JP2005242651A - High quality mesh model generation system and generation program - Google Patents

Abstract

A high quality mesh model is generated from a low quality mesh model even for a complicated shape.
[MEANS FOR SOLVING PROBLEMS] A mesh subdivision unit (2) subdivides a low-quality mesh model (5) so that the edge of each face is smaller than a subdivision parameter (σ _size) to increase the degree of freedom of operation of the mesh, and then simplifies the mesh. _{Verifier 3} narrows down the vertex pairs whose shape approximation error of the mesh model after integration of the vertex pairs is suppressed below the simplified parameter τ _tol that regulates the quality, and the vertex with the largest overall evaluation value for surface distortion and surface roughness By combining and simplifying pairs, a high-quality mesh model is generated.
[Selection] Figure 2

Description

  The present invention relates to a generation system and a generation program for generating a high quality mesh model from a low quality mesh model.

  In recent years, mesh models that represent the surface as a collection of fine surface segment elements (mesh) have become widely used not only as computer graphics display models but also in the design and production fields of industrial products. ing.

  The required mesh properties vary depending on the field, and display and product design require high shape representation accuracy and reduced surface fraction. In finite element analysis for evaluating product strength, impact, thermal deformation, etc., high mesh quality is required such that surface distortion is smaller.

Methods for improving mesh quality include a method based on Delaunay method and Laplacian smoothing method (see Non-Patent Document 1) and a method based on parameterization method (see Non-Patent Document 2). In addition, there are Non-Patent Document 3 and Non-Patent Document 4 as related documents.
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 Michael S. Floater: Parametarization and smooth approximation of surface triangulations, Computer Aided Geometric Design, pp. 231-250, 1997 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

  However, in the method of Non-Patent Document 1, when it is attempted to change the resolution of a high-quality mesh model, it is necessary to perform a process of changing the surface fraction using the low-quality mesh model in the initial state each time. There is a problem that the calculation cost is high.

  Further, the method of Non-Patent Document 2 has a problem that shape approximation cannot be managed, and it is difficult to apply to a complicated shape, and the calculation cost is high.

  The present invention has been made in view of the above, and an object of the present invention is to generate a high-quality mesh model capable of generating a high-quality mesh model at high speed from a low-quality mesh model even for complex shapes. It is to provide a system and a generation program.

  The high quality mesh model generation system according to the first aspect of the present invention reads out a low quality mesh model and subdivision parameters from a database storing low quality mesh models, subdivision parameters, and simplification parameters. Subdivision means for subdividing the surface segment elements to match the subdivision parameters, new vertex position calculation means for calculating the position of the new vertex when each vertex pair of the subdivided mesh model is integrated, and Integrated vertex pair determination that reads simplified parameters from the database, narrows down the vertex pairs whose new vertex positions match the simplified parameters, and determines the vertex pair with the largest overall evaluation value for surface distortion and surface roughness And a new vertex position that sets the position of a new vertex by integrating the determined vertex pair for the subdivided mesh model A high-quality mesh model generated by setting means and new vertex position setting is replaced with the subdivided mesh model, and the new vertex position calculating means, the integrated vertex pair determining means, and the new vertex position setting means are processed. And repeating means for repeating.

  A high quality mesh model generation program according to the second aspect of the present invention reads a low quality mesh model and a subdivision parameter from a database storing a low quality mesh model, a subdivision parameter, and a simplification parameter. The process of subdividing the surface segment elements to match the subdivision parameters, the process of calculating the position of the new vertex when each vertex pair of the subdivided mesh model is integrated, and the simplified parameter from the database Reading, narrowing down the vertex pairs whose new vertex positions match the simplification parameters, determining the vertex pair having the maximum comprehensive evaluation value regarding the surface segment distortion and surface segment density, and the subdivided mesh model For a message, a message is generated by integrating the determined vertex pair and setting the new vertex position and the new vertex position setting. The interchanged Yumoderu the subdivided mesh model calculation of the position of the new vertex, the determination of the pair of vertices, characterized in that to execute a process of repeating the setting of the position of the new vertex to the computer.

