JP7036207B2 - Mesh generation system, mesh generation program and mesh generation method - Google Patents

Description

The present invention relates to a mesh generation system, a mesh generation program, and a mesh generation method, and more 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 optimum mesh even for a non-manifold-shaped data structure by bubble filling using a kinetic model. Specifically, first, a plurality of bubbles are placed on the vertices and ridges of the non-manifold data model. Next, based on the inter-bubble force and bubble mass, the Newton equation including the viscosity term is solved by numerical analysis technique to move the bubble, and when the movement of the bubble is stable 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 when the movement of the bubble stabilizes to some extent, connect the center points of the bubble with a two-dimensional Delaunay triangulation. Generate a triangular element. Finally, place the bubble inside the solid region of the non-manifold data model, move the bubble, and when the movement of the bubble stabilizes to some extent, connect the center points of the bubble with a three-dimensional Delaunay triangulation to form four faces. Generate a body element.

Japanese Unexamined Patent Publication No. 7-23487

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

In order to solve such a problem, the first invention provides a mesh generation system having a data conversion unit, a one-dimensional processing unit, an n-dimensional processing unit, and a mesh generation unit, and using an agent-based model. .. The data conversion unit converts the structural 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 one-dimensional processing 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 (n is a number of dimensions 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 is better than the current one. The quality index indicates the shape quality of the agent, and is calculated for each agent by a predetermined objective function. The mesh generation unit generates a mesh based on a group of agents filled in an n-dimensional polytope.

Here, in the first invention, it is preferable that the quality index is better as the variation in the internal angle in the agent is smaller, and in addition, it is preferable that the quality index is better as the variation in the edge length in the agent is smaller.

In the first invention, it is preferable that the one-dimensional processing unit adjusts the number of divisions of the one-dimensional polytope owned by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. Further, the one-dimensional processing unit may adjust the reference length according to at least one of the physical characteristics and the surface shape of the object.

In the first invention, the n-dimensional processing unit performs n-dimensional processing on a polytope having a facet number of not 2n, and does not perform n-dimensional processing on a polytope having a facet number of 2n. preferable. Further, 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 master-slave relationship of the polytope between the dimensions in the shape data, and updates the master-slave relationship of the polytope according to the one-dimensional processing and the n-dimensional processing. Further, the mesh generation unit may generate a mesh by further subdividing the agent group filled in the 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 step to the fourth step. In the first step, the structural data of the object is converted into the shape data expressed by the polytope. In the second step, as a one-dimensional process for the shape data, the side which 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 an n-dimensional process for the shape data that has been processed in the (n-1) dimension (n is a number of dimensions of 2 or more). In this filling process, the 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 is better than the current one. The quality index indicates the shape quality of the agent, and is calculated for each agent by a predetermined objective function. In the fourth step, a mesh is generated based on a group of agents filled in an n-dimensional polytope.

Here, in the second invention, it is preferable that the quality index is better as the variation in the internal angle in the agent is smaller, and in addition, it is preferable that the quality index is better as the variation in the edge length in 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 owned by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. Further, the second step may include a step of adjusting the reference length according to at least one of the physical characteristics and the surface shape of the object.

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

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

The third invention comprises a first step to a fourth step and provides a mesh generation method using an agent-based model. In the first step, the structural data of the object is converted into the shape data expressed by the polytope. In the second step, as a one-dimensional process for the shape data, the side which 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 an n-dimensional process for the shape data that has been processed in the (n-1) dimension (n is a number of dimensions of 2 or more). In this filling process, the 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 is better than the current one. The quality index indicates the shape quality of the agent, and is calculated for each agent by a predetermined objective function. In the fourth step, a mesh is generated based on a group of agents filled in the n-dimensional polytope.

According to the present invention, the (n-1) dimensional processing is performed after dividing the side which is a one-dimensional polytope based on the reference length with respect to the shape data which is converted from the structural data and expressed by the polytope. As an n-dimensional process for the performed shape data, an agent is placed in the n-dimensional polytope. The size of the agent depends on the reference length, and its shape is set to maximize the quality index. In addition, the shapes of adjacent agents are optimized so that the sum of these quality indicators is better than the current state, that is, the state before the optimization. As a result, the internal space of the n-dimensional polytope is filled and subdivided without gaps by a group of agents having a good shape, so that a high-quality mesh can be generated.

