JP2005242647A - Resolution control system and resolution control program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To generate a mesh model of low resolution which is suited to finite element analysis while maintaining quality even in the case of a complicated shape. <P>SOLUTION: The positions of new vertexes k obtained when a high-resolution mesh model 2 is converted into a low-resolution mesh model are calculated, the new vertexes K are converged into vertexes suited to a target value for the infinite element analysis to adopt vertex pairs (i, j) suited to the finite element analysis as targets to be integrated. Then vertex pairs in which an integrated evaluation value ε<SB>ij</SB>concerned with region distortion and region roughness/denseness is maximum out of these vertex pairs (i, j) are integrated to set new vertexes. The low-resolution mesh model generated by these processing is substituted for the high-resolution mesh model and a series of processing described above is repeated. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a resolution control system and a resolution control program for generating a low resolution mesh model suitable for finite element analysis from a high resolution mesh model.

  When evaluating product strength, collision, thermal deformation, etc., a mesh model is used in which a solid model obtained by computer graphics of a product design shape is expressed as a set of fine surface segment elements (mesh). Such analysis using a mesh model is called finite element analysis, and its accuracy and efficiency are greatly affected by the number, density, and shape of the surface segment elements of the mesh model.

  As a conventional mesh model generation method, for example, the method of Non-Patent Document 1 is known. In this method, as shown in the processing flow of FIG. 16, the solid model is divided into mesh segment elements by FEM mesher based on the set target segment size and shape approximation error (mesh segmentation), and a desired density is obtained. A mesh model is generated. The mesh division time increases as the density of the surface segment elements increases.

Further, as a technique for improving the quality of a mesh model, for example, those of Non-Patent Document 2 and Non-Patent Document 3 are known. Other related documents include Non-Patent Document 4.
Luebke Reddy, Cohen Varshney and Watson Huebner: LEVEL of DETAIL FOR 3D GRAPHICS, Morgan Kaufman, 2003 E. Bechet, JC Cuilliere and F. Trochu: Generation of a finite element MESH from stereolithography (STL) files, Computer Aided Design, 34, pp. 1-17, 2002 A. LEE, Sweldents, P. Schroder, L Cowsar, and D. Dobkin. Maps: Multiresolution adaptive parameterization of surfaces Computer Graphics (SIGGRAPH '98 Proceedings), pp. 95-104, 1998 M. Garland and PS Heckbert: Surface Simplification Using Quadric Error Metrics, proc. Of SIGGRAPH 97, pp. 209-216, 1997 H. Hoppe: Progressive Meshes, Computer Graphics (SIGGRAPH'96), pp. 98-108, 1996

  In the method of Non-Patent Document 1, it is necessary to divide a solid model into meshes every time a mesh model with different number of area elements is generated, which requires processing cost. In a complicated shape, the shape of a rough mesh is unstable. There is a problem of becoming.

  The method of Non-Patent Document 2 has a problem that it is difficult to control the density and number of surface segment elements and to assure quality assurance.

  The method of Non-Patent Document 3 has a problem that it is difficult to manage the shape approximation degree and the density / quality of the surface segment element, and cannot be applied to a mesh model having a complicated shape.

  The present invention has been made in view of the above, and an object of the present invention is to perform resolution control capable of generating a low-resolution mesh model suitable for finite element analysis while maintaining quality even for a complicated shape. To provide a system and a resolution control program.

  The resolution control system according to the first aspect of the present invention reads out the high resolution mesh model from the database storing the target values for the new vertex when the high resolution mesh model and the vertex pair are integrated, and integrates each vertex pair New vertex position calculating means for calculating the position of the new vertex, and reading the target value from the database, narrowing down new vertices that match the target value, and surface distortion from the vertex pair corresponding to the new vertex Integrated vertex pair determining means for determining the vertex pair having the maximum overall evaluation value for the surface density, and new vertex position setting means for setting the position of the new vertex by integrating the determined vertex pair for the high resolution mesh model And replacing the mesh model generated by the position setting of the new vertex with the high-resolution mesh model, the new vertex position calculating means, the integrated vertex pair determining means , Characterized by having a a repeating means for repeating the process to the new vertex position setting means.

