JPH08221471A - Overlap-evading display method for mesh structure model and simulation device - Google Patents

Abstract

PURPOSE: To evade the overlap of elastic models by translating the centroids of mesh structure models and a lattice point when the sum of average distances between both mesh structure models is larger than the distance between both centroids of the models. CONSTITUTION: The centroids c1 , c2 , etc., of (n) time steps are calculated for the particle models which are scattered in a lattice shape. Then, the average distance (radiuses R1 and R2 of virtual circles) between the centroid of each particle model and the outermost lattice point, e.g. the total length of segments c1 i1 , c1 j1 , c1 k1 , c1 , l1 ... is divided by the number of segments. Then, two particle models to be judged are selected and it is judged whether the sum of average distances (radiuses of virtual circles) of both particle models, e.g. the distance between the centroids of both particle models of (R1+R2) is larger than the length L12 of the segments c1 and c2 . If the distance (R1+R2) is larger than the length L12, the overlap evading processing of the particle models is carried out. Then, the centroid of a mesh structure model and the lattice point are translated along the line connecting together both centroids. As the result, the overlap is avoided among the elastic models.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mesh capable of avoiding overlapping display of mesh structure models which are mechanically deformed by mathematical and physical factors in the fields of numerical simulation and computer graphics. The present invention relates to a method for avoiding overlapping of structural models and a simulation apparatus for implementing the method.

[0002]

2. Description of the Related Art Various inanimate objects and creatures in the natural world have their own unique attributes, and they often cause elastic-mechanical deformation. In recent years, attempts have been made to analyze the elasto-mechanical behavior by numerical simulation using computer graphics or the like, or to explore by experiments. However, due to their strong non-linearity, many unsolved points remain. In addition, it is an important issue to visually represent the enormous amount of data required for numerical calculation.

In the field of computer graphics,
For example, attempts have been made to visually express elastic mechanical deformation when a ball falls on the ground or a car collides with a wall, mechanical interaction between red blood cells and blood flow, and stretching motion of muscles. Attention has been paid. In this case, the design of the mesh structure model of the object of expression has a great influence on the accuracy of the solution and the richness of the visual expression in visually expressing from the precise numerical simulation to the visualization.

In the case of representing a collision between models with computer graphics, the models may overlap with each other, giving a visually unnatural feeling. Further, in the case of performing a numerical simulation using the elastic motion equation of an object, if no constraint is imposed on the mesh structure model, as shown in FIG. 8, after the ball model M1 reaches the ground, it is actually measured with time. It may be expressed too crushed. Therefore, along with the progress of computer technology, research on an expression method for avoiding the overlap between models and an expression method for suppressing the extreme deformation of the models is being advanced.

As an expression technique for avoiding the overlap between the models, there is a particle model overlap avoidance method for judging whether or not the rigid particle models collide with each other at any time and expressing so as not to overlap the particle models. . This particle model overlap avoidance method is used when simulating a collision between rigid particle models M2 (assumed to be circles or spheres), as shown in FIG. In this method, a collision is determined by simply checking the length of the radius of both particle models M2 and the distance between the centers of gravity, and a process is performed in advance so that the particle models M2 do not overlap each other. In such a method, if the time advance width is increased and represented by computer graphics, it is not possible to completely avoid the overlap of the particle models with only one correction. Therefore, the collision determination is performed using a virtual circle or sphere larger than the radius of the particle model.

As an expression method for suppressing the deformation of the mesh structure model of the target object, there is an elasticity correction method in which a spring model is incorporated between the lattices of the mesh structure model.

[0007]

By the way, the following problems occur in the above-described expression method for avoiding the overlap between models and for the expression method for suppressing the extreme deformation of the models.

In the overlap avoiding method for avoiding the overlap between the models, since the applicable range is limited to the collision between the rigid particles, as shown in FIG. 10, the elastic particle models M3 are appropriately overlapped. There is a problem that it cannot be avoided and expressed.

In the elasticity correction method for suppressing the extreme deformation of the model, in order to increase the calculation speed, if the lattice point density of the mesh structure model is suppressed to be low and the rigid deformation of the spring model having a large spring constant is simulated, an external force is applied. There is a problem that the mesh structure model is greatly deformed depending on the size of.

