JP2016192143A - Simulation method, simulation device, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for simulating a three-dimensional space in which a plurality of objects including a tabular object are placed.SOLUTION: A method repeatedly executes: a movement object selection step S12 for selecting at least one movement object to be moved from among a plurality of objects; a movement information generation step S14 for generating movement information indicating a manner of how the movement object is moved; an object movement step S16 for generating a provisional spatial state data including information relating to the placement state of at least the movement object in the three-dimensional space after the movement object is moved on the basis of the movement information; an interference determination step S70 for determining whether or not the plurality of objects are interfering each other in the three-dimensional space; and a next state determination step S18 which, when it is determined that the plurality of objects are not interfering each other, defines information indicating the placement states of the plurality of objects in the three-dimensional space after the movement object is moved on the basis of the movement information as new spatial state data.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a simulation method, a simulation apparatus, and a computer program.

  In order to research and develop manufacturing processes for various products that use powder, particles, etc., a simulation technique for mixing and filling a plurality of objects in a three-dimensional space is required. Patent Document 1 describes that a stirring state of particles is simulated based on a discrete element method.

JP 2000-214134 A

  The shapes of powders and particles used industrially are not limited to spherical shapes and are diversified, and there is a need for simulation methods that can be used in such cases.

  However, in the method of Patent Document 1, each particle is modeled as a sphere, and plate-like particles having anisotropy in shape cannot be handled accurately.

  In particular, a method for simulating an arrangement state including elements of the position and orientation of an object in a three-dimensional space where a plurality of objects including a plate-like object are arranged is required.

  The present invention provides a simulation method for a three-dimensional space in which a plurality of objects including a plate-like object are arranged.

According to the present invention,
A simulation method of a three-dimensional space in which a plurality of objects are arranged,
A moving object selection step of acquiring space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selecting at least one moving object to be moved among the plurality of objects;
A movement information generating step for generating movement information indicating how to move the moving object;
An object moving step of generating temporary space state data, including information on an arrangement state of at least the moving object in the three-dimensional space after moving the moving object based on the movement information;
An interference determination step for determining whether or not the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after moving the moving object based on the movement information when it is determined in the interference determination step that the plurality of objects do not interfere with each other Information indicating a state is the new space state data, and when it is determined that there is interference, the next state determination step that does not change the space state data; and
Repeat the state change process to perform
In the object moving step, at least one of parallel movement and rotational movement of the moving object is performed,
At least one of the plurality of objects is a plate-like object;
A simulation method is provided.

According to the present invention,
A three-dimensional simulation apparatus in which a plurality of objects are arranged,
A moving object selection unit that acquires space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selects at least one moving object to be moved among the plurality of objects;
A movement information generating unit that generates movement information indicating how to move the moving object;
An object moving unit that generates temporary space state data including at least information regarding an arrangement state of the moving object in the three-dimensional space after moving the moving object based on the movement information;
An interference determination unit that determines whether or not the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after the movement target is moved based on the movement information when the interference determination unit determines that the plurality of objects do not interfere with each other Information indicating a state is the new space state data, and when it is determined that there is interference, the next state determination unit that does not change the space state data;
Including a state change processing unit including
The state change processing unit repeatedly performs a state change process that operates the moving object selection unit, the movement information generation unit, the object movement unit, the interference determination unit, and the next state determination unit,
The object moving unit performs at least one of a parallel movement and a rotational movement of the moving object,
At least one of the plurality of objects is a plate-like object;
A simulation device is provided.

According to the present invention,
A computer program for realizing a three-dimensional space simulation apparatus in which a plurality of objects are arranged,
Computer
Moving object selection means for acquiring space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selecting at least one moving object to be moved among the plurality of objects;
Movement information generating means for generating movement information indicating how to move the moving object;
An object moving means for generating temporary space state data including information on an arrangement state of at least the moving object in the three-dimensional space after moving the moving object based on the movement information;
Interference determining means for determining whether the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after moving the moving object based on the movement information when the interference determination unit determines that the plurality of objects do not interfere with each other Information indicating a state is used as the new space state data, and when it is determined that there is interference, a next state determination unit that does not change the space state data;
Function as a state change processing means including
The state change processing means repeatedly performs a state change process for operating the moving object selecting means, the movement information generating means, the object moving means, the interference determining means, and the next state determining means,
The object moving means performs at least one of a parallel movement and a rotational movement of the moving object,
At least one of the plurality of objects is a plate-like object;
A computer program is provided.

  According to the present invention, a simulation method of a three-dimensional space in which a plurality of objects including a plate-like object are arranged is provided.

It is a flow of the simulation method concerning an embodiment. It is a schematic diagram which shows the example of the some object in three-dimensional space. It is a perspective view which shows the shape of the disk-shaped object which concerns on embodiment. It is a block diagram which shows the structure of the simulation apparatus which concerns on embodiment. It is a figure for demonstrating the determination method of whether a plate-shaped object and an external area | region interfere. It is the flow of the interference determination process which concerns on embodiment. It is a block diagram of the interference determination part which concerns on embodiment. It is a figure which shows the orthogonal coordinate system defined by a coordinate definition process. It is a flow which shows the content of a projection image determination process and a solid determination process. It is a flow which shows the content of the 1st reference plane determination process. (A) is a schematic diagram which shows the example of the projection image of the 1st target object in a 1st reference plane, and the projection image of a 2nd target object, (b) is for demonstrating a 1st partial determination process. It is a schematic diagram. (A) is a schematic diagram which shows the projection image of the 1st target object in a 1st reference plane, and the projection image of a 2nd target object, (b) is a figure which shows the 3rd area | region which concerns on this embodiment. It is. (A) is a schematic diagram which shows the example of the projection image of the 1st target object in a 2nd reference plane, and the projection image of a 2nd target object, (b) is a figure which shows a 1st determination area | region. (A) And (b) is a figure which shows a determination target line and a determination target point. (A) is a diagram showing a determination region A, (b) is a diagram showing a determination region B, and (c) is a diagram showing a determination region C. It is the flow of the process of determining whether one determination object point exists in a 1st determination area | region. (A) is a schematic diagram which shows the example of the projection image of the 1st target object in a 3rd reference plane, and the projection image of a 2nd target object, (b) is a figure which shows a 2nd determination area | region, (C) is a figure which shows the relationship between a 2nd determination area | region and a division area. It is a figure which shows the example of positional relationship of triangle OA _i A _j and the center point P of the projection image of a 2nd target object. (A) is a perspective view which shows the example of arrangement | positioning relationship between a plate-shaped object and a spherical object. FIG. 4B is a cross-sectional view of the plate-like object and the spherical object on a plane including the center of the upper surface of the plate-like object, the center of the lower surface of the plate-like object, and the center of the spherical object. It is a figure for demonstrating the determination method whether the cross section of a plate-shaped object and the cross section of a spherical object overlap.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In all the drawings, the same reference numerals are given to the same components, and the description will be omitted as appropriate.