Block diagram of the mesh generation system Flowchart of mesh generation process Diagram showing 2D structure data Diagram showing 2D shape data Conceptual diagram showing the master-slave relationship of polytopes between dimensions The figure which shows the shape data after one-dimensional crystallization processing. Flowchart of n-dimensional crystallization process routine Explanatory diagram of a simple method for optimizing agent shape Arrangement explanatory diagram of agents A1 and A2 Arrangement explanatory diagram of agent A3 Explanatory drawing for optimizing the shape of the agent according to the arrangement of the agent A3 Arrangement explanatory diagram of agent A4 Arrangement explanatory diagram of agent A5 Explanatory drawing of filling state by agent group 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 takes structural data of an object as an input and outputs mesh data expressing the shape of the object with a mesh. In the mesh generation process, an agent-based model (ABM) is used. Here, the "agent-based model" is one of the simulation models for evaluating the influence of the autonomous agent behavior and the interaction between agents on the entire system, and is called multi-agent simulation. Sometimes. In addition, the "agent" means an entity that acts autonomously under predetermined rules based on its own situation and the situation around it. The feature of this embodiment is to use an agent-based model to subdivide the area of an object, and more specifically, to arrange agents in the internal space of a certain area while considering the interaction of adjacent agents. It is to generate a mesh based on the agent group filled in this area.

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 conversion unit 2 converts the structural data input as the processing target into shape data. The structural data before conversion is data in an arbitrary format that defines the structure (including the shape) of the object, and is two-dimensional CAD data or three-dimensional CAD data such as STEP format or STL format. This structural data may include a curve or a curved surface as a shape defined by itself. On the other hand, the shape data after conversion is data in which the shape of an object is expressed by a polytope. In particular, when the structural data includes curves and curved surfaces, these are discretized by line segments, and the curves are approximated by straight lines and the curved surfaces are approximated by planes. The method of implementing the shape data (class definition) is arbitrary, but as will be described later, it is preferable to maintain and manage the correspondence between the polytope and the facet because the crystallization process that refers to different dimensions is performed. Here, the "polytope" refers to a superpolytope in elementary geometry, a 0-dimensional polytope is a "point", a 1-dimensional polytope is a "side", a 2-dimensional polytope is a "face", and a 3-dimensional polytope is a "solid". be. Further, "facet" means a lower dimensional polytope owned by a certain dimensional polytope. For example, a "face" for a three-dimensional polytope (solid), a "side" for a two-dimensional polytope (face), 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 one-dimensional polytope (side) included in the shape data that satisfies the conditions described later. Here, the reference length is defined by the user, which defines the size of the agent. Specifically, the longer the reference length, the larger the agent (regional resolution = coarse), and the shorter the reference length, the smaller the agent (regional resolution = dense). Further, the reference length may be fixedly applied to the entire object, or may be applied to a variable value according to at least one of the physical characteristics and the surface shape of the object. For example, for a part where the material is soft and easily deformed, the reference length is made shorter than other parts, and for a part where the surface curvature is large, the reference length is made shorter than other parts.

The n-dimensional processing unit 4 sets the internal space of the n-dimensional polytope as an agent group (agent) as an n-dimensional crystallization process for the shape data that has been processed in the (n-1) dimension (n is a number of dimensions of 2 or more). Filling and subdividing by the number of dimensions = n). For example, when n = 2, two-dimensional crystallization processing is performed on the shape data that has been one-dimensional crystallization processing by the one-dimensional processing unit 3, and the internal space of the two-dimensional polytope (plane) is 2. Filled and subdivided by a group of dimensional agents. Further, when n = 3, a three-dimensional crystallization process is performed on the shape data that has been two-dimensionally crystallized by the n-dimensional processing unit 4, and the internal space of the three-dimensional polytope (three-dimensional) is 3. Filled and subdivided by a group of dimensional 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 n ≧ 5 is not particularly excluded.

In the n-dimensional crystallization process excluding the one-dimensional process, agents that are autonomous action subjects are individually arranged in the internal space of the n-dimensional polytope. A plurality of adjacent agents (adjacent agents) interact with each other in this internal space, and the shape of these agents is optimized based on this interaction. The shape of each agent and the optimized shape of neighboring agents including self are determined based on the concept of quality index. Although the details will be described 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 the agent is set so that the quality index of this agent is maximized. In addition, the optimized shape of the adjacent agent including the self is set so that the sum of these quality indicators is better than the current state, that is, the state before the optimization.

