WO2019229965A1

WO2019229965A1 - Mesh generation system, mesh generation program, and mesh generation method

Info

Publication number: WO2019229965A1
Application number: PCT/JP2018/021098
Authority: WO
Inventors: 朋典菅野
Original assignee: 株式会社プルートス
Priority date: 2018-06-01
Filing date: 2018-06-01
Publication date: 2019-12-05
Also published as: TW202004538A; JP7036207B2; JPWO2019229965A1

Abstract

[Problem] To provide a novel mesh generation method for generating a mesh of high quality. [Solution] According to the present invention, a data conversion unit 2 converts structure data about an object into shape data that is represented by a polytope. A one-dimensional processing unit 3 divides a side of a one-dimensional polytope on the basis of a specific reference length, as a one-dimensional crystallization process for the shape data. An n-dimensional processing unit 4 fills the inside of the n-dimensional polytope with an agent group, as an n-dimensional (n is the number of dimensions of at least 2) crystallization process for the shape data. In the filling process, agents are arranged inside the n-dimensional polytope in a shape by which quality indexes of the agents are maximally favorable. In addition, the shapes of adjacent agents are optimized so that the sum of quality indexes in the adjacent agents in the n-dimensional polytope is better than that in the current state. A mesh generation unit 5 generates a mesh on the basis of the agent group filled inside the n-dimensional polytope.

Description

Mesh generation system, mesh generation program, and mesh generation method

The present invention relates to a mesh generation system, a mesh generation program, and a mesh generation method, and particularly to a mesh generation method using an agent-based model (ABM).

For example, Patent Document 1 describes an automatic mesh generation method for generating an optimal mesh even with a non-manifold shape data structure by bubble filling using a dynamic model. Specifically, first, a plurality of bubbles are arranged on the vertices and ridgelines of the non-manifold data model. Next, based on the force between the bubbles and the bubble mass, the bubble is moved by solving the Newton equation using numerical analysis techniques, including the viscosity term, and when the bubble movement is stabilized to some extent, the center point of the bubble is connected. Generate a line segment. Next, place the bubble on the surface of the non-manifold data model, move the bubble in the same way, and connect the center point of the bubble with a two-dimensional Delaunay triangulation when the movement of the bubble is stabilized to some extent. Generate triangular elements. Finally, after placing the bubble inside the solid area of the non-manifold data model and moving the bubble, when the movement of the bubble is stabilized to some extent, connect the center point of the bubble with a three-dimensional Delaunay triangulation, Create a body element.

Japanese Patent Laid-Open No. 7-230487

An object of the present invention is to provide a novel mesh generation method for generating a high-quality mesh.

In order to solve this problem, the first invention provides a mesh generation system that includes a data conversion unit, a one-dimensional processing unit, an n-dimensional processing unit, and a mesh generation unit, and uses an agent-based model. . The data conversion unit converts the structure data of the object into shape data expressed by a polytope. The one-dimensional processing unit divides a side that is a one-dimensional polytope based on a specific reference length as a one-dimensional process for shape data. The n-dimensional processing unit fills the n-dimensional polytope with an agent group as n-dimensional processing for shape data that has been processed in (n-1) dimensions (where n is a dimension number of 2 or more). In this filling process, the agent is arranged in the n-dimensional polytope in a shape that maximizes the quality index of the agent. At the same time, the shape of the adjacent agents is optimized so that the total quality index of the adjacent agents in the n-dimensional polytope becomes better than the current state. The quality index indicates the shape quality of the agent, and is calculated for each agent using a predetermined objective function. The mesh generation unit generates a mesh based on the agent group filled in the n-dimensional polytope.

Here, in the first invention, the quality index is preferably better as the variation in the inner angle at the agent is smaller, and in addition, the quality index is preferably as the variation in the edge length at the agent is smaller.

In the first invention, the one-dimensional processing unit preferably adjusts the number of divisions of the one-dimensional polytope possessed by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. The one-dimensional processing unit may adjust the reference length according to at least one of the physical property and the surface shape of the object.

In the first invention, the n-dimensional processing unit may perform n-dimensional processing on a polytope having a facet number other than 2n, and may not perform n-dimensional processing on a polytope having a facet number of 2n. preferable. The number of facets of the agent is preferably 2n.

In the first invention, a polytope management unit may be provided. The polytope management unit manages the polytope master-slave relationship between dimensions in the shape data, and updates the polytope master-slave relationship according to the one-dimensional process and the n-dimensional process. The mesh generation unit may generate a mesh by further subdividing an agent group filled in an n-dimensional polytope.