For example, when there is unevenness on the colliding ground, the model M4 may be divided as shown in FIG. 11 or may be expressed as a very soft attribute. The theory of elastic deformation is divided into two, a small deformation problem and a large deformation problem.
Especially, in the latter problem, not only is the nonlinear differential equation that governs the system complicated, but
It is thought that this is because the stability problem in the numerical solution occurs at the same time.

The main objects to be solved by the present invention are as follows. A first object of the present invention is to provide a mesh structure model overlap avoidance display method and a simulation device which can be represented by avoiding overlap of elastic body models in the field of computer graphics as visualization from numerical simulation. It is something to do.

A second object of the present invention is to provide an overlap avoidance display method and a simulation device for a mesh structure model, which can suppress various extreme deformations of an elastic body model and express various physical deformations. It is something to do.

A third object of the present invention is to provide a method for avoiding overlapping of mesh structure models and a simulation apparatus capable of reducing the calculation cost and naturally expressing the physical deformation. .

Other objects of the present invention include the specification, drawings,
In particular, it will be apparent from the description of the claims.

[0015]

In order to solve the above-mentioned problems, the above-mentioned object is achieved by adopting the novel characteristic construction method and means listed below by the present invention. That is, a first feature of the method of the present invention is that a computer that generates a mesh structure model that moves and deforms by a computer based on input external factors and various conditions of a target object, and displays a dynamic deformation by simulation. In the image processing of graphics, the center of gravity is calculated for each of the mesh structure models, and the average distance between the center of gravity and the grid point on the outermost periphery of the mesh structure model (the radius of the virtual circle or sphere) is calculated, Two relevant mesh structure models are selected, the sum of the average distances of both the relevant mesh structure models is compared with the length of the distance between the centers of gravity of both, and the sum of the average distances of both the relevant mesh structure models is calculated. , When the distance between the two centers of gravity is longer, the center of gravity of the mesh structure model and the grid point are translated along the line connecting the two centers of gravity. Te, in overlap avoidance display method of the mesh structure model consisting be corrected so as to avoid overlapping thereof.

The second feature of the method of the present invention is that the correction for avoiding the overlapping of the mesh structure models in the first feature of the method of the present invention is carried out as a pre-processing, between the grid points in the circumferential direction of the mesh structure model. Is a display method for avoiding overlap of mesh structure models, in which the elastic deformation is locally corrected by keeping the expansion of the length within a predetermined range.

A third feature of the method of the present invention is that the correction for avoiding the overlap between the mesh structure models in the first or second feature of the method of the present invention determines the amount thereof as the center of gravity of the mesh structure model, This is a display method for avoiding overlapping of the mesh structure models, which is the minimum distance from the outermost grid points of the mesh structure model.

A fourth feature of the method of the present invention is that the correction for avoiding the overlapping of the mesh structure models in the first, second or third feature of the method of the present invention is performed by the average distance of both mesh structure models. Is a method of avoiding overlapping of mesh structure models, which is repeatedly executed until the sum of is shorter than the distance between the centers of gravity.

The fifth feature of the method of the present invention is that the mesh structure model according to the first, second, third or fourth feature of the method of the present invention is a display method for avoiding overlap of mesh structure models consisting of particle shapes. is there.

A sixth feature of the method of the present invention is that the mesh structure model in the first, second, third, fourth or fifth feature of the method of the present invention has a plane structure or a three-dimensional structure. There is a display method for avoiding overlapping of structural models.

A first feature of the device of the present invention is a simulation device having an operating device, an image display device, an image storage device, and an image processing device, wherein the image processing device comprises:
Model generation means for generating a mesh structure model that moves and deforms based on external factors and various conditions of the target object, and local correction for keeping the expansion of the length between the lattice points of the mesh structure model itself within a predetermined range. Means and an overlap avoiding means for avoiding geometrical overlap between the mesh structure models, the overlap avoiding means calculates a center of gravity for each mesh structure model, and the center of gravity and the outermost circumference. An average distance (radius of a virtual circle or a sphere) to each of the grid points is calculated, two mesh structure models are selected, and the sum of the average distances of both mesh structure models and the distance between the centers of gravity of both mesh structures are calculated. When the sum of the average distances of both mesh structure models is longer than the distance between the centroids of both mesh structures, the centroids of the mesh structure models and the grid are compared. It was allowed to translate along a line connecting the center of gravity of both, in the simulation apparatus consisting of an algorithm for avoiding freely correct these overlap.