  In the first and second aspects of the present invention, the low-quality mesh model is subdivided so as to match the subdivision parameters, thereby increasing the degree of freedom of mesh operation. A high quality mesh model is generated from a low quality mesh model by simplifying the mesh model to fit.

  In the simplification process, new vertices of the subdivided mesh model are calculated, and the new vertices are narrowed down to vertex pairs that match the simplification parameters, so that vertex pairs suitable for higher quality are targeted for integration. The mesh model is generated by setting new vertices by integrating the vertex evaluations with the largest comprehensive evaluation value for surface distortion and surface density in the vertex pair, and replacing this mesh model with a low-quality mesh model. By repeating the above series of processing, high quality can be achieved even for complicated shapes.

  In addition, the high-resolution mesh model has a multi-resolution representation that has a different number of vertices for each degree of processing, so that once the high-quality mesh model is generated, the process of changing the number of facets can be performed at high speed. ing.

  According to the high quality mesh model generation system and generation program according to the present invention, a high quality mesh model can be generated from a low quality mesh model even for a complex shape. In addition, mesh models having different surface fractions can be generated at high speed.

[1] Basic Concept First, the basic concept of the high quality mesh model generation method in the present embodiment will be described with reference to FIG. In this figure, the approach directions of this method are indicated by a1 and a2, and those of the methods of Non-Patent Literature 1 and Non-Patent Literature 2 are indicated by a3. As shown in the figure, both of Non-Patent Document 1 and Non-Patent Document 2 attempt to generate a high-quality mesh model directly from a low-quality mesh model.

  On the other hand, the high-quality mesh model generation system of this embodiment subdivides by increasing the surface fraction of the low-quality mesh model (a1), considers the quality after increasing the density and improving the operability. However, the generation of a high-quality mesh model is realized by taking the approach of simplifying (a2) by reducing the number of surface fractions.

  Here, high quality is defined as one having a small area distortion and a uniform surface distribution. The mesh model handled in the present embodiment is a triangular mesh model in which all surface segments are represented by triangles.

[2] Schematic Configuration of System As shown in the functional block diagram of FIG. 2, the high quality mesh model generation system 1 includes a mesh subdivision unit 2 and a mesh simplification unit 3. The generation system 1 is configured by a computer, and the database 4 is configured by a large-capacity storage device. The database 4 has a low quality, in which a solid model obtained by computer graphics of a product design shape is divided (mesh divided) into fine surface segment elements by CG 3D CAD (Computer Adied Design), CG (Computer Graphics) modeler, etc. The mesh model 5 stores a refinement parameter σ _size and a simplified parameter τ _tol indicating a shape approximation allowable error as threshold values for designating the upper limit of the length of the longest side of the surface.

  Each process in the mesh subdivision unit 2 and the mesh simplification unit 3 is executed by a generation program installed in this system. Hereinafter, processing of each unit will be described in detail.

[3] Configuration / Processing of Mesh Subdivision Unit 2 As shown in the functional block diagram of FIG. 3, the mesh subdivision unit 2 includes a ridge line midpoint generation unit 8 and a surface segment division unit 9. The mesh subdivision unit 2 reads the low quality mesh model 5 and the subdivision parameter σ _size from the database 4 and subdivides the low quality mesh model 5 to generate a high density mesh model 6. At the time of subdivision, the surface size (length of the longest side of the surface) is made uniform without impairing the basic shape of the input low quality mesh model 5.

Specifically, first, the ridge line midpoint generation unit 8 generates a midpoint on a ridge line longer than the subdivision parameter σ _size for each surface segment element. Next, as shown in FIG. 4A, the surface segment dividing unit 9 divides the surface segment where midpoints occur on all three sides by connecting the three midpoints. As shown in FIG. 4 (c), as shown in FIG. 4 (c), as shown in FIG. 4 (c), as shown in FIG. In addition, a surface segment where a midpoint occurs on one side is divided by connecting the midpoint and the opposite vertex.

The mesh subdivision unit 2 generates the high-density mesh model 6 by performing this process until the length of all the ridge lines becomes smaller than the subdivision parameter σ _size , and outputs it to the mesh simplification unit 3.