The second invention provides a mesh generation program using an agent-based model that causes a computer to execute a process having the first to fourth steps. In the first step, the structure data of the object is converted into shape data expressed by a polytope. In the second step, as a one-dimensional process for the shape data, a side that is a one-dimensional polytope is divided based on a specific reference length. In the third step, the n-dimensional polytope is filled with an agent group as n-dimensional processing for shape data that has been processed in (n-1) dimensions (n is a dimension number of 2 or more). In this filling process, an agent is placed in the n-dimensional polytope in a shape that maximizes the quality index. At the same time, the shape of the adjacent agents is optimized so that the total quality index of the adjacent agents in the n-dimensional polytope becomes better than the current state. The quality index indicates the shape quality of the agent, and is calculated for each agent using a predetermined objective function. In the fourth step, a mesh is generated based on the agent group filled in the n-dimensional polytope.

Here, in the second invention, the quality index is preferably better as the variation in the internal angle at the agent is smaller, and in addition to this, the quality index is preferably as the variation in the edge length at the agent is smaller.

In the second invention, it is preferable that the second step includes a step of adjusting the number of divisions of the one-dimensional polytope possessed by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. The second step may include a step of adjusting the reference length according to at least one of the physical property and surface shape of the object.

In the second invention, it is preferable that the n-dimensional processing in step 3 is executed for a polytope having a facet number not 2n and not for a polytope having a facet number 2n. The number of facets of the agent is preferably 2n.

In the second invention, the computer may further execute processing having a fifth step. In a fifth step, the master-slave relationship between dimensions in the shape data is managed, and the master-slave relationship is updated according to the one-dimensional process and the n-dimensional process. Further, the fourth step may include a step of further subdividing the agent group filled in the n-dimensional polytope.

The third invention provides a mesh generation method using the agent-based model, which includes the first step to the fourth step. In the first step, the structure data of the object is converted into shape data expressed by a polytope. In the second step, as a one-dimensional process for the shape data, a side that is a one-dimensional polytope is divided based on a specific reference length. In the third step, the n-dimensional polytope is filled with an agent group as n-dimensional processing for shape data that has been processed in (n-1) dimensions (n is a dimension number of 2 or more). In this filling process, an agent is placed in the n-dimensional polytope in a shape that maximizes the quality index. At the same time, the shape of the adjacent agents is optimized so that the total quality index of the adjacent agents in the n-dimensional polytope becomes better than the current state. The quality index indicates the shape quality of the agent, and is calculated for each agent using a predetermined objective function. In the fourth step, a mesh is generated based on the agent group filled in the n-dimensional polytope.

According to the present invention, the shape data converted from the structure data and represented by the polytope is divided into one-dimensional polytope sides based on the reference length, and (n−1) -dimensional processing is performed. As an n-dimensional process for the shape data performed, agents are arranged in an n-dimensional polytope. The size of the agent depends on the reference length, and its shape is set so that the quality index is as good as possible. Further, the shapes of the adjacent agents are optimized so that the sum of these quality indexes is better than the current state, that is, the state before the optimization is performed. Thereby, the internal space of the n-dimensional polytope is filled and subdivided without gaps by the agent group having a good shape, so that a high-quality mesh can be generated.

Block diagram of mesh generation system Flow chart of mesh generation process Diagram showing 2D structure data Diagram showing 2D shape data Conceptual diagram showing the master-detail relationship of polytopes between dimensions Figure showing shape data after one-dimensional crystallization treatment Flow chart of n-dimensional crystallization processing routine Illustration of a simple method for agent shape optimization Illustration of arrangement of agents A1 and A2 Illustration of arrangement of agent A3 Explanation of optimization of agent shape accompanying arrangement of agent A3 Illustration of arrangement of agent A4 Illustration of arrangement of agent A5 Explanatory drawing of filling state by agent groups A1 to A9 Diagram showing mesh data

FIG. 1 is a block diagram of a mesh generation system according to the present embodiment. The mesh generation system 1 receives the structure data of an object, and outputs mesh data representing the shape of the object as a mesh. In the mesh generation process, an agent-based model (ABM) is used. Here, the “agent-based model” is one of simulation models for evaluating the influence of autonomous agent behavior and interaction between agents on the entire system, and is called multi-agent simulation. Sometimes. An “agent” refers to a subject that acts autonomously under predetermined rules based on the situation of the person and the situation around him. The feature of this embodiment is that an agent-based model is used to subdivide an object area. More specifically, agents are arranged in an internal space of a certain area while considering the interaction of adjacent agents. Then, the mesh is generated based on the agent group filled in this region.