  In the following description, the state change processing unit 24, the movement target selection unit 12, the movement information generation unit 14, the object movement unit 16, the interference determination unit 70, the next state determination unit 18, and the degree of randomness determination of the simulation apparatus 100 will be described. Unit 22, storage unit 26, determination target selection unit 10, coordinate definition unit 20, projection image determination unit 30, first reference surface determination unit 32, second reference surface determination unit 34, third reference surface determination unit 36, and The solid determination unit 40 is not a hardware unit configuration but a functional unit block. State change processing unit 24, movement target selection unit 12, movement information generation unit 14, object movement unit 16, interference determination unit 70, next state determination unit 18, randomness determination unit 22, storage unit 26, determination of simulation apparatus 100 The object selection unit 10, the coordinate definition unit 20, the projection image determination unit 30, the first reference plane determination unit 32, the second reference plane determination unit 34, the third reference plane determination unit 36, and the three-dimensional determination unit 40 are arbitrary. Realized by any combination of hardware and software, mainly the computer CPU, memory, the program that implements the components shown in the figure loaded in the memory, the storage medium such as the hard disk that stores the program, and the network connection interface Is done. There are various modifications of the implementation method and apparatus.

  FIG. 1 is a flow of the simulation method according to the present embodiment. FIG. 2 is a schematic diagram illustrating an example of a plurality of objects 50 in the three-dimensional space. The simulation method according to the present embodiment is a simulation method for a three-dimensional space in which a plurality of objects 50 are arranged. In the simulation method according to the present embodiment, the state change process for performing the movement target selection step S12, the movement information generation step S14, the object movement step S16, the interference determination step S70, and the next state determination step S18 is repeatedly performed. In the movement target selection step S12, spatial state data indicating the arrangement state of the plurality of objects 50 in the three-dimensional space is acquired, and at least one movement target 56 to be moved is selected from the plurality of objects 50. . In the movement information generation step S14, movement information indicating how to move the movement target 56 is generated. In the object moving step S16, temporary space state data including information on at least the arrangement state of the moving object 56 in the three-dimensional space after the moving object 56 is moved based on the movement information is generated. In the interference determination step S70, it is determined whether or not the plurality of objects 50 interfere with each other in the three-dimensional space based on the temporary space state data. In the next state determination step S18, when it is determined in the interference determination step S70 that the plurality of objects 50 do not interfere with each other, the plurality of objects in the three-dimensional space after the movement target 56 is moved based on the movement information. When the information indicating the arrangement state of the object 50 is made into new space state data and it is determined that there is interference, the space state data is not changed. In the object moving step S16, at least one of the parallel movement and the rotational movement of the moving object 56 is performed. At least one of the plurality of objects 50 is a plate-like object. This will be described in detail below.

  The simulation method according to the present embodiment further includes a randomness determination step S22 after the next state determination step S18. In the randomness determination step S22, randomness data indicating the randomness of the plurality of objects 50 is generated in the three-dimensional space based on the space state data, and it is determined whether the randomness satisfies a predetermined criterion. . Then, when the degree of randomness does not satisfy the standard, the state change process is repeated, and when the degree of randomness satisfies the standard, the state change process is repeated.

  The state change process is a process including the movement target selection step S12, the movement information generation step S14, the object movement step S16, the interference determination step S70, and the next state determination step S18 once. Here, the arrangement state indicated by the space state data is not necessarily changed by one state change process, and may or may not be changed.

  The simulation method according to the present embodiment is a method of simulating the arrangement state of a plurality of objects 50 in a three-dimensional space. At least one of the plurality of objects 50 is a plate-like object. In the present embodiment, the plate-shaped object is a disk-shaped object.

  FIG. 3 is a perspective view showing the shape of the disk-shaped object 50 according to the present embodiment. However, the shape of the object 50 is not particularly limited. Here, the plate shape is a shape determined by a plane figure and a thickness l, and in the case of a disk shape, the plane figure is a circle determined by a radius r. The thickness may be smaller than the width of the plane figure, or may be greater than or equal to the width of the plane figure. The plurality of objects 50 may have the same shape or different shapes. Alternatively, the plurality of objects 50 may include objects having a plurality of types of shapes. In the present embodiment, the two flat surfaces 500 of the surface of the plate-like object 50 are hereinafter referred to as “main surfaces”.

The “arrangement state” of each object 50 is defined by information including at least one of the position of the object 50 in the three-dimensional space and the direction of the plate-like object 50. For example, in the three-dimensional space, the position of each object 50 is represented by the coordinates (x _i , y _i , z _i ) of the center point of the object 50 in the orthogonal coordinate system. The arrangement of the plate-like object 50 is defined by the position and direction. Here, the center point of the object 50 is the center of gravity of the object 50, and in the plate-like object 50, it is the center in the thickness direction and the center in a cross section parallel to the main surface. In the present embodiment, the direction of the plate-like object 50 in the three-dimensional space is represented by the normal vector N _i (n _xi , n _yi , n _zi ) of the main surface. The normal vector N _i is a unit vector and has a length of 1. However, the position and orientation of the object 50 in the three-dimensional space may be represented by another coordinate system or the like.

  Returning to FIG. 2, the plurality of objects 50 according to the present embodiment further includes a spherical object. In the present embodiment, an example in which the plurality of objects 50 include a disk-shaped object and a spherical object will be described. However, the present invention is not limited to this, and the plurality of objects 50 may be formed of an arbitrary shape.

  In the present embodiment, all of the plurality of objects 50 are disposed in the filling region 60 having a finite volume. By moving the objects 50 within the filling region 60 so as not to interfere with each other, various arrangement states can be reproduced. In addition, the shape of the filling area | region 60 is not specifically limited. For example, the shape of the filling region 60 may be a polyhedron such as a cube or a rectangular parallelepiped, a sphere, an elliptic rotating body, a columnar body, a cone, or the like.