[4] Configuration / Processing of Mesh Simplification Unit 3 As shown in the functional block diagram of FIG. 5, the mesh simplification unit 3 includes a new vertex position calculation unit 11, an integrated vertex pair determination unit 12, and a new vertex position setting unit 13. It is the structure provided with. The mesh simplification unit 3 generates a low-resolution high-quality mesh model 7 using the high-density mesh model 6 and the simplification parameter τ _tol read from the database 4. Hereinafter, processing of each unit will be described in detail.

[5] Processing of New Vertex Position Calculation Unit 11 The new vertex position calculation unit 11 reduces the number of vertices of the high-density mesh model 6 to reduce the resolution. any pair of vertices (i, j) calculates the position p _k of the new vertex k when integrated.

  In calculating the position of the new vertex, the center of gravity of the vertex adjacent to the vertex pair (i, j) is calculated, or the position where the sum of the square distances between the set of surface portions in contact with the vertex pair 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, k ^* represents a 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 3. Specifically, first, as shown in FIG. 7, calculated based on the sum of the squared distances between the set F _i and the new vertex position p _k of each surface fraction f position contacts the vertex i of p _i in the following equation To do.

Δ _i (p _k ) = Σ _(f∈Fi) (f _f ^T p _k ) ²
= P _k ^T (Σ _(f∈Fi) K _f ) p _k
= P _k ^T Q _i p _k (2)
Here, Q _i is a (4 × 4) matrix.

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

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

In the expression (3), the following condition ∂Δ _ij / ∂x = ∂Δ _ij / ∂y = ∂Δ _ij / ∂z = 0
The 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 the positions of new vertices as candidates after integration for all vertex pairs by repeating the above processing.

[6] Processing of Integrated Vertex Pair Determining Unit 12 The integrated vertex pair determining unit 12 uses the high-density mesh model 6 and the simplified parameter τ _tol among the new vertex position candidates calculated by the new vertex position calculating unit 11. One of the most appropriate new vertices is selected from the above, and the corresponding vertex pair to be integrated is determined.

The simplified parameter τ _tol is a shape approximation allowable value. For the shape approximation error, Δ _ij (p _k ) expressed by Equation (3) is used. The database 4 stores the following in advance.

G: Number of surface segment elements v _n : Area product threshold value 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. This is a configuration provided. Each process of the vertex pair narrowing unit 21, the evaluation value calculating unit 22, and the vertex pair selecting unit 23 is executed by a generation program installed in this system. Hereinafter, processing of each unit will be described.

[7] the process vertex Taishibo addition unit 21 of the vertex Taishibo addition unit 21, a simplified parameter tau _tol from the database 4, reads the surface region inner product threshold v _n, vertex pair set of dense mesh model 6, the new vertex position calculation unit Using the new vertex position set {p _k } calculated by 11, the vertex pairs whose new vertexes 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 ≦ τ _tol (5)
[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 (6)
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. As shown in FIG. 9, F _i ∪F _j is a set of planes in contact with the vertex pair (i, j), and F _k is a set of planes in contact with the new vertex k.

  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 that match the target values to the evaluation value calculating unit 22 and the vertex pair selecting unit 23.

[8] Process of Evaluation Value Calculation Unit 22 The evaluation value calculation unit 22 uses the vertex pair set narrowed down by the vertex pair narrowing unit 21 and the new vertex position set {p _k } calculated by the new vertex position calculation unit 11. Among the new vertices included in the new vertex position set {p _k }, the evaluation values of the surface segment distortion and the surface segment roughness are calculated for the vertexes corresponding to the vertex pairs narrowed down by the vertex pair narrowing unit 21.

In this embodiment, stretch is used as an index of surface distortion. Stretching is an index indicating surface distortion, and is defined as inscribed circle radius of surface element × √ (12) / (longest side length of surface element). The stretch for the surface area f is expressed by the following equation (7).

Here, s = (l ₁ ^f + l ₂ ^f + l ₃ ^f ) / 2. As shown in FIG. 10, 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. The evaluation value calculation unit 22 performs the following process using the stretch.

[Calculation of surface distortion evaluation value]
As shown in the following equation (8), the minimum value of the stretch for the surface segment set F _i ∪F _j that contacts the vertex pair (i, j) before integration, and the surface segment set F that contacts the new vertex k after integration. _A distortion minimum value evaluation value is calculated by obtaining a ratio of _k to the minimum stretch value.

