device having stored therein computer readable instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of the surface triangulation method according to any of the embodiments above.

Schematically, as shown in fig. 6, fig. 6 is a schematic internal structure of a computer device provided in an embodiment of the present application, and the computer device 300 may be provided as a server. Referring to FIG. 6, computer device 300 includes a processing component 302 that further includes one or more processors, and memory resources represented by memory 301, for storing instructions, such as applications, executable by processing component 302. The application program stored in the memory 301 may include one or more modules each corresponding to a set of instructions. Further, the processing component 302 is configured to execute instructions to perform the surface triangulation method of any of the embodiments described above.

The computer device 300 may also include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input output (I/O) interface 305. The computer device 300 may operate based on an operating system stored in memory 301, such as Windows Server TM, mac OS XTM, unix TM, linux TM, free BSDTM, or the like.

It will be appreciated by those skilled in the art that the structure shown in fig. 6 is merely a block diagram of some of the structures associated with the present application and is not limiting of the computer device to which the present application may be applied, and that a particular computer device may include more or fewer components than shown, or may combine certain components, or have a different arrangement of components.

Finally, it is further noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

In the present specification, each embodiment is described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and may be combined according to needs, and the same similar parts may be referred to each other.

The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of surface triangulation, the method comprising:

determining a sampling point set and an auxiliary triangle of a curved surface to be split by adopting a computer auxiliary tool;

performing boundary adjustment on the final triangulated mesh according to the boundary line and the shape characteristic of the curved surface to be split to obtain a triangulated mesh of the curved surface to be split;

the adjusting the dividing direction of the triangle related to the current sampling point in the initial triangle grid according to the energy field of the corresponding region of the current sampling point in the initial triangle grid comprises the following steps:

2. The surface triangulation method of claim 1, wherein triangulating the auxiliary triangle with the starting point to form an initial triangulated mesh comprises:

3. The surface triangulation method according to claim 1, wherein the determining the quadrangle corresponding to the current sampling point according to the connection result includes:

4. A surface triangulation method according to claim 3, characterized in that said adjusting the division direction of triangles in the initial triangulated mesh in relation to the current sample point according to the local energy field comprises:

5. The surface triangulation method of claim 1, wherein said constructing the quadrilateral local energy field comprises:

6. The surface triangulation method according to claim 1, wherein the performing boundary adjustment on the final triangulated mesh according to the boundary line and the shape feature of the surface to be segmented to obtain the triangulated mesh of the surface to be segmented comprises:

7. A surface triangulation device, comprising:

the triangle construction module is used for determining a sampling point set of the curved surface to be split and an auxiliary triangle by adopting a computer auxiliary tool;

the grid boundary adjusting module is used for carrying out boundary adjustment on the final triangulated grid according to the boundary line and the shape characteristic of the curved surface to be split to obtain a triangulated grid of the curved surface to be split;

wherein, the division direction adjustment module includes:

8. A computer-readable storage medium, characterized by: the storage medium having stored therein computer readable instructions which, when executed by one or more processors, cause the one or more processors to perform the steps of the surface triangulation method according to any one of claims 1 to 6.

9. A computer device, comprising: one or more processors, and memory;

stored in the memory are computer readable instructions which, when executed by the one or more processors, perform the steps of the surface triangulation method according to any one of claims 1 to 6.