  For example, by using the simulation method according to the present embodiment, various arrangement states such as particles filled at a specific volume filling rate in a space, a solid, or a liquid can be modeled. Moreover, the process of the change can be reproduced. In particular, a model close to the actual situation can be obtained by reproducing the particles and the like whose positions and directions are randomized to some extent. Specifically, a model having a desired degree of randomness can be obtained by gradually randomizing the objects aligned in a specific filling region. Using such a model, it is possible to calculate thermal conductivity, electrical resistivity, etc. in research and development.

FIG. 4 is a block diagram illustrating a configuration of the simulation apparatus 100 according to the present embodiment.
The simulation apparatus 100 according to the present embodiment is a three-dimensional space simulation apparatus in which a plurality of objects 50 are arranged. The simulation apparatus 100 includes a state change processing unit 24. The state change processing unit 24 includes a movement target selection unit 12, a movement information generation unit 14, an object movement unit 16, an interference determination unit 70, and a next state determination unit 18. The movement target selection unit 12 acquires space state data indicating the arrangement state of the plurality of objects 50 in the three-dimensional space. Then, the movement target selection unit 12 selects at least one movement target 56 to be moved among the plurality of objects 50 (movement target selection step S12). The movement information generation unit 14 generates movement information indicating how to move the moving object 56 (movement information generation step S14). The object moving unit 16 generates temporary space state data including information on the arrangement state of at least the moving object 56 in the three-dimensional space after moving the moving object 56 based on the movement information (object movement Step S16). The interference determination unit 70 determines whether or not the plurality of objects 50 interfere with each other in the three-dimensional space based on the temporary space state data (interference determination step S70). When the interference determination unit 70 determines that the plurality of objects 50 do not interfere with each other, the next state determination unit 18 moves the moving object 56 based on the movement information, and then moves the moving object 56 in the three-dimensional space. The information indicating the arrangement state of the object 50 is used as new space state data, and when it is determined that there is interference, the space state data is not changed (next state determination step S18). The state change processing unit 24 repeatedly performs state change processing for operating the movement target selection unit 12, the movement information generation unit 14, the object movement unit 16, the interference determination unit 70, and the next state determination unit 18. The object moving unit 16 performs at least one of the parallel movement and the rotation movement of the moving object 56. Details will be described below.

  The simulation apparatus 100 according to the present embodiment further includes a randomness determination unit 22 and a storage unit 26 that perform the randomness determination step S220. The randomness determination unit 22 generates randomness data indicating the randomness of the plurality of objects 50 in the three-dimensional space based on the spatial state data, and determines whether or not the randomness satisfies a predetermined criterion. Then, when the degree of randomness does not satisfy the standard, the state change process is repeated, and when the degree of randomness satisfies the standard, the state change process is repeated. Details including the contents of each step will be described below.

  The movement target selection unit 12 performs a movement target selection step S12. That is, the movement target selection unit 12 acquires space state data indicating the arrangement state of all the plurality of objects 50 in the three-dimensional space. Then, the movement target selection unit 12 selects at least one movement target 56 to be moved from among the plurality of objects 50.

The spatial state data is data indicating the arrangement state of all the plurality of objects 50 in the three-dimensional space. Here, the three-dimensional space in the spatial state data is defined using, for example, an orthogonal coordinate system (an “xyz coordinate system”) including an x axis, a y axis, and a z axis that are orthogonal to each other. The space state data includes state data of each object 50 included in the three-dimensional space. The state data is data indicating the shape, position, and orientation of the object 50. For example, the radius r, the thickness l, the coordinates of the center point (x _i , y _i , z _i ), and the normal vector N _i (n of the principal surface) _xi , n _yi , n _zi ). For the object 50 that is a spherical object, the data indicating the thickness l and the normal vector N _i (n _xi , n _yi , n _zi ) of the principal surface may be omitted. For example, the space state data may be a table indicating the state data of each object 50. The movement target selection unit 12 can read out and acquire the space state data stored in the storage unit 26 in advance. The spatial state data is not limited to the above, and may be information expressed using other coordinate systems and parameters.

  In the present embodiment, the space state data further includes boundary data indicating the inner and outer boundaries of the filling region 60.

  The movement target selection unit 12 selects at least one movement target 56 to be moved from among the plurality of objects 50. The moving object 56 can be arbitrarily selected from all of the plurality of objects 50. From the viewpoint of randomizing the arrangement state, it is preferable to randomly select from a plurality of numbered objects 50 using a uniform random number or the like.

  In the initial space state data, the arrangement state is not particularly limited. For example, a plurality of objects 50 may be regularly arranged in the filling region 60.

  The movement information generation unit 14 performs a movement information generation step S14. That is, the movement information generation unit 14 generates movement information indicating how to move the moving object 56. The movement information generation unit 14 according to the present embodiment generates movement information using a uniform random number for randomization. The movement of the moving object 56 includes parallel movement and rotational movement.

The information related to the parallel movement is expressed by, for example, differences Δx _p , Δy _p and Δz _p between the coordinates before and after the movement. Here, Δx _p , Δy _p and Δz _p are uniform random numbers a _p , θ _p , and φ _p (0 ≦ a _p <a _pmax , 0 ≦ θ _p <2π, −π / 2 ≦ φ _p <+ π / 2) respectively, using the _{Δx p = a p · cosφ p} · cosθ p, Δy p = a p · cosφ p · sinθ p, represented by _{Δz p = a p · sinφ p} . However, it is not limited to this. The information regarding the parallel movement may be information representing coordinates after the movement, for example.

Information about the rotational movement is expressed by, for example, a normal vector (n _xr , n _yr , n _zr ) after movement. _Here, n _{xr, n yr,} and _{n zr} are uniform random number theta _r and _{φ r (0 ≦ θr <2π} , -π / 2 ≦ φ r <+ π / 2) respectively, using the _n xr = _{cosφ r} Cos θ _r , n _yr = cos φ _r · sin θ _r , and n _zr = sin φ _r However, it is not limited to this. The information regarding the rotational movement may be information indicating a difference in the direction of the normal vector before and after the movement, for example.