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

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

The polytope management unit 6 has a master-slave relationship of polytopes between dimensions in the shape data converted by the data conversion unit 2 in the memory space included in the mesh generation system 1, that is, which low-dimensional polytope the high-dimensional polytope owns. Memorize and manage if you are there. 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. Further, in the processing process of the one-dimensional processing unit 3, the master-slave relationship of the polytope is updated at any time according to the division of the one-dimensional polytope (side) and the addition of the zero-dimensional polytope (point) accompanying the division. Further, in the processing process of the n-dimensional processing unit 4, the master-slave relationship of the polytope is updated at any time 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 at any time by both the one-dimensional processing unit 3 and the n-dimensional processing unit 4.

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) on the computer and operating the computer according to the procedure specified by this program. Hereinafter, the content of this process will be described in detail using the two-dimensional structure data of the shape shown in FIG. 3 as an example. First, in step 1, structural data to be processed is input to the data conversion unit 2.

Next, in step 2, the data conversion unit 2 converts the structural data into the 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 structural 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 conversion to shape data, one arc shown in FIG. 3 is linearly approximated by a plurality of line segments. As a result, each of the connection points connecting the adjacent line segments is converted into 0-dimensional polytopes P0 (4) to P0 (6), and each line segment becomes 1-dimensional polytopes P1 (3) to P1 (6). Be converted.

FIG. 5 is a conceptual diagram showing a master-slave relationship of a polytope 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, as in the case of the one-dimensional polytope P1 owned by the two-dimensional polytope P2 and the zero-dimensional polytope P0 owned by the one-dimensional polytope P2. In the example of the figure, the two-dimensional polytope P2 (1) possesses six one-dimensional polytopes P1 (1) to P1 (6) as its facets (sides). Further, for example, the one-dimensional polytope P1 (1) possesses two 0-dimensional polytopes P0 (1) and P0 (2) as facets (points). When a plurality of two-dimensional polytopes P2 exist, the master-slave relationship of the polytopes as described above is managed for each two-dimensional polytope P2. Further, in the case of three-dimensional shape data, the master-slave relationship of the polytope including the three-dimensional polytope (plane) is managed. Although the following description is omitted, the master-slave relationship of the polytope is changed / updated at any time in the processing 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 treatment is a one-dimensional polytope P1 longer than the reference length, and the one-dimensional polytope P1 (side) is divided into lengths of about the reference length. As the number of divisions of the sides, for example, the length of the one-dimensional polytope P1 can be divided by the reference length, and the divided value can be rounded down or rounded up to an integer.

FIG. 6 is a diagram showing shape data after one-dimensional crystallization processing. Each of the one-dimensional polytopes P1 (1) and P1 (2) corresponding to one side shown in FIG. 4 is divided into three parts. As a result, the one-dimensional polytope P1 (1) is deleted, and instead, the three one-dimensional polytopes P1 (1-1) to P1 (1-3) and the two 0-dimensional polytopes P0 (7) to P0 ( 8) and is added. Similarly, the one-dimensional polytope P1 (2) is deleted, and instead, three one-dimensional polytopes P1 (2-1) to P1 (2-3) and two 0-dimensional polytopes P0 (9) to P0 ( 10) and is 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 even. In the example of FIG. 6, since the number of facets of the two-dimensional polytope P2 (1) is 10, this condition is satisfied. The reason for adjusting the number of divisions is to prevent a polytope having a facet number other than 2n (n is a number of dimensions) from appearing in the subsequent processing process and to avoid the occurrence of exception handling for the polytope. In the case of a conventional mesher, a triangle may be mixed in a quadrangle or a tetrahedron may be mixed in a hexahedron in the process of meshing, so it is necessary to perform special exception handling to remove these. On the other hand, in this method, by adjusting the even numbering as described above, it is possible to effectively suppress the generation of polytopes having a number of fesets other than 2n in the subsequent processing process.

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 number of facets of the n-dimensional polytope to be processed is not 2n. Specifically, the number of facets of the two-dimensional polytope is not 4 in the two-dimensional crystallization process, and the facet of the three-dimensional polytope is not set in the three-dimensional crystallization process. The condition is that the number is not 6. That is, the n-dimensional crystallization process is performed on a polytope having a facet number of not 2n, and if the facet number is 2n, the polytope itself can be one agent, and thus the polytope is performed. do not have.