A second feature of the device of the present invention is that the overlap avoiding means in the first feature of the device of the present invention sets the correction amount as the minimum distance between the center of gravity of the mesh structure model and the outermost grid point. There is a simulation device.

A third feature of the device of the present invention is that the local correction means and the overlap avoiding means in the first or second feature of the invention device can be repeatedly executed until the mesh structure models do not overlap each other. It is in a simulation device configured as described above.

A fourth feature of the device of the present invention resides in a simulation device in which the mesh structure model in the first, second or third feature of the device of the present invention has a particle shape.

The fifth feature of the device of the present invention resides in a simulation device in which the mesh structure model in the first, second, third or fourth feature of the device of the present invention has a planar structure or a three-dimensional structure. .

[0026]

The present invention takes the following actions because it takes the novel method and means as described above.

In the present invention, the overlap avoiding means geometrically determines the overlap using a virtual circle or sphere whose radius is the average distance between the center of gravity of the mesh structure model and each lattice point on the outermost periphery, and these Avoid overlapping. As a result, it is possible to avoid the overlap even if the simulation target object is not only a rigid body but also an elastic body.

Further, in the present invention, when correcting the model deformation due to an external factor, a local correction means for holding the extension of the length between the lattice points in the circumferential direction of the mesh structure model within a predetermined range is used. . As a result, it is possible to suppress the extreme deformation of the elastic body model and to naturally express various physical deformations.

Further, since various physical deformations can be naturally expressed by the mesh structure model having a low lattice point density, the calculation cost at the time of simulation can be kept low. In the present specification, the “mesh structure model” refers to a model in which the target object is expressed in a grid pattern.

[0030]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will now be described in more detail with reference to the accompanying drawings on the basis of its apparatus and method.

(Example of Apparatus) FIG. 1 shows the configuration of a simulation apparatus according to an example of the apparatus of the present invention. The simulation device A includes an operating device 1, an image processing device 2, an image storage device 3, and an image display device 4.

The operating device 1 functions as a terminal for inputting various data of an object to be numerically simulated and physical conditions (external factors) of the simulation to the image processing device 2 and for operating the simulation.

The image processing apparatus 2 includes model generation means 2a,
It has a local correction means 2b and an overlap avoidance means 2c. The model generation means 2a generates a mesh structure model that moves and deforms based on the external factors and the data of various conditions of the target object received from the operation device 1, and transmits it to the local correction means 2b in the middle stage.

As shown in FIG. 5, the local correction means 2b can hold the expansion of the length (line segment i ₁ j ₁ etc.) between lattice points in the circumferential direction of each mesh structure model within a predetermined range, for example. Image data is processed as described above, and the overlap avoiding means 2 in the latter stage is processed.
Send to c. Here, FIG. 5 shows a specific configuration of the mesh structure model used in the present apparatus example and method example.

The overlap avoiding means 2c processes the image data so as to avoid geometrical overlap between the mesh structure models, and then transmits this data to the image storage device 3. When the overlapping of the mesh structure models cannot be avoided by one processing, the processing of the local correction means 2b and the overlapping avoidance means 2c is repeatedly executed.

The image storage device 3 stores the image data created by the image processing device 2 and, when receiving the simulation start signal S from the operating device 1, stores the stored image data in the image display device at an appropriate timing. Send to 4.

The image display device 4 displays a mesh structure model obtained by reconstructing the received image data on the monitor screen.

(Example of Method) Next, an example of a method for displaying overlap avoidance of mesh structure models applied to the simulation apparatus A of the above-described apparatus example will be specifically described with reference to the drawings. Here, FIG. 2 shows an overall processing procedure of the present method example, FIG. 3 shows a determination procedure for judging overlapping of mesh structure models, and FIG. 4 is a concrete avoidance processing of overlapping of mesh structure models. Shows the procedure. In this method example, the particle model of the elastic body is used as the target object, but the present invention is not limited to this and can be applied to the case of using another shape model.