  The movement information may be at least one of information related to parallel movement and information related to rotational movement, and may include both information related to parallel movement and information related to rotational movement. However, if the movement information is generated so that the parallel movement and the rotational movement are performed randomly while the state change process is repeated, the arrangement state can be randomized.

  The order of the movement target selection step S12 and the movement information generation step S14 is not limited, and the movement information generation step S14 may be performed after the movement target selection step S12, or the movement target selection step after the movement information generation step S14. S12 may be performed. Or movement object selection process S12 and movement information generation process S14 may be performed simultaneously.

  The object moving unit 16 performs an object moving process S16. That is, the object moving unit 16 generates temporary space state data including information on at least the arrangement state of the moving object in the three-dimensional space after moving the moving object 56 based on the movement information. In the present embodiment, a case where the temporary space state data is information indicating the arrangement state of all the objects 50 will be described.

The object movement unit 16 acquires data indicating the movement object 56 from the movement target selection unit 12, acquires movement information from the movement information generation unit 14, and generates a storage unit 26 in order to generate temporary space state data. Get spatial state data from. Then, the moving object 56 is moved as indicated by the movement information with respect to the arrangement state indicated by the space state data, and data indicating the arrangement state of the plurality of objects 50 in the subsequent three-dimensional space is generated as temporary space state data. . For example, in the example of the movement information described above, when the center coordinates of the moving object 56 before the movement are (x ₀ , y ₀ , z ₀ ), the center coordinates after the parallel movement are (x ₀ + Δx _p , y _0). + Δy _p , z ₀ + Δz _p ). For example, the normal vector after rotational movement is (n _xr , n _yr , n _zr ) regardless of the normal vector of the moving object 56 before movement.

  It should be noted that by limiting the movement, it is possible to randomize while controlling the direction of the object 50, and it is possible to create a model in which the direction of the object 50 has a desired anisotropy. As a method of limiting movement, for example, a method of limiting the range of random numbers used for generating movement information can be mentioned.

  The interference determination unit 70 performs an interference determination step S70. The interference determination unit 70 acquires temporary space state data from the object moving unit 16. Then, it is determined whether or not the plurality of objects 50 interfere with each other in the arrangement state indicated by the temporary space state data. For example, the interference determination unit 70 selects any two objects 50 from the plurality of objects 50 and determines whether or not the two objects 50 interfere with each other. When all the objects 50 do not interfere with other objects 50, it is determined that the plurality of objects 50 do not interfere with each other. On the other hand, when at least one object 50 interferes with another object 50, it is determined that interference between the objects 50 has occurred. Here, the state in which the objects 50 interfere with each other means a state in which a part of two or more objects 50 exists at one point in the three-dimensional space. In reality, such a state cannot occur, but such a state can be assumed in the calculation. When it is desired to perform a simulation in accordance with reality, the interference state needs to be prohibited as an unacceptable state, and it is important to determine whether or not an interference state has occurred.

  It should be noted that it is not necessary to determine whether or not the objects 50 interfere with each other, and it is determined that any one object 50 is determined to interfere with another object 50. Thus, it may be determined that interference between the objects 50 has occurred, and determination regarding the object 50 that has not yet been performed may be stopped. Here, the order of determining the plurality of objects 50 is not particularly limited.

  In the present embodiment, since the plurality of objects 50 include a plate-like object and a spherical object, as a type of determination as to whether or not two objects 50 interfere with each other, There is a determination between an object and a spherical object, and a determination between spherical objects. Of these, the determination of spherical objects is determined as interference if the distance between the centers of the two spherical objects is less than or equal to the sum of the radii of both spherical objects, and interference occurs in other cases. It is determined that there is no. The determination between the plate-like objects and the determination between the plate-like object and the spherical object will be described in detail later.

  Further, as described above, in the present embodiment, all of the plurality of objects 50 are arranged in the filling region 60 having a finite volume. In order to maintain this state, in the interference determination step S70, it is further determined whether or not an area outside the filling area 60 interferes with at least one object 50. Hereinafter, the area outside the filling area is referred to as “external area”.

  For example, the interference determination unit 70 selects any one object 50 from the plurality of objects 50 and determines whether or not the object 50 interferes with an external region. Then, when at least one of the plurality of objects 50 interferes with the external area, it is determined that interference between the object 50 and the external area has occurred. On the other hand, when all of the plurality of objects 50 do not interfere with the external region, it is determined that interference between the object 50 and the external region has not occurred. Here, the state where the object 50 and the external region interfere with each other means a state where at least a part of the object 50 is outside the filling region 60.

  Note that it is not necessary to determine whether or not the interference between the object 50 and the external area has occurred, and it is determined that any one object 50 is interfering with the external area. At the time, it may be determined that interference between the object 50 and the external region has occurred, and determination regarding the object 50 that has not been performed may be stopped. Here, the order of determining the plurality of objects 50 is not particularly limited.

  In the present embodiment, since the plurality of objects 50 include a plate-like object and a spherical object, as a type of determination as to whether or not the object 50 and the external area interfere with each other, the determination of the plate-like object and the external area , And a spherical object and an external region. Among these, the determination of the spherical object and the external region is determined as interference if the minimum distance between the center point of the spherical object and the external region is equal to or less than the radius of the spherical object, and the spherical object If the minimum distance between the center point of the object and the outer region is larger than the radius of the spherical object, it is determined that there is no interference.

  FIG. 5 is a diagram for explaining a method for determining whether or not a plate-like object and an external region interfere with each other. In the following example, it is determined whether or not the filling region 60 is a rectangular parallelepiped having a plane orthogonal to each axis of xyz, and the entire plate-like object 50 is inside two mutually facing surfaces perpendicular to the z axis. Will be explained. Whether or not the entire plate-like object 50 is inside the two opposing surfaces perpendicular to the x axis and whether it is inside the two opposing surfaces perpendicular to the y axis are the same. Can be determined. If it is determined that all the three directions are determined to be inside, it is determined that the plate-like object 50 and the external region do not interfere with each other. On the other hand, when it is determined that at least one of the determinations in the three directions is not inside, it is determined that the plate-like object 50 and the external region interfere. The determination in all three directions may be performed, or when it is determined that any one of the three directions is not inside, it is determined that the plate-like object and the external region interfere with each other, and the determination that has not been performed is cancelled. May be. Here, the order of determination is not particularly limited. Note that a method for determining whether or not a plate-like object and an external region interfere with each other is not limited to this example.