Next, in step 42, the placement location of the agent is designated in the internal space of the processing target designated in step 41. It is arbitrary to set the rules for the placement location and the order of the agents, but in the present embodiment, as an example, (i) placement at two ends (A1), as shown in FIG. → A2), (ii) Placement on the side connecting these (A3), (iii) Placement on all sides based on the above (i), (ii) (A4 → A5 → A6 → A7), ( iv) Individual agents are sequentially arranged in the order of arrangement inside the space (A8).

The following are examples of 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 quadrangle, 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 hexahedron mesh. As a second rule, agent facets share existing facets in the vicinity of this agent location. The "existing facet" is the facet of the n-dimensional polytope to which the agent belongs, or the facet of another agent already placed in this n-dimensional polytope. This is due to the fact that 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 quality index Q of the agent indicates the shape quality of this agent, and as an example, it can be the "dissatisfaction degree" calculated by the following objective function.

(Dissatisfaction) = (Dispersion of internal angle) * a + (Edge length (longest / shortest)) * b

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

(Dispersion of internal angle) = 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 in the edge length in the agency. Here, the "edge length" is the length of the side, that is, the one-dimensional polytope P1 in the case of the two-dimensional crystallization process. The variation in edge length may be evaluated by an index showing the degree of dispersion such as edge dispersion instead of the edge length ratio.

The degree of dissatisfaction tends to be smaller as the variation in the internal angle becomes smaller and as the variation in the edge length becomes smaller, and the square or the regular hexahedron becomes the minimum. The smaller the dissatisfaction level, the better the shape quality of the agent, and the larger the dissatisfaction level, the poorer the quality. As can be understood from this tendency, a shape that "maximizes the quality index Q" is a shape that is as close as possible to a square or a regular hexahedron under the constraint of sharing an existing facet. It can be said. In addition, "the quality index Q becomes the best" may be a condition that the quality index Q takes the maximum value, but for example, the degree of dissatisfaction is smaller than a predetermined threshold value, or is as follows. This condition may be satisfied when the quality index Q is so good that it exceeds a predetermined threshold value, such that the stated happiness is larger than a predetermined threshold value.

The quality index Q is not limited to the above formula, and various ones can be considered. For example, only the variation in the internal 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, the degree of dissatisfaction in the above formula multiplied by -1 may be defined as "happiness", and this degree of happiness may be used as the evaluation index Q. In this case, the larger the happiness level, the better the shape quality of the agent, and the smaller the happiness level, the poorer the quality.

In step 44, these shapes are optimized (smoothing) for a plurality of adjacent agents (including self) in the internal space of the n-dimensional polytope. This optimization is achieved by transforming the sum of the individual quality indicators Q in the adjacent agents including self, that is, the overall quality indicator Qsum to be better than the current state, that is, the state before the optimization. Will be done.

Here, the overall quality index Qsum (hereinafter referred to as “function U”) is determined depending on each internal angle (θ) and each edge length (l), but the internal angle and edge length are the coordinates of each P0 (hereinafter referred to as “function U”). Since it can be expressed by the vector x), it can be expressed as follows.

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

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

In the above simulation, by making Δt sufficiently small, an increase in the overall quality index Qsum is strictly guaranteed. However, if the calculation cost is very high, a simple method that approximates the calculation can be used. In this simple method, the movement amount of each P0 is a value derived from the deviation between the length and the reference length of P1 (δ vector xlength) and a value derived from the deviation of the angle formed between P1s from π / 2 (δ vector). xangle) and. Two values are evaluated for each agent in each time step, and the movement amount is added to P0. At the timing when the evaluation for all agents is completed, P0 is actually calculated by the total movement amount (Δ vector x). Move it.

FIG. 8 is an explanatory diagram of a simple method for optimizing the agent shape. The figure illustrates P0 to which two P1s are connected. For the sake of simplicity, the two P1s will be replaced with the vectors Vi and Vj, respectively.