Δ _ij ^STmin = min _f′∈Fk STCH (f ′) / min _f∈w STCH (f) (8)
Here, w = F _i ∪F _j .

Further, as shown in the following equation (9), the average value of the stretches for the surface segment set F _i ∪F _j in contact with the vertex pair (i, j) before integration and the surface segment set F k in contact with the new vertex _k. The strain average value evaluation value is calculated by determining the ratio of the average value of the stretch to the.

^{_{Δ ij STave = | w | Σ}} f'∈Fk STCH (f ') / (| F k | Σ f∈w STCH (f)) (9)
When the minimum strain value evaluation value and the average strain value evaluation value are large, there is an extremely distorted surface portion or a mesh with a large average strain near the vertex pair, but after the integration, the strain is extremely distorted near the new vertex. It can be evaluated that it has no surface area and high shape quality.

[Calculation of area density evaluation value]
In order to make the distribution of the surface segments in the mesh uniform, vertex pairs that can remove small surface segments by integration are integrated. For the evaluation value for this purpose, the reciprocal of the total area of each surface in contact with the vertices i and j expressed by the following equation is used.

α _ij = 1 / _{Σf∈Fi∩Fj} Area (f) (10)
Here, Area (f) is the area of the surface segment f. The evaluation value calculation unit 22 outputs the calculated set of evaluation values to the vertex pair selection unit 23.

[9] 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 = Δ _ij ^STmin × Δ _ij ^STave × α _ij (11)
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.

[10] Processing of New Vertex Position Setting Unit 13 The new vertex position setting unit 13 uses the high-density mesh model 6, the new vertex position p _k , and the integrated vertex pair (i, j), and the edge collapse method (Non-Patent Document 4). The position of the new vertex is set by integrating the integrated vertex pair (i, j). 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 high quality mesh model 7 generated in this way.

[11] Iterative processing The mesh simplification unit 3 replaces the high-quality mesh model 7 output from the new vertex position setting unit 13 with the high-density mesh model 6 used in the above processes, and integrates the new vertex position calculation unit 11. 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 high quality mesh model 7 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 4, and if the high-quality mesh model 7 has a larger number of surface segment elements than G, the new vertex position setting unit 13 renews the high-quality mesh model 7. Output to the vertex position calculation unit 11, the integrated vertex pair determination unit 12, and the new vertex position setting unit 13 to repeat the above processes, and stop each process when the number of surface segment elements of the high quality mesh model 7 matches G Let

[12] Application Result and Evaluation Next, the result and evaluation of applying this method will be described.

  FIG. 11A is a diagram illustrating a solid model for generating a low-quality mesh model to be processed by the generation system 1. FIG. 11B shows a low quality mesh model generated by the FEM mesher using the solid model. The number of surface segment elements in this low quality mesh model was 8,720.

FIG. 12A is a diagram showing a high-density mesh model subdivided by the mesh subdivision unit 2 of the generation system 1 using the low-quality mesh model of FIG. 11B, and the number of surface segment elements is 68,844. It has become. The value of the refinement parameter σ _size was 0.2.

FIGS. 12B to 12E are high-quality mesh models simplified by the mesh simplification unit 3 using the high-density mesh model of FIG. 12A, and the number of surface segment elements is 15,000, 9,000, respectively. 6,000 and 3,092. The value of the simplified parameter τ _tol was set to 0.01.

  When processing was performed with a commercially available personal computer, the processing time for subdivision was 2.16 seconds, and the processing time for simplification from FIGS. 12 (a) to 12 (e) was 11.59 seconds.

  FIG. 13 is a graph summarizing the stretch distribution for each mesh model. The graphs (1), (2), (3), (4), and (5) are the meshes of FIGS. 11 (b), 12 (a), (b), (c), and (d), respectively. It corresponds to the model.

  The stretch distribution ((5) in the graph) of the high-quality mesh model with 6,000 area elements generated by this generation system 1 is a mesh model (8) Compared with (1)) of the graph, it was confirmed that a mesh model with a large distribution near the value of 1.0 and less distortion was generated.