The mesh generation system 1 includes a data conversion unit 2, a one-dimensional processing unit 3, an n-dimensional processing unit 4, a mesh generation unit 5, and a polytope management unit 6. The data converter 2 converts the structure data input as a processing target into shape data. The structure data before conversion is data in an arbitrary format that defines the structure (including shape) of the object, and is two-dimensional CAD data, or three-dimensional CAD data such as a STEP format or an STL format. This structure data may include a curve or a curved surface as a shape defined by itself. On the other hand, the converted shape data is data representing the shape of an object with a polytope. In particular, when the structure data includes a curve or a curved surface, these are discretized by line segments, and the curve is approximated by a straight line group and the curved surface is approximated by a plane group. The manner of implementation of shape data (class definition) is arbitrary, but as will be described later, it is preferable to maintain and manage the correspondence between polytopes and facets because of the crystallization process that refers to different dimensions. Here, “polytope” refers to a super polyhedron in elementary geometry. A zero-dimensional polytope is “point”, a one-dimensional polytope is “side”, a two-dimensional polytope is “face”, and a three-dimensional polytope is “solid”. is there. “Facet” refers to a one-dimensional lower polytope owned by a one-dimensional polytope. For example, a “surface” for a three-dimensional polytope (solid), a “side” for a two-dimensional polytope (surface), and a “point” for a one-dimensional polytope (side) correspond to facets.

The one-dimensional processing unit 3 divides a side that is a one-dimensional polytope based on a specific reference length as a one-dimensional crystallization process for the shape data converted by the data conversion unit 2. The one-dimensional crystallization process is performed on the one-dimensional polytope (side) included in the shape data that satisfies the conditions described later. Here, the reference length is defined by the user, and thereby the size of the agent is defined. Specifically, the longer the reference length, the larger the agent (region resolution = coarse), and the shorter the reference length, the smaller the agent (region resolution = fine). In addition, a fixed value may be fixedly applied to the entire object, but a variable value may be applied according to at least one of the physical properties and the surface shape of the object. For example, the reference length is made shorter than the other parts for a part where the material is soft and easily deformed, and the reference length is made shorter than the other part for a part having a large surface curvature.

The n-dimensional processing unit 4 uses the internal space of the n-dimensional polytope as an agent group (agents) as an n-dimensional crystallization process for shape data that has been processed in (n-1) dimensions (n is a dimension number of 2 or more). The number of dimensions = n). For example, when n = 2, a two-dimensional crystallization process is performed on the shape data subjected to the one-dimensional crystallization process by the one-dimensional processing unit 3, and the internal space of the two-dimensional polytope (surface) is 2 Filled and subdivided by dimension agents. Further, when n = 3, the three-dimensional crystallization process is performed on the shape data subjected to the two-dimensional crystallization process by the n-dimensional processing unit 4, and the internal space of the three-dimensional polytope (solid) is 3 Filled and subdivided by dimension agents. The upper limit of n that can be expected to be effective is considered to be 4, that is, a four-dimensional polytope (polychoron), but does not specifically exclude n ≧ 5.

In the n-dimensional crystallization process excluding the first dimension, agents that are autonomous behavior subjects are individually placed in the internal space of the n-dimensional polytope. A plurality of adjacent agents (adjacent agents) in the internal space interact with each other, and the shapes of these agents are optimized based on the interaction. The shape of each agent and the optimized shape of neighboring agents including itself are determined based on the concept of quality index. As will be described in detail later, this quality index indicates the shape quality of the agent and is calculated for each agent by a predetermined objective function (utility function). Generally speaking, the individual shape of an agent is set so that the quality index of the agent is as good as possible. Further, the optimized shape of the neighboring agent including itself is set so that the sum of these quality indexes is better than the current state, that is, the state before being optimized.

The n-dimensional processing unit 4 executes the crystallization process with the number of times corresponding to the number of dimensions of mesh data that is the output target. For example, when outputting two-dimensional mesh data, a single process called a crystallization process for a two-dimensional polytope (plane) is performed. Further, when outputting three-dimensional mesh data, a total of two processes, a crystallization process for a two-dimensional polytope (plane) and a subsequent crystallization process for a three-dimensional polytope (solid), are performed.

The mesh generation unit 5 generates a mesh expressed by an element group such as a quadrangle and a hexahedron based on the agent group filled in the n-dimensional polytope. At that time, in order to ensure a desired mesh resolution, the inside of each agent may be further subdivided, for example, by equally dividing the inside of each agent. The generated mesh is converted into a predetermined output format and then output to the outside as mesh data.