This figure is a cross-sectional view of the object 50 by a plane orthogonal to two planes perpendicular to the z-axis and including the center axis of the plate-like object 50 (the axis passing through the center point of the object 50 and parallel to the normal vector). is there. In the figure, Z _max and Z _min are threshold values indicating the boundary between the filling region 60 and the external region. A square 502 is the outline of the object 50, and a dotted line 504 is a center line in the thickness direction of the object 50. The point P _max is a point where the z coordinate is maximum in the object 50, and the point P _min is a point where the z coordinate is minimum in the object 50.

The difference in the z coordinate between the center point O _d and the point P _max of the plate-like object 50 is divided into a length indicated by d ₁ and a length indicated by d ₂ in the drawing. The length of d ₁ is represented by the absolute value of the difference between the z coordinate of the intersection of the dotted line 504 and the side surface of the object 50 and the z coordinate of the point P _max . The length of d ₂ is represented by the absolute value of the difference between the z coordinate of the intersection of the dotted line 504 and the side surface of the object 50 and the z coordinate of the center point O _d . Specifically, the lengths of d ₁ and d ₂ are expressed by the following equations (1) and (2), respectively, and using the normal vector N _i (n _xi , n _yi , n _zi ), the equation (3) ) And formula (4). Note that _Ni is a unit normal vector as described above. Here, the angle θ _z is an angle formed between the normal vector _Ni and the z axis.

Here, using the z coordinate z _i of the center point O _d of the object 50, the z coordinate of P _max is expressed as z _i + d ₁ + d ₂ , and the z coordinate of P _min is z _i −d ₁ −d ₂ . Therefore, when both of the following expressions (5) and (6) hold, it can be determined that the entire object 50 is inside two opposing surfaces perpendicular to the z axis. On the other hand, when at least one of Expression (5) and Expression (6) does not hold, it can be determined that at least a part of the object 50 is not inside the two opposing surfaces perpendicular to the z-axis. Whether the expressions (5) and (6) are satisfied is sequentially determined. When it is determined that one of the expressions is not satisfied, at least a part of the object 50 is not inside the two opposing surfaces perpendicular to the z axis. The other determination that has not yet been performed may be canceled. The order of determination is not particularly limited.

  In addition, when the filling area | region 60 is spherical, based on the state in the cross section in the plane in which each center point of the two main surfaces 500 of the plate-shaped object 50 and the center of the sphere of the filling area | region 60 are included, plate shape It can be determined whether or not the object and the external area interfere with each other. In the cross section, when the four vertices of the quadrangle that is the outline of the object 50 are all inside the circle that is the outline of the sphere, it is determined that the plate-like object and the external region do not interfere with each other. On the other hand, when at least one vertex is outside the circle, it is determined that the plate-like object and the external region interfere with each other. The determination of all four vertices may be performed, and when it is determined that any one of the vertices is not inside the circle, it is determined that the plate-like object and the external region interfere with each other, and has not yet been performed. The determination may be stopped. Here, the order of determination is not particularly limited. Note that a method for determining whether or not a plate-like object and a spherical outer region interfere with each other is not limited to this example.

  The interference determination unit 70 may determine all the objects 50 every time the state change process is performed, or may determine only the moving object 56. By doing so, the amount of calculation can be reduced.

  In the case where it is not necessary to strictly limit the occupied volume of the object 50 in the filling region 60, the interference determination unit 70 instead of determining whether or not the object 50 and the external region interfere with each other, It may be determined whether 50 center points are inside the filling region 60. Then, the amount of calculation can be reduced. In that case, when the center point of the object 50 is inside the filling region 60, it is considered that the object 50 and the external region do not interfere with each other, and in other cases, the object 50 and the external region interfere with each other. What is necessary is just to perform subsequent processes.

  Returning to FIG. 4, the next state determination unit 18 performs a next state determination step S18. In the present embodiment, an example will be described in which the next state determination unit 18 operates in consideration of the presence or absence of interference between the objects 50 and the presence or absence of interference between the object 50 and an external region.

  The next state determination unit 18 acquires temporary space state data and data indicating the determination result by the interference determination unit 70 from the interference determination unit 70. Then, in the interference determination step S70, the next state determination unit 18 determines that the plurality of objects 50 do not interfere with each other, and if it is determined that none of the objects 50 interfere with the external region, The temporary space state data generated by the object moving unit 16 is used as new space state data. On the other hand, in other cases, that is, when any object 50 interferes with each other, or when any object 50 interferes with an external region, the spatial state data is not changed. The changed space state data may be stored in the storage unit 26 in place of the space state data before the change. At that time, the space state data before the change may be deleted from the storage unit 26 or may be continuously held in the storage unit 26 as the space state data at the previous time point. By arranging the spatial state data at each time point in order, the randomization process can be simulated.

  In the case where a simulation is performed without providing the condition that the plurality of objects 50 are arranged in the filling region 60 having a finite volume, the interference determination unit 70 uses the region outside the filling region 60, the plurality of objects 50, and the like. Can be omitted. In that case, the next state determination unit 18 sets the temporary space state data as new space state data when the interference determination unit 70 determines that the plurality of objects 50 do not interfere with each other, and in other cases, It is not necessary to change the space state data.

  The randomness determination unit 22 acquires spatial state data from the next state determination unit 18. The space state data is the latest space state data at that time. That is, when the next state determination unit 18 changes the spatial state data in the state change process, the latest spatial state data acquired by the randomness degree determination unit 22 is generated by the object moving unit 16 in the state change process. This is the same as the temporary space state data. Alternatively, when the next state determination unit 18 does not change the spatial state data in the state change process, the latest spatial state data acquired by the randomness determination unit 22 is the spatial state acquired first by the movement target selection unit 12. Same as data. The next state determination unit 18 may hold the latest space state data in the storage unit 26. In that case, the randomness determination unit 22 may acquire the latest spatial state data from the storage unit 26 instead of acquiring it from the next state determination unit 18.

  The randomness determination unit 22 generates randomness data indicating the randomness of the plurality of objects 50 in the three-dimensional space based on the acquired latest space state data. Then, it is determined whether or not the degree of randomness satisfies a predetermined criterion. When the degree of randomness does not satisfy the standard, the state change process is repeated, and when the degree of randomness satisfies the standard, the state change process is repeated.