First, the operator inputs the external factors of the target object and various conditions of the target object to the image processing apparatus 2 by using the operation device 1 (ST1). In this method example, initial conditions such as the particle shape of the elastic body, the arrangement, the deformation conditions, and the number of particles are input.

When the input of the initial conditions is completed, the model generating means 2a of the image processing apparatus 2 generates a particle model that has moved and deformed in n time steps based on external factors and various conditions of the target object (ST2). ).

In the image processing apparatus 2, the local correction means 2b then performs a correction process for suppressing unnatural large deformation of each particle model (ST3). In the local correction means 2b, the length between the lattice points in the circumferential direction of the particle model (line segments i ₁ j ₁ , j ₁ k ₁ , k ₁ l ₁ , l ₁ m _1, etc. in FIG. 5).
A local shape preserving method is used to keep the expansion of a. The correction process is repeatedly executed between all the lattice points in the circumferential direction of each particle model until the correction amount becomes a certain amount or less.

As described above, the image processing apparatus 2 performs the geometrical correction by the local shape preservation method. Therefore, apparently the particle model is deformed so that the degree of freedom around the lattice points is large and the distance between the lattice points in the circumferential direction is approximately constant with the initial length.

Then, in the image processing apparatus 2, the overlap avoiding means 2c (described later) determines whether or not the particle models overlap each other (ST4). Is executed (described later) (ST
5). Then, when it is determined that there is no overlap, the process proceeds to the process of n + 1 time step (ST7).

The processing from ST2 to ST5 is repeated until the steps of the entire time are completed (ST6),
All image data of the simulation are stored in the image storage device 3.

Next, a method of determining whether or not the particle models overlap with each other in ST4 will be described. FIG. 3 shows the procedure of the overlap determination processing of particle models, and FIG. 6 shows the overlapping state of particle models.

First, n of a particle model discretized in a lattice pattern
The center of gravity (c ₁ , c _2, etc. in FIG. 6) at the time step is calculated (ST4a). Then, the average distance between the center of gravity and the outermost grid point in each particle model (radius R1 of the virtual circle,
R2), for example, line segments c ₁ i ₁ , c ₁ j ₁ , c ₁ k ₁ ,
A value is calculated by dividing the total length of c ₁ l ₁ ... By the number of line segments (ST4b).

Next, two particle models to be judged are selected (ST4c), and the sum of the average distances (radius of virtual circles) of both particle models, for example, R1 + R2 is the distance between the center of gravity of both particle models, It is determined whether the line segment c ₁ c ₂ is longer than the length L12 (ST4d). And R1 + R2>
In the case of L12, the particle model overlap avoidance processing is executed, and in the case of R1 + R2 <L12, it is checked whether or not the overlap determination has been made for all the particle models (ST4e).

Then, if the result of the check in ST4e is NO, the process returns to ST4c, and the overlap determination of the particle models is executed until all the particle models have no overlap.

Next, a method of avoiding overlap between particle models performed in ST5 will be described. FIG. 4 shows the procedure of the overlap avoidance processing between particle models.

In each particle model after the local correction processing, the distance between the center of gravity and each lattice point on the outermost periphery (line segment c ₁ i ₁ ,
After calculating the values of c ₁ j ₁ , c ₁ k ₁ , c ₁ l _1, ..., The minimum distance Rmin is also obtained (ST5a). continue,
The minimum distance Rmi for the position of the center of gravity of overlapping particle models
The movement is corrected by n (ST5b). The correction direction in this case is, for example, the position coordinate of the center of gravity c ₁ along the line c ₁ c ₂ connecting the centers of gravity of the overlapping particle models.
The position coordinates of are to be separated.

Then, the lattice points of the particle model, for example, i
The position coordinates of ₁ , j ₁ , k ₁ , l _1, ... Are corrected in the same direction and by the same amount as the center of gravity c ₁ (parallel movement correction) (ST
5c). The local correction unit 2b and the overlap avoiding unit 2c are repeatedly executed until the particle models do not overlap each other.

Using the example of the apparatus and the example of the method described above, it was decided to perform a simulation in which a large number of particle models M are suspended in the inside B of the blood vessel. As a result, as shown in FIG. 7, each of the particle models was deformed, and in particular, it became possible to perform a graphic representation of passing through without narrowing while becoming elongated at the narrowed portion P.