The polytope management unit 6 has a master-slave relationship between dimensions in the shape data converted by the data conversion unit 2 in the memory space of the mesh generation system 1, that is, the low-dimensional polytope that the high-dimensional polytope owns. Memorize and manage if you are. Specifically, when the shape data is generated by the data conversion unit 2, the master-slave relationship of the polytope related to the shape data is registered. Also, in the processing process of the one-dimensional processing unit 3, the master-slave relationship of the polytope is updated as needed in accordance with the division of the one-dimensional polytope (side) and the addition of the zero-dimensional polytope (point) associated therewith. Further, in the process of the n-dimensional processing unit 4, the master-slave relationship of the polytope is updated as needed according to the subdivision of the n-dimensional polytope. The master-slave relationship of the polytope managed by the polytope management unit 6 is referred to by both the one-dimensional processing unit 3 and the n-dimensional processing unit 4 as needed.

FIG. 2 is a flowchart of the mesh generation process. The mesh generation process shown in the figure is realized by installing a program (mesh generation program) in a computer and operating the computer according to a procedure defined by the program. Hereinafter, the contents of this processing will be described in detail by taking the two-dimensional structure data having the shape shown in FIG. First, in step 1, structure data to be processed is input to the data conversion unit 2.

Next, in step 2, the data conversion unit 2 converts the structure data into shape data. For example, the two-dimensional structure data shown in FIG. 3 is converted into the two-dimensional shape data shown in FIG. Specifically, three points in the structure data are converted into 0-dimensional polytopes P0 (1) to P0 (3), and two straight lines are converted into one-dimensional polytopes P1 (1) to P1 (2). Further, in the process of converting to shape data, the single arc shown in FIG. 3 is linearly approximated by a plurality of line segments. As a result, each of the connection points connecting adjacent line segments is converted into 0-dimensional polytopes P0 (4) to P0 (6), and the respective line segments are converted into 1-dimensional polytopes P1 (3) to P1 (6). Converted.

FIG. 5 is a conceptual diagram showing a polytope master-slave relationship with respect to the shape data of FIG. The master-slave relationship of the polytope defines the relationship between the polytope and the facet for each dimension, such as a one-dimensional polytope P1 owned by the two-dimensional polytope P2 and a zero-dimensional polytope P0 owned by the one-dimensional polytope P2. In the example shown in the figure, the two-dimensional polytope P2 (1) has six one-dimensional polytopes P1 (1) to P1 (6) as facets (sides). For example, the one-dimensional polytope P1 (1) has two 0-dimensional polytopes P0 (1) and P0 (2) as facets (points). When there are a plurality of two-dimensional polytopes P2, the master-slave relationship of the polytopes as described above is managed for each two-dimensional polytope P2. In the case of three-dimensional shape data, the master-slave relationship of the polytope including the three-dimensional polytope (surface) is managed. Although the subsequent description is omitted, the master-slave relationship of the polytope is changed / updated as needed in the process of

steps

3 and 4 below.

In step 3, the one-dimensional processing unit 3 performs a one-dimensional crystallization process using a specific reference length. The target of the one-dimensional crystallization process is a one-dimensional polytope P1 longer than the reference length, and this one-dimensional polytope P1 (side) is divided into lengths about the reference length. As the number of sides divided, for example, the length of the one-dimensional polytope P1 can be divided by a reference length, and the divided value can be rounded down or rounded up.

FIG. 6 is a diagram showing shape data after a one-dimensional crystallization process. Each of the one-dimensional polytopes P1 (1) and P1 (2) corresponding to one side shown in FIG. 4 is divided into three. As a result, the one-dimensional polytope P1 (1) is deleted. Instead, three one-dimensional polytopes P1 (1-1) to P1 (1-3) and two zero-dimensional polytopes P0 (7) to P0 ( 8) and are added. Similarly, the one-dimensional polytope P1 (2) is deleted. Instead, three one-dimensional polytopes P1 (2-1) to P1 (2-3) and two zero-dimensional polytopes P0 (9) to P0 ( 10) and are added.

In the one-dimensional crystallization process, the number of divisions of the one-dimensional polytope P1 is adjusted so that the number of one-dimensional polytopes P1 owned by the two-dimensional polytope P2, that is, the number of facets of the two-dimensional polytope P2 is an even number. In the example of FIG. 6, the number of facets of the two-dimensional polytope P2 (1) is 10, so this condition is satisfied. The reason for adjusting the number of divisions is to prevent occurrence of exception processing for the polytope by preventing the occurrence of a polytope other than the facet number 2n (n is the number of dimensions) in the subsequent processing steps. In the case of a conventional mesher, a triangle in a square or a tetrahedron in a hexahedron may be mixed in the process of meshing. Therefore, special exception processing needs to be performed to remove these. On the other hand, in the present method, by adjusting the even number as described above, it is possible to effectively suppress the occurrence of a polytope having a facet number other than 2n in the subsequent processing.