  Therefore, according to the present embodiment, the low-quality mesh model is subdivided so as to conform to the subdivision parameters that define the edge line length, thereby improving the degree of freedom of mesh operation, and then simplifying the specification of quality. By simplifying so as to conform to the optimization parameters, it is possible to reliably improve the quality of the low-quality mesh model with high accuracy.

  According to the present embodiment, the simplified parameter is defined as the shape approximation allowable error, and the vertex pair of the subdivided mesh model is narrowed down to the vertex pair that can suppress the shape approximation error of the new vertex to the simplified parameter or less. Thus, vertex pairs suitable for high quality can be targeted for integration.

  According to the present embodiment, the mesh model is generated by setting the new vertex by integrating the narrowed vertex pairs having the largest comprehensive evaluation value regarding the surface distortion and the surface roughness, and generating the mesh model. By replacing the model with a low-quality mesh model and repeating a series of processing, it is possible to achieve high quality with high accuracy and accuracy even for complex shapes.

  According to the present embodiment, each time the process is repeated, the multi-resolution representation in which the number of vertices of the high-quality mesh model is changed by one is performed. The process of changing the surface fraction can be executed at high speed.

  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 can be reduced, and the area between adjacent surfaces can be made uniform.

  According to the present embodiment, when calculating the new vertex k, the position at which the sum of the square distances between the set of surface portions in contact with the vertex pair (i, j) and the new vertex k is the minimum is set as the position of the new vertex k. By calculating, the position of the new vertex k that minimizes the shape approximation error can be calculated.

It is a conceptual diagram which shows the approach of a high quality mesh model production | generation method. It is a functional block diagram which shows the structure of the production | generation system of the high quality mesh model in one Embodiment. It is a functional block diagram which shows the structure of a mesh subdivision part. It is a figure for demonstrating the rule of surface segmentation. It is a functional block diagram which shows the structure of a mesh simplification part. 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 functional block diagram which shows the structure of an integrated vertex pair determination part. FIG. 6A is a diagram showing a surface segment set in contact with a vertex pair before integration, and FIG. 5B is a diagram showing a surface segment set in contact with a new vertex after integration. It is a figure for demonstrating stretch. FIG. 4A shows a solid model, and FIG. 4B shows a high-density mesh model obtained by dividing the mesh. (A) of the figure shows a high-density mesh model subdivided by the generation system, and the number of surface segment elements is 68,844. (B) to (e) are simplified high-quality mesh models. The number of area elements in FIG. (B) is 15,000, and the number of area elements in FIG. (C) is 9,000. The number of area elements in d) is 6,000, and the number of area elements in FIG. It is a graph which shows distribution of the stretch about each mesh model generated by mesh division, subdivision, and simplification.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Generation system of high quality mesh model 2 ... Mesh subdivision part 3 ... Mesh simplification part 4 ... Database 5 ... Low quality mesh model 6 ... High density mesh model 7 ... High quality mesh model 8 ... Ridge midpoint generation part 9 ... Surface segment dividing unit 11 ... New vertex position calculating unit 12 ... Integrated vertex pair determining unit 13 ... New vertex position setting unit 21 ... Vertex pair narrowing unit 22 ... Evaluation value calculating unit 23 ... Vertex pair selecting unit

Claims (12)