  If the degree of randomness is determined to satisfy the criterion, the randomness determination unit 22 may end the state change process at that time, or may end after performing a specific number of state change processes. You may let them.

Here, the degree of randomness can be obtained based on normal vectors of a plurality of objects 50, for example. For example, calculation of the normal vectors of all of the plate-like object 50, the average value _{n Xave} of the squares of the elements _{n xi,} average _{n Yave} of the squares of the elements _{n yi,} and the mean value _{n Zave} of the squares of the elements _{n zi} And it can be said that the degree of randomness is higher as each of n _xave , n _yave , and n _zave is closer to 1/3.

In this embodiment, clutter level determination unit 22, based on the normal vector of all of the objects 50, and calculates the average value _{n Xave,} average _{n Yave,} and an average value _{n Zave.} For example, the absolute value of the value obtained by subtracting 1/3 from each average value is obtained as the randomness, and when the randomness is equal to or less than a predetermined reference value, the randomness satisfies the standard. Ends the repetition of the state change process. On the other hand, when the degree of randomness exceeds a predetermined reference value, the state change process is performed again, assuming that the degree of randomness does not satisfy the standard. Here, the smaller the reference value is, the higher the randomness is. The reference value of the degree of randomness may be acquired by the randomness degree determination unit 22 by reading information previously stored in the storage unit 26 or by acquiring information input to an input unit (not shown). Also good.

  Note that the definition of the degree of randomness in the randomness degree determination unit 22 and the method of determining the reference are not limited to the above method. For example, the randomness determination unit 22 may further determine the randomness based on the positions of the plurality of objects 50. As the degree of randomness based on the position, for example, the standard deviation of the coordinate value of the object 50 can be used.

  In addition, when space state data are not changed by state determination process S18, disorder degree determination process S22 may be abbreviate | omitted and a state change process may be performed again.

  The randomness determination step S22 is not necessarily performed every time the state change process is performed. Since the degree of randomness hardly changes when only a small number of objects 50 are moved, the randomness determination step S22 is not performed every time, and may be performed once for several state change processes. By doing so, the amount of calculation can be reduced. Moreover, since it is clear that the standard is not satisfied at the initial stage when the randomization is started from the state in which the plurality of objects 50 are arranged, the randomness determination step S22 can be omitted. The randomness determination step S22 may be performed for the first time after the state change process is performed a specific number of times from the initial state or the space state data is changed.

  It should be noted that the repetition of the state change process may be terminated when the state change process is performed a specific number of times without performing the randomness determination step S22. In this case, it is not necessary to provide the randomness determination unit 22.

  In the present embodiment, the case where the temporary space state data is information indicating the arrangement state of all the objects 50 has been described. However, the present invention is not limited to this. For example, the temporary space state data may include at least information indicating the arrangement state of the moving object 56, may be information indicating the arrangement state of only the moving object 56, or the moving object 56 and its surroundings. Information indicating the arrangement state of some objects 50 may be used. In addition, the temporary space state data may include all of the elements such as the shape, position, and orientation that make up the space state data, or may include only some of the elements related to movement. . In the case of these examples, the interference determination unit 70, for example, all after the moving object 56 has moved based on the temporary space state data acquired from the object moving unit 16 and the space state data acquired from the storage unit 26. The information indicating the arrangement state of the object 50 can be generated and determined. Alternatively, for example, the interference determination unit 70 may perform the interference determination on only the arrangement state of the moving object 56 and some surrounding objects 50 based on the temporary space state data acquired from the object moving unit 16. .

  By using the simulation method according to the present embodiment, it is possible to obtain a model in a three-dimensional space in which a plurality of objects 50 are arranged at random with arbitrary randomness.

[Judgment of interference between plate-like objects]
Next, the plurality of objects 50 include at least a first plate-like object and a second plate-like object, and the interference determination unit 70 causes the first plate-like object and the second plate-like object to interfere with each other. The method for determining whether or not to do so will be described in detail.

FIG. 6 is a flow of the interference determination step S70 according to the present embodiment.
The interference determination step S70 according to the present embodiment is an interference determination step S70 for a plurality of objects 50 in a three-dimensional space. The interference determination step S70 includes a determination object selection step S10, a coordinate definition step S20, a projection image determination step S30, and a solid determination step S40. In the determination object selection step S <b> 10, the first plate-like object is selected as the first object 52 from the plurality of objects 50, and the second plate-like object is selected as the second object 54. In the coordinate definition step S20, one orthogonal coordinate system is defined for the first object 52 and the second object 54. In the projection image determination step S30, it is determined whether or not the projection images of the first object 52 and the second object 54 projected onto the reference plane of the orthogonal coordinate system overlap each other. In the solid determination step S40, it is determined whether or not the first object 52 and the second object 54 interfere in the three-dimensional space. Here, the first object 52 and the second object 54 are plate-shaped, and the orthogonal coordinate system includes an e ₁ axis, an e ₂ axis, and an e ₃ axis that are orthogonal to each other.

The projection image determination step S30 includes at least one of a first reference surface determination step, a second reference surface determination step, and a third reference surface determination step. In the first reference plane determination step, it is determined whether or not the projected images of the first object 52 and the second object 54 overlap each other on the first reference plane including the e ₁ axis and the e ₂ axis. In the second reference surface determining step, in the second reference plane consisting of e ₂ axes and e ₃ axes, whether the projected image of the first object 52 and second object 54 overlap each other is determined. In the third reference surface determining step, the third reference plane consisting of a e ₃ axes and e ₁ axis, whether the projected image of the first object 52 and second object 54 overlap each other is determined. When it is determined in the projection image determination step S30 that the projected images of the first object 52 and the second object 54 do not overlap each other on at least one of the first reference surface, the second reference surface, and the third reference surface. Moreover, in the solid determination step S40, it is determined that the first object 52 and the second object 54 are not in a state of interference. This will be described in detail below.

  In the interference determination step S70 according to the present embodiment, it is determined whether or not the projected images of the first object 52 and the second object 54 projected onto at least one reference plane overlap each other, and these projected images are mutually connected. Based on the determination result of whether or not they overlap, it is determined whether or not the first object 52 and the second object 54 interfere with each other.

  In the interference determination step S70 according to the present embodiment, it is determined whether or not a plurality of plate-like objects 50 having arbitrary positions and angles in the three-dimensional space interfere with each other.