In step 4, the n-dimensional processing unit 4 performs an n-dimensional crystallization process using an agent that is an autonomous action subject. FIG. 7 is a flowchart of an n-dimensional crystallization processing routine. First, in step 41, an n-dimensional polytope to be processed (for example, the two-dimensional polytope P2 (1) shown in FIG. 6) is designated. The n-dimensional polytope to be processed has a facet number that is not 2n, specifically, the facet number of the two-dimensional polytope is not 4 in the two-dimensional crystallization process, and the facet of the three-dimensional polytope in the three-dimensional crystallization process The condition is that the number is not six. That is, the n-dimensional crystallization process is performed on a polytope having a facet number other than 2n, and if the number of facets is 2n, the polytope itself can be an agent. Absent.

Next, in step 42, an agent placement location is specified in the processing target internal space specified in step 41. Although what kind of rule is set as the agent placement location and its order is arbitrary, in this embodiment, as shown in FIG. 14, as an example, as shown in FIG. 14, (i) placement at two ends (A1 → A2), (ii) Arrangement on the side connecting them (A3), (iii) Arrangement on all sides based on the above (i) and (ii) (A4 → A5 → A6 → A7), ( iv) The individual agents are sequentially arranged in the order of arrangement inside the space (A8).

The following rules can be cited as rules regarding the placement of agents. As a first rule, the number of facets of the agent is 2n. That is, the two-dimensional agent in the two-dimensional crystallization process is a rectangle, and the three-dimensional agent in the three-dimensional crystallization process is a hexahedron. This is because the two-dimensional shape is represented by a quadrilateral mesh and the three-dimensional shape is represented by a hexahedral mesh. As a second rule, agent facets share existing facets in the vicinity of the agent's location. An “existing facet” is a facet of an n-dimensional polytope to which an agent belongs, or a facet of another agent already arranged in the n-dimensional polytope. This is because the agents are arranged without gaps in the internal space of the n-dimensional polytope.

In step 43, the shape of the agent is set so that the quality index Q of the agent is as good as possible. As described above, the agent quality index Q indicates the shape quality of the agent, and can be, for example, the “dissatisfaction level” calculated by the following objective function.

(Dissatisfaction) = (Inner angle variance) * a + (Edge length (longest / shortest)) * b

In the above formula, a and b are user-defined constants. Further, (dispersion of inner angle) indicates variation in inner angle in the agent. If the agent is a quadrangle, there are four internal angles θi (i = 4), and if the agent is a hexahedron, there are 24 internal angles θi (i = 24), and their variances are calculated based on the following equation. In addition, the variation of the inner angle may be evaluated by an index representing the degree of dispersion such as (maximum / minimum) of the inner angle instead of the dispersion of the inner angle.

(Inner angle dispersion) = 1 / N * Σ (θi−Π / 2) ²

The edge length (longest / shortest), that is, the length-to-short ratio of the edge length indicates the variation of the edge length in the agent. Here, the “edge length” is the length of the side, that is, the one-dimensional polytope P1, in the case of a two-dimensional crystallization process. Note that the variation in edge length may be evaluated by an index representing the degree of dispersion such as edge dispersion instead of the edge length ratio.

The degree of dissatisfaction becomes smaller as the variation in the inner angle becomes smaller and the variation in the edge length becomes smaller, and the square and the regular hexahedron are minimized. Then, the smaller the dissatisfaction level, the better the shape quality of the agent, and the higher the dissatisfaction level, the less good the quality. As can be understood from this tendency, the shape that “quality index Q is maximally favorable” is a shape that is as close as possible to a square or a regular hexahedron under the constraint of sharing existing facets. It can be said. Note that “the quality index Q is maximally favorable” may be on condition that the quality index Q takes the maximum value. For example, the degree of dissatisfaction is smaller than a predetermined threshold, or This condition may be satisfied if the quality index Q exceeds the predetermined threshold value so that the happiness level described is greater than the predetermined threshold value.

The quality index Q is not limited to the above mathematical formula, but can be various. For example, only the variation in the inner angle may be evaluated without considering the variation in the edge length. Further, in addition to the variation in the internal angle, the evaluation may be performed in consideration of other requirements (for example, the edge length should be as large as possible). Further, a value obtained by multiplying the degree of dissatisfaction in the above formula by −1 may be used as the “happiness level”, and this happiness level may be used as the evaluation index Q. In this case, the higher the happiness level, the better the shape quality of the agent, and the lower the happiness level, the lower the quality.