A subdivision that reads out a low quality mesh model and subdivision parameters from a database that stores low quality mesh models, subdivision parameters, and simplification parameters, and subdivides each segment element of the low quality mesh model to match the subdivision parameters. And
A new vertex position calculating means for calculating the position of a new vertex when integrating each vertex pair of the subdivided mesh model;
Integrated vertex pair that reads simplified parameters from the database, narrows down vertex pairs whose new vertex positions match the simplified parameters, and determines a vertex pair having the maximum comprehensive evaluation value regarding surface distortion and surface density. A determination means;
New vertex position setting means for setting the position of a new vertex by integrating the determined vertex pair for the subdivided mesh model;
Repeating means for replacing the mesh model generated by the position setting of the new vertex with the subdivided mesh model and causing the new vertex position calculating means, the integrated vertex pair determining means, and the new vertex position setting means to repeat the process. When,
A high-quality mesh model generation system characterized by comprising: The subdivision parameter defines the length of the ridge line of the surface,
The subdivision means includes a ridge line midpoint generation means for generating a midpoint on a ridge line longer than the subdivision parameter;
A surface segmentation means for dividing the surface segment by connecting the midpoint to other midpoints or vertices;
The high-quality mesh model generation system according to claim 1, wherein:   3. The high-quality mesh model generation 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.   3. The high vertex position calculation unit according to claim 1, wherein the new vertex position calculation unit calculates a position at which the sum of the square distances of each surface segment in contact with the vertex pair and the new vertex is minimum as the position of the new vertex. Quality mesh model generation system. The simplification parameter defines a shape approximation tolerance,
The integrated vertex pair determining means includes:
Among the new vertices calculated by the new vertex position calculating means, vertex pair narrowing means for narrowing down vertex pairs corresponding to new vertices whose shape approximation error is equal to or less than the simplified parameter; and
For each narrowed vertex pair, find the ratio between the minimum and average stretch values for each face that touches the vertex pair and the minimum and average stretch values for each face that touches the new vertex. The minimum strain value evaluation value and the average strain value evaluation value are calculated, and the reciprocal of the surface area in contact with the vertex pair is calculated to calculate the surface density evaluation value. An evaluation value calculation means for calculating a comprehensive evaluation value by multiplying the partial density evaluation value;
A vertex pair selecting means for selecting the vertex pair having the maximum comprehensive evaluation value;
5. The high-quality mesh model generation system according to claim 1, comprising: The database stores the number of area 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 high quality mesh model matches the number of surface segment elements. The high quality mesh model generation system according to any one of 1 to 5. Processing to read out the low quality mesh model and subdivision parameters from the database storing the low quality mesh model, subdivision parameters, and simplification parameters, and subdivide each segment element of the low quality mesh model to match the subdivision parameters. When,
A process of calculating the position of a new vertex when integrating each vertex pair of the subdivided mesh model;
A process of reading the simplified parameters from the database, narrowing down the vertex pairs whose new vertex positions match the simplified parameters, and determining the vertex pair having the maximum comprehensive evaluation value regarding surface distortion and surface roughness from among them,
For the subdivided mesh model, a process of setting the position of a new vertex by integrating the determined vertex pair;
A process of repeating the calculation of the position of the new vertex, the determination of the vertex pair, and the setting of the position of the new vertex by replacing the mesh model generated by the position setting of the new vertex with the subdivided mesh model,
A computer program for generating a high-quality mesh model characterized by causing a computer to execute. The subdivision parameter defines the length of the ridge line of the surface,
The subdividing process includes a process of generating a midpoint on a ridge line longer than a subdivision parameter;
Processing to divide the face segment by connecting the midpoint to other midpoints or vertices;
The high-quality mesh model generation program according to claim 7, wherein:   The high-quality mesh model generation program according to claim 7 or 8, 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.   9. The process of calculating the position of the new vertex calculates the position where the sum of the square distance between each surface segment in contact with the vertex pair and the new vertex is the minimum as the position of the new vertex. The high-quality mesh model generation program described. The simplification parameter defines a shape approximation tolerance,
The process of determining the vertex pair is as follows:
Among the calculated new vertices, a process of narrowing down vertex pairs corresponding to new vertices whose shape approximation error is equal to or less than the simplified parameter;
For each narrowed vertex pair, find the ratio between the minimum and average stretch values for each face that touches the vertex pair and the minimum and average stretch values for each face that touches the new vertex. The minimum strain value evaluation value and the average strain value evaluation value are calculated, and the reciprocal of the surface area in contact with the vertex pair is calculated to calculate the surface density evaluation value. A process of calculating a comprehensive evaluation value by multiplying the partial density evaluation value,
A process of selecting a vertex pair having the maximum comprehensive evaluation value;
The high-quality mesh model generation program according to claim 7, wherein: The database stores the number of area elements,
8. The repeating process is characterized in that the number of surface segment elements is read from the database, and is repeated until the number of surface segment elements of the generated high-quality mesh model matches the number of surface segment elements. The high quality mesh model generation program according to any one of claims 11 to 11.