  The resolution control program according to the second aspect of the present invention reads the high resolution mesh model from the database storing the target values for the new vertex when the high resolution mesh model and the vertex pair are integrated, and integrates each vertex pair Processing for calculating the position of the new vertex, reading out the target value from the database, narrowing down new vertices that match the target value, and regarding surface distortion and surface density from the vertex pair corresponding to the new vertex Processing for determining the vertex pair having the maximum comprehensive evaluation value, processing for setting the position of the new vertex by integrating the determined vertex pair for the high-resolution mesh model, and mesh generated by setting the position of the new vertex A process of replacing the model with the high-resolution mesh model, repeatedly calculating the position of the new vertex, determining the vertex pair, and setting the position of the new vertex; And characterized by causing a computer to execute the.

  In the first and second aspects of the present invention, new vertices are calculated when the vertex pairs of the high-resolution mesh model are integrated, and the new vertices are narrowed down to those suitable for target values suitable for finite element analysis. As a result, the vertex pair suitable for finite element analysis is the target of integration, and the vertex evaluation with the largest overall evaluation value for surface segment distortion and surface segment density is integrated to set one new vertex. The mesh model generated here is replaced with a high-resolution mesh model and the above-described series of processing is repeated, so that the resolution can be reduced while maintaining the quality even for a complicated shape.

  According to the resolution control system and the resolution control program according to the present invention, it is possible to generate a low-resolution mesh model suitable for finite element analysis while maintaining quality even for a complicated shape.

[1] Basic Concept First, the basic concept of the low-resolution mesh model generation method in the resolution control system of the present embodiment will be described with reference to FIG. In this figure, the approach direction of this method is indicated by a1, the method of Non-Patent Document 2 by a2, and the method of Non-Patent Document 3 by a3. As shown in the figure, both methods of Non-Patent Document 2 and Non-Patent Document 3 attempt to improve the quality of a low-quality mesh model. In contrast, this method realizes the generation of a low-resolution mesh model suitable for finite element analysis by taking the approach of reducing the number of surface segment elements while maintaining the quality of a high-quality high-resolution mesh model. Is.

[2] Outline of the present system As shown in FIG. 2, the present resolution control system 1 includes a high-quality / high-density high-resolution mesh model 2 generated from a solid model by a technique such as FEM mesher, etc. Based on the target value, the resolution is controlled so that the low-resolution mesh models 3a and 3b having a desired density are generated. As the mesh model, a triangular mesh model in which all surface segment elements are composed of triangles is used. The target values of density / quality are set so that the low resolution mesh models 3a and 3b have properties suitable for finite element analysis. The mesh model used for finite element analysis is required to have the following properties.

[Characteristic 1] Number and density of area elements suitable for analysis conditions The number and density of area elements have a great influence on analysis time and analysis accuracy. For this reason, it is desirable that the number and density of the surface segment elements are appropriately set according to the required analysis purpose and environment.

[Property 2] High mesh quality In order to improve analysis accuracy and generate a stable mesh, it is desirable that the surface mesh be a high-quality mesh with little distortion of the surface segment elements and less area change between adjacent surface segment elements.

[Property 3] Less Shape Approximation Error From the viewpoint of analysis accuracy, it is desirable that the mesh model used for the finite element analysis closely approximates the shape to be analyzed.
[Characteristic 4] Limit of upper limit value of valence The upper limit value of valence is within a certain value because analysis is impossible or the analysis accuracy is reduced with a mesh model that includes vertices with a large valence (number of tangent lines). It is desirable to be suppressed.

  As shown in the functional block diagram of FIG. 3, the resolution control system 1 includes a new vertex position calculation unit 11, an integrated vertex pair determination unit 12, a new vertex position setting unit 13, and a database 14. The resolution control system 1 is configured by a computer, and the database 14 is configured by a large-capacity storage device. Each process in the new vertex position calculation unit 11, the integrated vertex pair determination unit 12, and the new vertex position setting unit 13 is executed by a resolution control program installed in the resolution control system 1. Hereinafter, the process in each part 11-13 for satisfy | filling said each property is demonstrated.

[3] Processing of New Vertex Position Calculation Unit 11 The new vertex position calculation unit 11 reads the high resolution mesh model 2 from the database 14 and reduces the number of vertices of the high resolution mesh model 2 to reduce the resolution. As shown in FIG. 4, for all pair of vertices in the high-resolution mesh model 2 (i, j), calculates the position p _k of the new vertex k when integrated vertex i, vertex j.