In step 44, these shapes are optimized (smoothing) for a plurality of agents (including self) adjacent in the internal space of the n-dimensional polytope. This optimization is achieved by performing a modification such that the sum of the individual quality indexes Q of neighboring agents including itself, that is, the overall quality index Qsum is better than the current state, that is, the state before the optimization is performed. Is done.

Here, the overall quality index Qsum (hereinafter referred to as “function U”) is determined depending on each interior angle (θ) and each edge length (l). Since it can be expressed by the vector x), it can be expressed as follows.

At this time, an arbitrary movement amount of P0 (Δ vector xi) is defined as follows.

This operation is repeated at the timing of shape optimization. The condition for the repetition end is that | Δvector x | / Δt falls below a predetermined threshold for all i.

In the above simulation, the increase of the overall quality index Qsum is strictly guaranteed by making Δt sufficiently small. However, when the calculation cost is very high, a simple method that approximates the calculation can be used. In this simple method, the amount of movement of each P0 is a value (δ vector xlength) derived from the difference between the length of P1 and the reference length (δ vector xlength), and a value derived from the deviation from π / 2 of the angle formed by P1 (δ vector). xangle). At each time step, two values are evaluated for each agent and the amount of movement is added to P0. At the timing when the evaluation for all agents is completed, P0 is actually calculated by the total amount of movement (Δ vector x). Move.

FIG. 8 is an explanatory diagram of a simple method for optimizing the agent shape. The figure illustrates P0 connected by two P1. For simplicity, the description will be made by replacing two P1 with vectors Vi and Vj, respectively.

However, kangle and klength are predetermined constants proportional to the degree of dissatisfaction of the agent. Further, in the above formula, an operation symbol that adds the operands while incrementing the iterator i by 1 under a certain condition (cond.) Is expressed as follows.

The above simple method does not directly calculate the overall quality index Qsum, but as a result of processing based on this, a modification is made so that the overall quality index Qsum is better than the current state. In the flowchart shown in FIG. 7, the shape optimization is performed every time the agent is arranged. However, it is not always necessary to perform the shape optimization, and may be performed only when a predetermined condition is satisfied.

In step 45, it is determined whether or not the internal space of the n-dimensional polytope to be processed has been filled by the agent group. If the determination result is negative, that is, if the filling in the n-dimensional polytope has not been completed, the processing target is shifted to the next agent (step 46), and the processing for this agent is performed (step 42). ~ 44). If the filling in the n-dimensional polytope is completed by the repetition process for each agent, the determination result in step 45 changes from negative to affirmative, and the process proceeds to step 47.

In step 47, it is determined whether or not processing for all n-dimensional polytopes has been completed. If this determination result is negative, that is, if processing for all polytopes belonging to the same dimension has not been completed, the processing target is shifted to the next polytope in the same dimension (step 48), and the same processing is performed. (Steps 41 to 46). Then, by repeating the processing for each polytope in the same dimension, when the processing of all the polytopes is completed, the determination result of step 47 is changed from negative to affirmative, and this routine ends.

In the case of generating a two-dimensional mesh, the processing in step 4 ends when the two-dimensional crystallization process ends. Further, when generating a three-dimensional mesh, a two-dimensional crystallization process is followed by a three-dimensional crystallization process for a three-dimensional polytope.

Hereinafter, the filling process of the two-dimensional polytope P2 (1) by the agent group will be described with reference to FIGS. First, as shown in FIG. 9, the agent A1 is arranged at the lower right end of the two-dimensional polytope P2 (1). Agent A1 shares facets P1 (2-3) and P1 (1-1) owned by two-dimensional polytope P2 (1). As a mounting method related to facet sharing, for example, it can be handled by separately generating and possessing a mirrored facet called a conjugate facet. The degree of freedom left under the constraint condition in which the three points P0 (1), P0 (7), and P0 (10) have already been identified is the location of the remaining point X1. The point X1 is arranged at a position where the quality index Q1 of the agent A1 is maximally favorable, whereby the shape of the agent A1 is determined. For agent A1, since there is no adjacent agent, shape optimization is not performed.

Next, the agent A2 is arranged at the lower left corner of the two-dimensional polytope P2 (1). Agent A2 shares facets P1 (2-1) and P1 (6) owned by the two-dimensional polytope P2 (1). The degree of freedom left under the constraint conditions in which the three points P0 (3), P0 (6), and P0 (9) have already been identified is the location of the remaining point X2. The point X2 is arranged at a position where the quality index Q2 of the agent A2 is maximally favorable, whereby the shape of the agent A2 is determined. For agent A2, since there is no adjacent agent, shape optimization is not performed.