However, kangle and length are predetermined constants proportional to the degree of dissatisfaction of the agent. Further, in the above formula, the operation symbol for adding 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 processing result based on this, the overall quality index Qsum is modified to be better than the current state. In the flowchart shown in FIG. 7, the shape is optimized every time the agent is arranged, but it is not always necessary to perform it every time, and it 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 is filled by the agent group. If this determination result is negative, that is, if the filling in the n-dimensional polytope is not completed, the processing target is transferred to the next agent (step 46), and processing for this agent is performed (step 42). ~ 44). Then, when the filling in the n-dimensional polytope is completed by the iterative processing 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 the processing for all n-dimensional polytopes is completed. If this determination result is negative, that is, if the processing for all polytopes belonging to the same dimension is not completed, the processing target is transferred to the next polytope in the same dimension (step 48), and the same processing is performed. (Steps 41 to 46). Then, when the processing for all polytopes is completed by repeating the processing for each polytope in the same dimension, the determination result in step 47 changes from negative to affirmative, and this routine ends.

When the two-dimensional mesh is generated, the process of step 4 is completed by the end of the two-dimensional crystallization process. Further, when the three-dimensional mesh is generated, the two-dimensional crystallization process is followed by the three-dimensional crystallization process for the three-dimensional polytope, and the process of step 4 ends when the process is completed.

Hereinafter, the filling process of the two-dimensional polytope P2 (1) by the agent group will be described with reference to FIGS. 9 to 14. 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 the two-dimensional polytope P2 (1). As an implementation method for sharing facets, for example, it can be handled by separately generating and possessing a facet such as a mirror copy called a conjugated facet. The degree of freedom left under the constraint that the three points P0 (1), P0 (7), and P0 (10) have already been specified is the place where the remaining points X1 are placed. The point X1 is arranged at a position where the quality index Q1 of the agent A1 becomes as good as possible, whereby the shape of the agent A1 is determined. As for the agent A1, since there are no adjacent agents, the shape is not optimized.

Next, the agent A2 is arranged at the lower left end 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 that the three points P0 (3), P0 (6), and P0 (9) have already been specified is the place where the remaining points X2 are placed. The point X2 is arranged at a position where the quality index Q2 of the agent A2 becomes as good as possible, whereby the shape of the agent A2 is determined. As for the agent A2, since there are no adjacent agents, the shape is not optimized.

Next, as shown in FIG. 10, the agent A3 is arranged between the two agents A1 and A2. The agent A3 shares the facet P1 (2-2) owned by the two-dimensional polytope P2 (1) with the facets of the agents A1 and A2. Therefore, the shape of the agent A4 is uniquely specified without having to evaluate the quality index Q3 of the agent A3. Further, 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 state of the broken line to the state of the solid line, as shown in FIG.

Next, as shown in FIG. 12, the 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, the shape of the agent A4 is determined so that the quality index Q4 of the agent A4 is as good as possible. As for the agent A4, since there are no adjacent agents, the shape is not optimized.

Next, as shown in FIG. 13, the agent A5 is arranged between the two agents A1 and A4. The agent A5 shares the facet P1 (1-2) owned by the two-dimensional polytope P2 (1) with the facets of the agents A1 and A4. Therefore, the shape of the agent A5 is uniquely specified without having to evaluate the quality index Q5 of the agent A5. Further, 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, and A5 is better than the current state.

After that, as shown in FIG. 14, the agents A6 to A8 are sequentially arranged while optimizing the shape. As a result, the internal space of the two-dimensional polytope P2 (1) is completely filled 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 needed, thereby generating mesh data as shown in FIG. The generated mesh data is output to the outside as final output data.

As described above, according to the present embodiment, the side that is the one-dimensional polytope P1 is divided based on the reference length with respect to the shape data that is converted from the structural data and expressed by the polytope. Then, as an n-dimensional process for the shape data for which the (n-1) -dimensional process has been performed, an agent is arranged in the n-dimensional polytope. The size of the agent depends on the reference length, and the shape is set so that the quality index Q of the agent is as good as possible. In addition, the shapes of adjacent agents are optimized so that the overall quality index Qsum is better than the current state, that is, the state before the optimization. As a result, the internal space of the n-dimensional polytope is filled and subdivided without gaps by a group of agents 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 to perform crystallization processing from one dimension to two dimensions in the case of two-dimensional data, and 1 in the case of three-dimensional data. By performing the crystallization process from one dimension to three dimensions, it is possible to stably perform meshing of almost any shape, and it is possible to guarantee the completion of meshing without requiring exception processing. Being able to prevent the inability to continue in the middle of meshing is very important and effective in comparison with conventional meshers.