  Specifically, the center of gravity of the vertex adjacent to the vertex pair (i, j) is calculated, or the position at which the sum of the square distances of the respective surface segments in contact with the vertex pair (i, j) and the new vertex is minimized. (QEM point (Quadric Error Metrics)) is calculated as the position of the new vertex.

  The center of gravity is calculated based on the following equation.

p _k = Σ _{m∈k *} p _m / | k ^* | (1)
Here, p _m is the position of each vertex adjacent to the vertex k, k ^* denotes the set of vertices adjacent to the vertex k. When the center of gravity is calculated, it is possible to reduce the distortion of the surface after the vertex pair is integrated, and to uniformize the area between adjacent surfaces.

On the other hand, the QEM point is obtained by the method described in Non-Patent Document 4. Specifically, first, as shown in FIG. 5, calculated on the basis of positions the sum of the squared distances between the set F _i and the new vertex position p _k of the surface region f in contact with the vertex i of p _i in the following equation .

Δ _i (p _k ) = Σ _fεFi (f _f ^T p _k ) ²
= P _k ^T ( _ΣfεFi K _f ) p _k
= P _k ^T Q _i p _k (2)
Here, Q _i is a Q matrix (4 × 4) of the vertex i.

Then calculated based on the vertex pair (i, j) the sum of the squared distances between the new vertex position p _k and set the surface region in contact with the following equation.

Δ _ij (p _k ) = p _k ^T (Q _i + Q _j ) p _k (3)
New vertex position _{p k} where the squared distance delta _{ij (p k)} is minimized is QEM point.

In the expression (3), the following condition is set: ∂Δ _ij / ∂x = ∂Δ _ij / ∂y = ∂Δ _ij / ∂z = 0
A new vertex position pk that satisfies the above is _obtained by the following equation (4).

Here, Q _i + Q _j = {q _mn }. When the QEM point is calculated, the position of the new vertex can be made to minimize the shape approximation error.

  The new vertex position calculation unit 11 calculates new vertex positions that are candidates for integration for all vertex pairs by repeating the above processing.

[4] Process of Integrated Vertex Pair Determining Unit 12 The integrated vertex pair determining unit 12 reads the high resolution mesh model 2 and each target value from the database 14, and among the new vertex position candidates calculated by the new vertex position calculating unit 11. 1 is selected as the most appropriate new vertex, and the vertex pair to be integrated corresponding to this new vertex is determined.

  In order to satisfy the above properties, the following values are stored in advance in the database 14 as target values.

E _max : Shape approximation error upper limit value V _max : Valence upper limit value SZ _max : Surface segment size upper limit value SZ _min : Surface segment size lower limit value SZ _nom : Surface segment size standard value ST _min : Stretch lower limit value G: Surface segment element Number v _n : area segment inner product threshold Δ _ij (p _k ) expressed by equation (3) is used for the shape approximation error, and E _max is set as the upper limit value.

The surface segment size is the length of the longest side of the three sides of the surface segment element. As shown in FIG. 6, when the length of each side of the surface segment ^f is defined by l ₁ ^f , l ₂ ^f , and l ₃ ^f , the surface segment size of the surface segment f is expressed by the following equation.

SIZE (f) = maxl _m ^f (5)
Stretching is an index indicating surface segment distortion, and is defined as inscribed circle radius of surface segment element × √ (12) / (longest side length of surface segment element). The stretch of the surface area f is expressed by the following formula (6).

Here, s = (l ₁ ^f + l ₂ ^f + l ₃ ^f ) / 2. As shown in FIG. 7, the closer the stretch value is to 1, the closer the shape of the surface segment element is to an equilateral triangle, and the closer to 0, the greater the distortion.

  As shown in the functional block diagram of FIG. 8, the integrated vertex pair determination unit 12 includes a vertex pair narrowing unit 21, an evaluation value calculation unit 22, and a vertex pair selection unit 23. The processing of the vertex pair narrowing unit 21, the evaluation value calculating unit 22, and the vertex pair selecting unit 23 is executed by a resolution control program installed in this system.

[5] Processing of Vertex Pair Narrowing Unit 21 The vertex pair narrowing unit 21 is a new vertex calculated by the vertex pair set, each target value, and the new vertex position calculating unit 11 of the high resolution mesh model 2 read from the database 14. Using the position set {p _k }, the vertex pairs whose new vertices after integration match the target value are narrowed down. Specifically, the following processing is performed.