(Application Example) Next, the results of an application example of the concrete particle model overlap avoidance expression using the present invention will be described with reference to schematic diagrams (FIGS. 12 to 16). The original color drawings of these schematic drawings are attached to the property submission form of this application document.

[Application Example 1] FIG. 12 (reference color drawing 1)
Shows the overlapping (collision) situation of the particle models when the present invention is not used, and FIG. 13 (reference color drawing 2) shows the avoidance situation of the overlapping of the particle models when the present invention is used. ing.

In this application example, 10 particle models are initially arranged in the vicinity of the entrance in a flow with obstacles, and when the particle model is passing through while it is narrowing, the mesh structure model of the present invention is used. The case where the overlap avoidance display method is not used and the case where the present invention is used are represented by simulation. The vector in the flow path indicates the direction and magnitude of the flow, and represents the vector length in proportion to the velocity of the flow.

As can be seen from FIGS. 12 and 13,
In the case of using the present invention (b), since the overlap avoidance process is performed, only 8 (10 circles and 1 deformation) of 10 particle models are displayed on the monitor screen. Was done. Also, from these figures, it is possible to confirm that the particle model is deforming and moving along the nearby flow field. In addition, a stagnation region was found behind the obstacle because the flow velocity increased in the stenosis.

[Application 2] FIGS. 14, 15 and 16 show the avoidance expression of the overlap of the particle models and the deformation, movement and dynamics of the particle models in the fluid when the present invention is used.

In this application example, 17 particle models are intentionally placed near the entrance in the flow with obstacles to confirm the model deformation and overlap avoidance processing. In (a) and (b) of FIG. 14 (reference color drawings 3 and 4), the states of the initial state, model deformation in the second step, and overlap avoidance processing are shown in (c) and (d) of FIG. 15 (reference color drawings). 5 and 6) show the model deformation and the overlap avoidance process in the sixth and eighth steps, and FIG. 16E (reference color drawing 7) shows the model deformation and the overlap avoidance process in the tenth step. The situation is shown.

Comparing the second step of FIG. 14 (b) with the initial state of FIG. 14 (a) and the arrangement of the particle model, it can be seen that the particle model spreads in the vertical and horizontal directions due to the action of the algorithm of the overlap avoidance processing. Can be confirmed. In addition, it was confirmed that the extreme deformation of the particle model was suppressed comprehensively, and the flow change of the particle model was naturally expressed.

[0060]

As described above, according to the present invention, in the field of computer graphics as a visualization from numerical simulation, it is possible to avoid the overlapping of elastic body models and to represent them. In particular, according to the device of the present invention, it is possible to suppress the extreme deformation of the elastic body model while keeping the calculation cost during simulation low, and to naturally express various physical deformations. It is also possible.

[Brief description of drawings]

FIG. 1 is a schematic diagram showing a block configuration of a simulation apparatus according to an apparatus example of the present invention.

FIG. 2 is an explanatory diagram showing an overall processing procedure of the method example.

FIG. 3 is an explanatory diagram showing a determination procedure for determining overlap between mesh structure models according to this method example.

FIG. 4 is an explanatory diagram showing a concrete procedure for avoiding overlapping of mesh structure models of this method example.

FIG. 5 is a schematic diagram showing the configuration of a particle model displayed by simulation in this method example.

FIG. 6 is a schematic diagram showing an overlapping state of particle models displayed by simulation in this method example.

FIG. 7 is an example of a simulation display using the present apparatus example and method example.

FIG. 8 is a diagram showing a state in which a model is crushed in a conventional simulation.

FIG. 9 is a diagram showing a collision state between rigid particle models in a conventional simulation.

FIG. 10 is a diagram showing a collision state between elastic particle models in a conventional simulation.

FIG. 11 is a diagram showing a large deformation state of a mesh structure model in a conventional simulation.

FIG. 12 is a schematic diagram of the overlapping (collision) situation of particle models represented without using the method of the present invention.

FIG. 13 is a schematic diagram of the overlapping (collision) situation of particle models obtained using the method of the present invention.