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

In the above-described embodiment, in the n-dimensional crystallization process, a sequential process in which agents are sequentially arranged in the internal space of the n-dimensional polytope has been described as an example, but it is possible to speed up the process. In the range, parallel processing may be performed in which a plurality of agents are arranged in parallel at the same time. For example, the agents A1 to A3 shown in FIG. 14 are independent of each other, and it is not necessary to consider the interaction with other agents, so that parallel processing is possible.

1 Mesh generation system 2 Data conversion unit 3 1-dimensional processing unit 4 n-dimensional processing unit 5 Mesh generation unit 6 Polytope management unit

Claims (19)

In a mesh generation system using an agent-based model,
A data conversion unit that converts the structural data of an object into shape data expressed by polytope,
As one-dimensional processing 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, and a one-dimensional processing unit.
(N-1) The shape quality of the agent is shown as n-dimensional processing for the shape data that has been processed in three dimensions (n is a number of dimensions of 2 or more), and is calculated for each agent by a predetermined objective function. Agents are placed in the n-dimensional polytope in a shape that maximizes the quality index to be obtained, and the total quality index of adjacent agents in the n-dimensional polytope becomes better than the current state. As described above, by optimizing the shapes of adjacent agents, the n-dimensional processing unit that fills the n-dimensional polytope with the agent group and
A mesh generation system comprising a mesh generation unit for generating 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 internal angle in the agent is smaller. 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 owned 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 the physical properties and the surface shape of the object. The n-dimensional processing unit is characterized in that the n-dimensional processing is performed on a polytope having a facet number of not 2n, and the n-dimensional processing is not performed 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 agent has a facet number of 2n. The claim is characterized in that it has a polytope management unit that manages the master-slave relationship of polytopes between dimensions in the shape data and updates the master-slave relationship in response to the one-dimensional processing and the n-dimensional processing. The mesh generation system according to 1. The mesh generation system according to claim 1, wherein the mesh generation unit further subdivides the agent group filled in the n-dimensional polytope to generate the mesh. In a mesh generation program using an agent-based model,
The first step of converting the structural data of an object into shape data expressed by polytope,
As a one-dimensional process for the shape data, a second step of dividing a side which is a one-dimensional polytope based on a specific reference length, and
(N-1) The shape quality of the agent is shown as n-dimensional processing for the shape data that has been processed in three dimensions (n is a number of dimensions of 2 or more), and is calculated for each agent by a predetermined objective function. Agents are placed in the n-dimensional polytope in a shape that maximizes the quality index to be obtained, and the total of the quality indexes in the agents adjacent to each other in the n-dimensional polytope becomes better than the current state. As described above, the third step of filling the n-dimensional polytope with the agent group by optimizing the shape of the adjacent agents, and
A mesh generation program comprising causing a computer to perform a process including a fourth step of generating a mesh based on a group of agents 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 internal angle in the agent is smaller. 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. The second step is described in claim 10, wherein the second step includes a step of adjusting the number of divisions of the one-dimensional polytope owned by the two-dimensional polytope so that the number of facets of the two-dimensional polytope becomes an even number. Mesh generator. 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 the physical properties and the surface shape of the object. One of claims 10, wherein the n-dimensional process in step 3 is performed on a polytope having a facet number of 2n and not on a polytope having a facet number of 2n. The described mesh generation program. The mesh generation program according to claim 10, wherein the agent has a facet number of 2n. A claim characterized by having a fifth step of managing the polytope master-slave relationship between dimensions in the shape data and updating the master-slave relationship in response to the one-dimensional process and the n-dimensional process. Item 10. The 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-based model,
The first step of converting the structural data of an object into shape data expressed by polytope,
As a one-dimensional process for the shape data, a second step of dividing a side which is a one-dimensional polytope based on a specific reference length, and
(N-1) The shape quality of the agent is shown as n-dimensional processing for the shape data that has been processed in three dimensions (n is a number of dimensions of 2 or more), and is calculated for each agent by a predetermined objective function. Agents are placed in the n-dimensional polytope in a shape that maximizes the quality index to be obtained, and the total of the quality indexes in the agents adjacent to each other in the n-dimensional polytope becomes better than the current state. As described above, the third step of filling the n-dimensional polytope with the agent group by optimizing the shape of each of the adjacent agents.
A mesh generation method comprising a fourth step of generating a mesh based on a group of agents filled in the n-dimensional polytope.

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