[Guarantee of shape approximation error]
Select vertex pairs that satisfy the following formula and the shape approximation error of the new vertex after integration is within a certain value.

p _k ^T (Q _i + Q _j ) p _k ≦ E _max (7)
[Guaranteed valence limit]
Select vertex pairs that satisfy the following formula and the valence of the new vertex after integration is within a certain value.

| i ^* | + | j ^* | -4 ≦ V _max (8)
Here, | i ^* | is the valence of vertex i, | j ^* | is the valence of vertex j, and when vertex pair (i, j) is integrated into vertex k over the entire left side of equation (8). The valence of the new vertex k is shown.

[Guaranteed lower limit of area distortion]
A vertex pair that satisfies the following equation and has a stretch of all the faces in contact with the new vertex k after integration is equal to or greater than the lower limit value is selected.

_{^{∀ f∈F k, STCH (f)}} ≧ ST min (9)
Here, F _k is a set of surface segments f in contact with the new vertex k (see FIG. 9B).

[Guaranteed upper and lower limit of area size]
A vertex pair that satisfies the following expression and has a surface segment size in contact with the new vertex k after integration within the range between the upper limit value and the lower limit value is selected.

_{^{∀ f∈F k, SIZE (f)}} ≦ SZ max (10)
_{^{∀ f∈F k, SIZE (f)}} ≧ SZ min (11)
[Suppression of turning over]
A vertex pair that satisfies the following expression and whose new vertex position is not on the opposite side of the face is selected.

^{_{∀ f a ∈F i ∪F j,}} ∀ f b ∈F k
n _fb · n _fa ≧ v _n (12)
Here, n _fa is a normal vector of the surface _segment f in contact with the vertex pair before integration, and n _fb is a normal vector of the surface segment f in contact with the new vertex after integration. Threshold _{v n} is a value from 0 - 0.9 as an example. Further, F _i ∪F _j represents a set of surface segments in contact with the vertex pair (i, j) (see FIG. 9A).

  As a result of the above processing, vertex pairs whose normal vector direction in contact with any vertex pair is inverted before and after the integration are excluded from integration.

  The vertex pair narrowing unit 21 outputs a set of vertex pairs suitable for each target value to the evaluation value calculating unit 22 and the vertex pair selecting unit 23.

[6] Process of Evaluation Value Calculation Unit 22 In the evaluation value calculation unit 22, the vertex pair set narrowed down by the vertex pair narrowing unit 21, the new vertex position set {p _k } calculated by the new vertex position calculation unit 11, and the database 14 Using the read surface segment size standard value SZ _nom , each evaluation value is calculated for the new vertexes included in the new vertex position set {p _k } corresponding to the vertex pairs narrowed down by the vertex pair narrowing unit 21. To do. Specifically, the following processing is performed.

[Calculation of surface distortion evaluation value]
As the surface segment distortion evaluation value, the minimum stretch value is calculated based on the following equation for the surface segment set F _k in contact with the new vertex k.

EST _min = min _fεFk STCH (f) (13)
Similarly, the average value of the stretch is calculated based on the following equation for the surface segment set F _k in contact with the new vertex k as the surface segment distortion evaluation value.

EST _ave = 1 / | F _k | Σ _{fεF k} STCH (f) (14)
[Calculation of area density evaluation value]
For the surface segment set F _i ∪F _j in contact with the vertex pair (i, j), a value for evaluating the roughness of the surface is calculated based on the following equation.

ESZ _ij = 1 / | w | _Σfεw SZ _nom / SIZE (f) (15)
Here, w = F _i ∪F _j . The evaluation value calculation unit 22 outputs the calculated set of evaluation values to the vertex pair selection unit 23.

[7] Processing of Vertex Pair Selection Unit 23 The vertex pair selection unit 23 selects one vertex pair most suitable for integration among the vertex pairs narrowed down by the vertex pair narrowing unit 21 based on each evaluation value. To do. Specifically, the total evaluation value ε _ij of the vertex pair (i, j) is calculated based on the following equation.

ε _ij = EST _min × EST _ave × ESZ _ij (16)
Then, the vertex pair (i, j) having the largest comprehensive evaluation value ε _ij is selected as the vertex pair to be integrated (integrated vertex pair). The vertex pair selection unit 23 outputs the selected integrated vertex pair (i, j) to the new vertex position setting unit 13.