FIG. 14A is a schematic diagram showing a model deformation and an overlap avoidance process in an initial state, and FIG. 14B is a schematic diagram showing a model deformation and an overlap avoidance process in the second step.

FIG. 15C is a schematic diagram showing the state of the model deformation and the overlap avoidance process in the sixth step, and FIG. 15D is a schematic diagram showing the state of the model deformation and the overlap avoidance process in the eighth step.

FIG. 16E is a schematic view showing the state of model deformation and overlap avoidance processing in the tenth step.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Operating device 2 ... Image processing device 3 ... Image storage device 4 ... Image display device 2a ... Model generation means 2b ... Local correction means 2c ... Overlap avoiding means A ... Simulation device B ... Blood vessel inside P ... Stenosis M ... Particles model

Claims (11)

[Claims] 1. A computer graphics image processing for generating and displaying a mechanical deformation by generating a mesh structure model which moves and deforms by a computer based on an inputted external factor and various conditions of a target object, The center of gravity is calculated for each of the mesh structure models, and the average distance (virtual circle or sphere radius) between the center of gravity and the grid point on the outermost periphery of the mesh structure model is calculated, and two mesh structure models are calculated. Select and compare the sum of the average distance of both mesh structure models and the length of the distance between the center of gravity of both, the sum of the average distance of both mesh structure models,
When it is longer than the distance between the two centers of gravity, the center of gravity of the mesh structure model and the grid point are translated along the line connecting the two centers of gravity, and correction is performed so as to avoid these overlapping. Method for avoiding overlapping of mesh structure models. 2. The correction for avoiding the overlap between mesh structure models is performed as a pre-processing by keeping the expansion of the length between lattice points in the circumferential direction of the mesh structure models within a predetermined range to locally elastically deform the mesh structure models. The overlap avoidance display method of the mesh structure model according to claim 1, wherein the overlap structure avoidance display method is performed. 3. The correction for avoiding the overlap between mesh structure models is characterized in that the amount is set as a minimum distance between the center of gravity of the mesh structure model and the outermost grid point of the mesh structure model. The overlap avoidance display method for mesh structure models according to claim 1 or 2. 4. The correction for avoiding the overlap between mesh structure models is repeatedly executed until the sum of the average distances of both mesh structure models becomes shorter than the distance between the centers of gravity of both mesh structure models. The overlap avoidance display method for mesh structure models according to claim 1, 2 or 3. 5. The mesh structure model overlap avoidance display method according to claim 1, 2, 3 or 4, wherein the mesh structure model has a particle shape. 6. The mesh structure model overlap avoidance display method according to claim 1, 2, 3, 4, or 5, wherein the mesh structure model has a planar structure or a three-dimensional structure. 7. An operating device, an image display device, an image storage device,
And a simulation device having an image processing device, wherein the image processing device is a model generation unit that generates a mesh structure model that moves and deforms based on external factors and various conditions of the target object, and a grid of the mesh structure model itself. The apparatus includes local correction means for holding the extension of the length between points within a predetermined range, and overlap avoiding means for avoiding geometrical overlap between the mesh structure models, and the overlap avoiding means is provided for each mesh structure. The center of gravity is calculated for each model, and the average distance (virtual circle or sphere radius) between the center of gravity and each of the grid points on the outermost circumference is calculated, and two mesh structure models are selected. Comparing the sum of the average distances of the mesh structure models and the length of the distance between the center of gravity of both, the sum of the average distances of both the mesh structure models is ,
When it is longer than the distance between the center of gravity of both meshes, the center of gravity of the mesh structure model and the lattice points are translated along a line connecting the center of gravity of both meshes, and an algorithm for correcting these overlaps in a freely avoidable manner, A simulation device characterized by the above. 8. The simulation apparatus according to claim 7, wherein the overlap avoiding means sets the correction amount to a minimum distance between the center of gravity of the mesh structure model and the outermost grid point. 9. The simulation apparatus according to claim 7, wherein the local correction means and the overlap avoiding means are configured to be repeatedly executable until mesh structure models do not overlap each other. 10. The simulation apparatus according to claim 7, wherein the mesh structure model has a particle shape. 11. The simulation apparatus according to claim 7, wherein the mesh structure model has a planar structure or a three-dimensional structure.