Next, as shown in FIG. 10, an agent A3 is arranged between the two agents A1 and A2. Agent A3 shares facet P1 (2-2) owned by two-dimensional polytope P2 (1) and the facets of agents A1 and A2. Therefore, the shape of the agent A4 is uniquely specified without evaluating the quality index Q3 of the agent A3. The agent A3 is adjacent to the two agents A1 and A2. Therefore, the shapes of the agents A1 to A3 are optimized so that the total quality index Qsum of the three agents A1 to A3 is better than the current state. As a result, the shapes of the agents A1 to A3 are optimized from the broken line state to the solid line state as shown in FIG.

Next, as shown in FIG. 12, an agent A4 is arranged at the upper right end of the two-dimensional polytope P2 (1). Agent A4 shares facets P1 (1-3) and P1 (3) owned by the two-dimensional polytope P2 (1). Under this constraint condition, the shape of the agent A4 is determined so that the quality index Q4 of the agent A4 is as good as possible. For agent A4, since there is no adjacent agent, shape optimization is not performed.

Next, as shown in FIG. 13, an agent A5 is arranged between the two agents A1 and A4. Agent A5 shares facet P1 (1-2) owned by two-dimensional polytope P2 (1) and the facets of agents A1 and A4. Therefore, the shape of the agent A5 is uniquely identified without evaluating the quality index Q5 of the agent A5. The agent A5 is adjacent to the two agents A1 and A2. Therefore, the shapes of the agents A1 to A3 are optimized from the broken line state to the solid line state so that the overall quality index Qsum of the three agents A1, A4, A5 is better than the current state.

Thereafter, as shown in FIG. 14, the agents A6 to A8 are sequentially arranged with the optimization of the shape. As a result, the internal space of the two-dimensional polytope P2 (1) is filled without gaps by the eight agents A1 to A8.

In step 5, mesh data is generated by the mesh generation unit 5. In this process, the agent area is equally divided as necessary, and mesh data as shown in FIG. 15 is generated. The generated mesh data is output to the outside as final output data.

Thus, according to the present embodiment, the side which is the one-dimensional polytope P1 is divided based on the reference length with respect to the shape data converted from the structure data and expressed by the polytope. Then, an agent is arranged in the n-dimensional polytope as an n-dimensional process for the shape data subjected to the (n−1) -dimensional process. The size of the agent depends on the reference length, and its shape is set so that the agent quality index Q is as good as possible. Further, the shapes of the adjacent agents are optimized so that the overall quality index Qsum is better than the current state, that is, the state before the optimization is performed. Thereby, the internal space of the n-dimensional polytope is filled and subdivided without gaps by the agent group having a good shape, so that a high-quality mesh can be generated.

Further, according to the present embodiment, the one-dimensional processing unit 3 and the n-dimensional processing unit 4 are combined, and in the case of two-dimensional data, crystallization processing from one dimension to two dimensions is performed, and in the case of three-dimensional data, 1 By performing the crystallization process from the 3rd dimension to the 3rd dimension, meshing of almost any shape can be stably performed, and the completion of the meshing can be guaranteed without requiring exception processing. The ability to prevent the inability to continue in the middle of meshing is very important and effective in comparison with conventional meshers.

Furthermore, according to the present embodiment, it is possible to improve the customization as a mesher. In the process of actually creating a mesh, in addition to simply cutting the mesh uniformly, the fineness of the mesh is often adjusted according to conditions such as physical properties (for example, material) and surface shape (for example, curvature) of the object. . In the present embodiment, these factors can be automatically reflected on the fineness of the mesh by adjusting the reference length according to at least one of the physical properties and the surface shape of the object.

In the above-described embodiment, an example of the sequential processing in which agents are sequentially arranged in the internal space of the n-dimensional polytope in the n-dimensional crystallization processing has been described. However, in order to increase the processing speed, it is possible. Within a range, parallel processing in which a plurality of agents are arranged in parallel may be performed. For example, the agents A1 to A3 shown in FIG. 14 are independent of each other and do not need to consider the interaction with other agents, and thus can be processed in parallel.