[8] Processing of New Vertex Position Setting Unit 13 The new vertex position setting unit 13 uses the high resolution mesh model 2, the new vertex position p _k , and the integrated vertex pair (i, j) read from the database 14, and uses the edge collapse method. (See Non-Patent Document 5) The integrated vertex pair (i, j) is integrated to set the position of the new vertex. As a result, the total vertex pair (i, j) and the edge line connected to the total vertex pair are deleted, and the new vertex and the edge line connected to the new vertex are set. The new vertex position setting unit 13 outputs the low resolution mesh model 3 generated in this way.

[9] Repetitive processing In this resolution control system 1, the low-resolution mesh model 3 output from the new vertex position setting unit 13 is replaced with the high-resolution mesh model 2 used in each of the above processes, and the new vertex position calculation unit 11 is integrated. The processing in each part of the vertex pair determination unit 12 and the new vertex position setting unit 13 is repeated.

  In one process, only two vertices of the entire mesh model are integrated into one, so that the resolution is reduced by repeatedly performing the process. The iterative process is repeated until the number of elements for the surface of the generated low-resolution mesh model matches the preset number G of surface elements.

  Specifically, the new vertex position setting unit 13 reads the surface segment element number G from the database 14, and if the generated low resolution mesh model 3 has a larger number of surface segment elements than G, the new vertex position setting unit 13 selects the low resolution mesh model 3. The new vertex position calculation unit 11, the integrated vertex pair determination unit 12, and the new vertex position setting unit 13 are output to repeat the above processes, and each process is performed when the number of surface segment elements of the low resolution mesh model 3 matches G. Stop.

[10] Application Result and Evaluation Next, the result and evaluation of applying this method will be described. For each target value, shape approximation error upper limit E _max = 0.8, valence upper limit value V _max = 10, surface segment size upper limit value SZ _max = 5, surface segment size lower limit value SZ _min = 0.05, surface segment distortion lower limit value ST _min = 0.05, surface segment element number G = 26,000, 16,000.

  FIG. 10A is a diagram illustrating a solid model for generating a high-resolution mesh model to be processed. Here, the width W = 49, the length d = 103, and the height h = 17. FIG. 10B is a diagram showing a high resolution mesh model generated from the solid model by the FEM mesher. The number of surface segment elements in this high resolution mesh model was 120,186.

  FIG. 11 is a diagram showing a low resolution mesh model generated by the resolution control system 1 using the high resolution mesh model of FIG. 10B. In FIG. 11A, the number of area elements is 26,000. In (b), the number of area elements is 16,000.

  FIG. 12 is a diagram showing a low-resolution mesh model generated by a simplified technique for computer graphics (CG). In FIG. 12A, the number of surface segment elements is 26,000, and in FIG. The number is 16,000.

  FIG. 13 is a diagram showing a low-resolution mesh model generated by the FEM mesher. In FIG. 13A, the number of surface segment elements is 11,982, and in FIG. 13B, the number of surface segment elements is 13,702.

  FIG. 14 is a table summarizing the minimum value, maximum value, minimum value of stretch, and maximum value of valence for each low-resolution mesh model generated by each method. In the table in FIG. 11, the models in FIGS. 11A and 11B correspond to (a) and (b) in the table, and the models in FIGS. 12A and 12B correspond to (c) in the table. ) And (d), the models of FIGS. 13A and 13B correspond to (e) and (f) in the table. The numerical value in parentheses is the set target value. From the table in the figure, the low-resolution mesh model generated by the present resolution control system 1 of the embodiment has a smaller surface area size with a smaller interval between the minimum value and the maximum value, and is evenly closer than other methods. The stretch is the largest, the valence is the smallest, and it is confirmed that the mesh model is most suitable for finite element analysis.

  FIG. 15 is a graph summarizing the distribution of stretch for the low-resolution mesh models generated by the respective methods. (B), (d), (e), and (f) in the graph correspond to the models (b), (d), (e), and (f) in FIG. 14, respectively. The low resolution mesh model (b) generated by the resolution control system 1 has 16,000 surface segment elements. From the graph in the figure, it was confirmed that the low-resolution mesh model (b) has substantially the same quality of surface distortion as the mesh models (e) and (f) generated by the FEM mesh.