  Whether or not a plurality of spherical objects interfere with each other can be easily determined only by the distance between the centers and the radius. Specifically, when the distance between the centers of the two spheres is smaller than the sum of the radii of the two spheres, it can be determined that there is interference. On the other hand, the plate-like object 50 according to the present embodiment has a three-dimensional anisotropic shape, and each has a direction. Cannot judge. For example, even when the distance between the centers of the two objects 50 is smaller than the sum of the radii of their circumscribed spheres, such as when the main surfaces are parallel to each other, there may be no interference. In the interference determination step S70 according to the present embodiment, since the determination is made in consideration of the shape and orientation of the object 50, more accurate interference determination is possible.

FIG. 7 is a block diagram of the interference determination unit 70 that performs interference determination using the interference determination step S70 according to the present embodiment.
The interference determination unit 70 is an interference determination device for a plurality of objects 50 in a three-dimensional space. The interference determination unit 70 includes a determination object selection unit 10, a coordinate definition unit 20, a projection image determination unit 30, and a solid determination unit 40. The determination target selection unit 10 selects the first target 52 and the second target 54 from the plurality of objects 50 (determination target selection step S10). The coordinate definition unit 20 defines one orthogonal coordinate system for the first object 52 and the second object 54 (coordinate definition step S20). The projection image determination unit 30 determines whether or not the projection images of the first object 52 and the second object 54 projected onto the reference plane of the orthogonal coordinate system overlap each other (projection image determination step S30). The solid determination unit 40 determines whether or not the first object 52 and the second object 54 interfere with each other in the three-dimensional space (stereoscopic determination step S40). Specifically, the solid determination unit 40 uses the projection image determination unit 30 to determine the first object 52 and the second object 54 on at least one of the first reference surface, the second reference surface, and the third reference surface. When it is determined that the projected images do not overlap with each other, it is determined that the first object 52 and the second object 54 do not interfere with each other. Below, the details of each process will be described.

  The determination target object selection unit 10 acquires temporary space state data indicating the states of all the plurality of objects 50 in the three-dimensional space from the next state determination unit 18. Note that the determination object selection unit 10 may read and acquire temporary space state data once stored in the storage unit 26.

The determination target object selection unit 10 performs a determination target object selection step S10 based on the acquired temporary space state data. In the determination object selection step S <b> 10, the first object 52 and the second object 54 are selected from the plurality of objects 50. As the first object 52 and the second object 54, two different plate-like objects 50 among the plurality of objects 50 can be arbitrarily selected. If the distance between the centers of the two objects 50 is larger than the sum of the circumscribed sphere radii r _cs of each object 50, the two objects 50 may be excluded from the selected combination because they do not interfere with each other. For example, the object 50 of the disc-shaped, the radius _{r cs} of the circumscribed sphere, disc center axis passing through the diagonal of the half of the length in a cross section, i.e. with ^{((l 2/4) +} r 2) 1/2 is there.

The determination object selection unit 10 extracts the state data of the selected first object 52 and second object 54 from the temporary space state data. In the following, the radius of the selected first object 52 is r _p , the thickness is l _p , the coordinates of the center point are (x _p , y _p , z _p ), and the normal vector is N _p (n _xp , n _yp , n _zp ), the radius of the second object 54 is r _c , the thickness is l _c , the coordinates of the center point are (x _c , y _c , z _c ), and the normal vector is N _c (n _xc , n _yc). , N _zc ). As described above, the normal vector is a unit vector and has a length of 1.

  The coordinate definition unit 20 performs a coordinate definition step S20. The coordinate definition unit 20 acquires state data of the first object 52 and the second object 54 extracted by the determination object selection unit 10. The coordinate defining unit 20 defines an orthogonal coordinate system based on the state data of the first object 52 and the second object 54.

FIG. 8 is a diagram showing an orthogonal coordinate system defined in the coordinate definition step S20.
The orthogonal coordinate system defined in the coordinate defining step S20 according to the present embodiment includes an e ₁ axis, an e ₂ axis, and an e ₃ axis that are orthogonal to each other. The coordinate definition step S20, the center of the first object 52 coincides with the origin, and the main surface e ₃ axis of the first object 52 are orthogonal, e of the normal vector of the principal surface of the second object 54 _The orthogonal coordinate system is defined so that the _two components are zero. By defining the orthogonal coordinate system in this way, the conditions used for the determination can be expressed by a simple mathematical expression, and the amount of calculation can be reduced.

As described above, the radius of the first object 52 is r _p , the thickness is l _p , the radius of the second object 54 is r _c , and the thickness is l _c , and the second object 54 in the orthogonal coordinate system The central coordinates are (a, b, c), and the angle formed between the normal vector of the main surface of the first object 52 and the normal vector of the main surface of the second object 54 is 0 rad or more and π / 2 rad or less. The angle θ can be expressed as Here, since the state does not change even if the object 50 is inverted, the normal vector may be inverted. In the drawing, N _p ′ represents a normal vector of the main surface of the first object 52, and N _c ′ represents a normal vector of the main surface of the second object 54.

  In addition, the coordinate system defined in coordinate definition process S20 is not specifically limited. When an axis different from the above is defined, the mathematical formula used for the following determination may be appropriately changed accordingly.

The orthogonal coordinate system defined in the coordinate definition step S20 may be the same as or different from the orthogonal coordinates in the temporary space state data of the three-dimensional space. Hereinafter, the coordinate system defined in the coordinate definition step S20 of the orthogonal coordinates in the temporary space state data of the three-dimensional space is referred to as “e ₁ e ₂ e ₃ coordinate system”.

The e ₁ e ₂ e ₃ coordinate system can be defined for any two plate-like objects 50 in a three-dimensional space. Here, the xyz coordinate system and the e ₁ e ₂ e ₃ coordinate system can be converted by the relationship of the following formula (7). However, A in Formula (1) is represented by the following Formula (8).

In the e ₁ e ₂ e ₃ coordinate system, the coordinates of the center point of the first object 52 are represented by (0, 0, 0), and the normal vector is represented by (0, 0, 1). Further, the coordinates (a, b, c) of the center point of the second object 54 and the normal vector N _c ′ ( _nxc ′, _nyc ′, _nzc ′) are expressed by the following equations (9) and (9), respectively. It is represented by (10). In Expression (9), Δx, Δy, and Δz are the coordinates of the center point of the first object 52 (x _p , y _p , z _p ) and the center point of the second object 53 in the xyz coordinate system, respectively. Using coordinates (x _c , y _c , z _c ), Δx = x _c −x _p , Δy = y _c −y _p , Δz = z _c −z _p

In this manner, the coordinate defining unit 20 is data indicating the coordinates (a, b, c) of the center point of the second object 54 and the normal vector N _c ′ ( _nxc ′, _nyc ′, _nzc ′). Is generated.