DESCRIPTION OF SYMBOLS 1 Mesh generation system 2 Data conversion part 3 One-dimensional processing part 4 n-dimensional processing part 5 Mesh generation part 6 Polytope management part

Claims

In a mesh generation system using an agent-based model,
A data conversion unit that converts the structure data of the object into shape data expressed in a polytope;
As a one-dimensional process for the shape data, a one-dimensional processing unit that divides a side that is a one-dimensional polytope based on a specific reference length;
(N-1) Indicates the shape quality of the agent as n-dimensional processing for shape data that has been processed in dimension (n is a dimension number of 2 or more), and is calculated for each agent using a predetermined objective function. An agent is arranged in the n-dimensional polytope in such a shape that the quality index to be obtained is as good as possible, and the sum of the quality indices in the adjacent agents in the n-dimensional polytope becomes better than the current state. As described above, an n-dimensional processing unit that fills the n-dimensional polytope with an agent group by optimizing the shape of adjacent agents;
A mesh generation system comprising: a mesh generation unit configured to generate a mesh based on a group of agents filled in the n-dimensional polytope.
The mesh generation system according to claim 1, wherein the quality index is better as the variation in the inner angle of the agent is smaller.
3. The mesh generation system according to claim 2, wherein the quality index is better as the variation in edge length in the agent is smaller.
The mesh generation according to claim 1, wherein the one-dimensional processing unit adjusts the number of divisions of the one-dimensional polytope possessed by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. system.
The mesh generation system according to claim 1, wherein the one-dimensional processing unit adjusts the reference length according to at least one of a physical property and a surface shape of the object.
The n-dimensional processing unit performs the n-dimensional process on a polytope having a facet number other than 2n, and does not perform the n-dimensional process on a polytope having a facet number of 2n. The mesh generation system according to claim 1.
The mesh generation system according to claim 1, wherein the number of facets of the agent is 2n.
The system further comprises a polytope management unit that manages a master-slave relationship between dimensions in the shape data and updates the master-slave relationship according to the one-dimensional process and the n-dimensional process. The mesh generation system described in 1.
The mesh generation system according to claim 1, wherein the mesh generation unit generates the mesh by further subdividing an agent group filled in the n-dimensional polytope.
In the mesh generation program using the agent base model,
A first step of converting the structure data of the object into shape data expressed in a polytope;
As a one-dimensional process for the shape data, a second step of dividing a side that is a one-dimensional polytope based on a specific reference length;
(N-1) Indicates the shape quality of the agent as n-dimensional processing for shape data that has been processed in dimension (n is a dimension number of 2 or more), and is calculated for each agent using a predetermined objective function. An agent is arranged in the n-dimensional polytope in such a shape that the quality index to be obtained is as good as possible, and the sum of the quality indices in the adjacent agents in the n-dimensional polytope becomes better than the current state. A third step of filling the n-dimensional polytope with agents by optimizing the shape of adjacent agents,
A mesh generation program that causes a computer to execute a process including a fourth step of generating a mesh based on an agent group filled in the n-dimensional polytope.
The mesh generation program according to claim 10, wherein the quality index is better as the variation in the inner angle of the agent is smaller.
12. The mesh generation program according to claim 11, wherein the quality index is better as the variation in edge length in the agent is smaller.
11. The method of claim 10, wherein the second step includes adjusting the number of divisions of the one-dimensional polytope possessed by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. Mesh generation program.
11. The mesh generation program according to claim 10, wherein the second step includes a step of adjusting the reference length according to at least one of a physical property and a surface shape of the object.
11. The n-dimensional process in step 3 is performed for a polytope having a facet number other than 2n, and is not performed for a polytope having a facet number of 2n. The described mesh generation program.
The mesh generation program according to claim 10, wherein the number of facets of the agent is 2n.
5. The method further comprises a fifth step of managing a master-slave relationship between dimensions in the shape data, and updating the master-slave relationship according to the one-dimensional process and the n-dimensional process. Item 15. A mesh generation program according to item 10.
The mesh generation program according to claim 10, wherein the fourth step includes a step of further subdividing the agent group filled in the n-dimensional polytope.
In the mesh generation method using the agent base model,
A first step of converting the structure data of the object into shape data expressed in a polytope;
As a one-dimensional process for the shape data, a second step of dividing a side that is a one-dimensional polytope based on a specific reference length;
(N-1) Indicates the shape quality of the agent as n-dimensional processing for shape data that has been processed in dimension (n is a dimension number of 2 or more), and is calculated for each agent using a predetermined objective function. An agent is arranged in the n-dimensional polytope in such a shape that the quality index to be obtained is as good as possible, and the sum of the quality indices in the adjacent agents in the n-dimensional polytope becomes better than the current state. A third step of filling the n-dimensional polytope with agents by optimizing the shape of each of the neighboring agents,
And a fourth step of generating a mesh based on the agent group filled in the n-dimensional polytope.