Therefore, according to the present embodiment, the position of the new vertex k when the vertex pairs (i, j) of the high resolution mesh model 2 are integrated is calculated, and the new vertex k is a target suitable for finite element analysis. By narrowing down to those that match the values, the vertex pair (i, j) suitable for the finite element analysis is the target of integration, and among the vertex pair (i, j), the surface distortion and surface roughness are related. A new vertex k is set by integrating the ones having the largest comprehensive evaluation value ε _ij , the low resolution mesh model 3 generated here is replaced with the high resolution mesh model 2, and the above-described series of processing is repeated, whereby a new Since vertices are set one by one, a low-resolution mesh model can be stably generated while maintaining quality even for complex shapes.

  According to the present embodiment, when calculating the new vertex k, the vertex pair (i, j) is integrated by calculating the center of gravity of the vertex adjacent to the vertex pair (i, j) as the position of the new vertex k. The distortion of the subsequent surface segment can be reduced, and the area between adjacent surface segment elements can be made uniform.

  According to the present embodiment, when the new vertex k is calculated, the position where the sum of the square distance between each surface segment in contact with the vertex pair (i, j) and the new vertex k is calculated as the position of the new vertex k. Thus, the position of the new vertex k that minimizes the shape approximation error can be calculated.

  According to the present embodiment, the process of setting one new vertex in one process is repeatedly performed, so that the number of surface segment elements of the generated low resolution mesh model is preset. The processing can be stopped at the point where the number of segment elements G is matched, so that a low resolution mesh model having a desired number of surface segment elements can be generated.

  According to the present embodiment, the mesh division of the resod model may be performed only once when the high-resolution mesh model is first generated. Therefore, every time the low-resolution mesh model having a desired density is generated as in the prior art, the sod model Therefore, high-speed processing can be performed. In addition, since the generated low-resolution mesh model is a multi-resolution representation in which the number of vertices is different by one each time the processing is different, the initial high-resolution mesh model 2 is changed again when changing the resolution. There is no need to use it, and the resolution can be changed at high speed.

It is a conceptual diagram which shows the approach of a low resolution mesh model production | generation method. It is a figure which shows the schematic process of the resolution control system in one Embodiment. It is a functional block diagram which shows the structure of the said resolution control system. It is a figure which shows a mode that a vertex pair is integrated into one new vertex. It is a figure for demonstrating the shape approximation error about a new vertex. It is a figure for demonstrating area size. It is a figure for demonstrating stretch. It is a functional block diagram which shows the structure of an integrated vertex pair determination part. FIG. 4A is a diagram showing a surface segment set in contact with a vertex pair before integration, and FIG. 4B is a diagram showing a surface segment set in contact with a new vertex after integration. FIG. 4A shows a solid model, and FIG. 4B shows a high resolution mesh model. It is a figure which shows the low resolution mesh model produced | generated by the said resolution control system, The figure (a) is a figure with 26,000 surface segment elements, and the figure (b) is a figure with 16,000 surface segment elements. It is a figure which shows the low-resolution mesh model produced | generated by the simplification method for computer graphics, The figure (a) has 26,000 surface segment elements, and the figure (b) has 16,000 surface segment elements. It is a figure which shows the low-resolution mesh model produced | generated by the FEM mesher, The figure (a) is the area element number 11,982, and the figure (b) is the area element number 13,702. It is a table | surface which shows the evaluation value about the low-resolution mesh model produced | generated by each method. It is a graph which shows the distribution of the stretch about the low-resolution mesh model produced | generated by each method. It is a figure which shows the process which produces | generates the conventional low resolution mesh model.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Resolution control system 2 ... High resolution mesh model 3 ... Low resolution mesh model 11 ... New vertex position calculation part 12 ... Integrated vertex pair determination part 13 ... New vertex position setting part 21 ... Vertex pair narrowing part 22 ... Evaluation value calculation part 23 ... Vertex pair selection unit

Claims (10)

New vertex position calculation that reads the high resolution mesh model from the database that stores the target value for the new vertex when the high resolution mesh model and vertex pair are integrated, and calculates the position of the new vertex when each vertex pair is integrated Means,
Read the target value from the database, narrow down new vertices that match the target value, and determine the vertex pair having the maximum overall evaluation value for surface distortion and surface roughness from the vertex pairs corresponding to the new vertex. An integrated vertex pair determination means;
For the high resolution mesh model, new vertex position setting means for setting the position of a new vertex by integrating the determined vertex pairs;
Replacing the mesh model generated by the position setting of the new vertex with the high resolution mesh model, the new vertex position calculating means, the integrated vertex pair determining means, the repeating means for repeating the new vertex position setting means,
A resolution control system comprising:   The resolution control system according to claim 1, wherein the new vertex position calculation means calculates the center of gravity of the vertex adjacent to the vertex pair as the position of the new vertex.   2. The resolution control system according to claim 1, wherein the new vertex position calculating means calculates a position at which the sum of square distances of each surface portion in contact with the vertex pair and the new vertex is minimum as the position of the new vertex. . The target value includes a shape approximation allowable error, a valence upper limit value, an area size upper limit value, an area size lower limit value, an area size reference value, and a stretch lower limit value,
The integrated vertex pair determining means includes:
Of the new vertices calculated by the new vertex position calculating means, the shape approximation error is not more than the shape approximation tolerance, the valence is not more than the valence upper limit value, and the surface segment size is not less than the surface segment size lower limit value. Vertex pair narrowing means for narrowing down vertex pairs corresponding to new vertices that satisfy the condition that the stretch is below the upper limit value and the stretch satisfies the stretch lower limit value or more,
For each narrowed pair of vertices, calculate the minimum and average stretch values of the surface that touches the new vertex as the surface segment distortion evaluation value, and the surface segment size for the surface portion that touches the vertex pair as the surface roughness evaluation value. An average value of a value obtained by dividing the reference value by the surface segment size, and an evaluation value calculating means for calculating the overall evaluation value by multiplying the minimum value of the stretch, the average value, and the surface roughness density evaluation value,
A vertex pair selecting means for selecting the vertex pair having the maximum comprehensive evaluation value;
The resolution control system according to claim 1, further comprising: The target value includes the number of surface segment elements,
The repeating means reads out the number of surface segment elements from the database and repeats until the number of surface segment elements of the generated low resolution mesh model matches the number of surface segment elements. 5. The resolution control system according to any one of items 4 to 4. A high-resolution mesh model, a process of reading the high-resolution mesh model from a database storing target values for new vertices when integrating vertex pairs, and calculating a position of the new vertex when integrating each vertex pair;
The target value is read from the database, new vertices that match the target value are narrowed down, and the vertex pair having the maximum comprehensive evaluation value for surface segment distortion and surface segment density is determined from the vertex pairs corresponding to the new vertex. Processing,
For the high-resolution mesh model, a process for setting the position of a new vertex by integrating the determined vertex pair;
A process of replacing the mesh model generated by setting the position of the new vertex with the high-resolution mesh model and repeatedly calculating the position of the new vertex, determining the vertex pair, and setting the position of the new vertex;
A resolution control program for causing a computer to execute.   The resolution control program according to claim 6, wherein the process of calculating the position of the new vertex calculates the center of gravity of the vertex adjacent to the vertex pair as the position of the new vertex.   7. The process of calculating the position of the new vertex calculates a position where the sum of the square distance between each surface segment in contact with the vertex pair and the new vertex is minimum as the position of the new vertex. Resolution control program. The target value includes a shape approximation allowable error, a valence upper limit value, an area size upper limit value, an area size lower limit value, an area size reference value, and a stretch lower limit value,
The process of determining the vertex pair is as follows:
Among the calculated new vertices, the shape approximation error is not more than the shape approximation tolerance, the valence is not more than the valence upper limit value, the area size is not less than the area size lower limit value and not more than the area size upper limit value, and the stretch is the above Processing to narrow down vertex pairs corresponding to new vertices that satisfy the stretch lower limit value or more;
For each narrowed pair of vertices, calculate the minimum and average stretch values of the surface that touches the new vertex as the surface segment distortion evaluation value, and the surface segment size for the surface portion that touches the vertex pair as the surface roughness evaluation value. A process of calculating an average value of values obtained by dividing the reference value by the surface segment size, and calculating the overall evaluation value by multiplying the minimum value of the stretch, the average value, and the surface portion roughness evaluation value;
A process of selecting a vertex pair having the maximum comprehensive evaluation value;
The resolution control program according to claim 6, wherein the resolution control program is executed. The target value includes the number of surface segment elements,
The number of surface segment elements is read from the database, and the process to be repeated is repeated until the number of surface segment elements of the generated low-resolution mesh model matches the number of surface segment elements. The resolution control program according to any one of Items 9 to 9.