Returning to FIG. 7, the projection image determination unit 30 receives the radius r _p and the thickness l _{p of} the first object 52, the radius r _c and the thickness l _{c of} the second object 54, and the center point from the coordinate definition unit 20. Data indicating the coordinates (a, b, c) and the normal vector N _c ′ (n _xc ′, _nyc ′, _nzc ′) is acquired, and the projection image determination step S30 is performed based on the data. In the projected image determination step S30, it is determined whether or not the projected images of the first object 52 and the second object 54 projected onto the three reference planes of the e ₁ e ₂ e ₃ coordinate system overlap each other.

FIG. 9 is a flowchart showing the contents of the projection image determination step S30 and the three-dimensional determination step S40. The projection image determination step S30 includes a first reference surface determination step S32, a second reference surface determination step S34, and a third reference surface determination step S36. In the first reference surface determining step S32, in the first reference plane consisting of e ₁ axis and e ₂ axis, whether the projected image of the projection image and the second object 54 of the first object 52 overlap each other the determination Is done. In the second reference surface determining step S34, in the second reference plane consisting of e ₂ axes and e ₃ axes, whether the projected image of the projection image and the second object 54 of the first object 52 overlap each other the determination Is done. In the third reference surface determining step S36, the third reference plane consisting of a e ₃ axes and e ₁ axis, whether the projected image of the projection image and the second object 54 of the first object 52 overlap each other the determination Is done.

  In the solid determination step S40, it is determined whether or not the first object 52 and the second object 54 interfere in the three-dimensional space. Specifically, based on the determination result of the projection image determination step S30, the first target in at least one of the first reference surface determination step S32, the second reference surface determination step S34, and the third reference surface determination step S36. When it is determined that the projection images of the object 52 and the second object 54 do not overlap with each other, it is determined that the first object 52 and the second object 54 are not in interference. On the other hand, in all of the first reference surface determination step S32, the second reference surface determination step S34, and the third reference surface determination step S36, it is determined that the projected images of the first object 52 and the second object 54 overlap each other. In this case, it is determined that the first object 52 and the second object 54 interfere with each other.

  The first reference surface determination step S32, the second reference surface determination step S34, and the third reference surface determination step S36 may all be performed, or any one of the first object 52 and the first reference surface determination step S36 may be performed. When it is determined that the projection images of the two objects 54 do not overlap with each other, other processes that have not yet been performed are stopped, and the first object 52 and the second object 54 do not interfere with each other. May be determined. In addition, the execution order of 1st reference plane determination process S32, 2nd reference plane determination process S34, and 3rd reference plane determination process S36 is not specifically limited.

  Returning to FIG. 7, the projection image determination unit 30 according to the present embodiment includes a first reference surface determination unit 32, a second reference surface determination unit 34, and a third reference surface determination unit 36. The first reference surface determination unit 32 performs a first reference surface determination step S32, the second reference surface determination unit 34 performs a second reference surface determination step S34, and the third reference surface determination unit 36 performs a third reference surface determination step. S36 is performed. The first reference surface determination step S32, the second reference surface determination step S34, and the third reference surface determination step S36 will be described in detail later.

  The first reference surface determination unit 32, the second reference surface determination unit 34, and the third reference surface determination unit 36 respectively include the first object 52 and the third reference surface in the first reference surface, the second reference surface, and the third reference surface, respectively. Determination data indicating a determination result of whether or not the projected images of the second object 54 overlap each other is generated.

  The solid determination unit 40 performs a solid determination step S40. The solid determination unit 40 acquires the determination data regarding each of the first reference plane, the second reference plane, and the third reference plane from the projection image determination unit 30. And the solid determination part 40 performs the solid determination process S40, and outputs the data which show the determination result which shows whether the 1st target object 52 and the 2nd target object 54 interfere in 3D space.

Further, the determination object selection unit 10 selects two other plate-like objects 50 from the plurality of objects 50 as the first object 52 and the second object 54, and similarly determines whether or not they interfere with each other. It may be broken. Whether or not an interference state between the plate-like objects 50 is generated in the three-dimensional space by performing the interference determination with the other plate-like objects 50 for all the plate-like objects 50 in the three-dimensional space. It is possible to determine whether. When the distance between the centers of the two objects 50 is larger than the sum of the radius _rcs of the circumscribed sphere of each object 50, it is determined that the two objects 50 do not interfere with each other, assuming that the two objects 50 do not interfere with each other. The above-described interference determination may be performed for other combinations.

<First reference plane determination step>
The first reference plane determination step S32 will be described below. In the first reference plane determination step S32 according to the present embodiment, a first projection area, a second projection area, and a third projection area, which are included in the projection images of the second object 54 on the first reference plane, are defined. It is determined whether or not each region and the projection image of the first object 52 overlap. Details will be described below.

FIG. 10 is a flow showing the contents of the first reference plane determination step S32.
The first reference plane determination step S32 includes at least one of a first partial determination step S320, a second partial determination step S322, and a third partial determination step S324. In the first part determination step S320, a first projection region that is a projection part of the upper surface of the second object 54 among the projection image of the first object 52 and the projection image of the second object 54 on the first reference plane. Are overlapped with each other. In the second part determination step S322, a second projection region that is a projection part of the lower surface of the second object 54 among the projection image of the first object 52 and the projection image of the second object 54 on the first reference plane. Are overlapped with each other. In the third partial determination step S324, an area that is not included in the first projection area or the second projection area in the projection image of the first object 52 and the projection image of the second object 54 on the first reference plane. It is determined whether or not the third projection area including all of the above overlaps. When it is determined that at least one of the first partial determination step S320, the second partial determination step S322, and the third partial determination step S324 is overlapped, the first object 52 and the second reference point on the first reference plane. It is determined that the projected images of the object 54 overlap each other. On the other hand, when it is determined in all of the first partial determination step S320, the second partial determination step S322, and the third partial determination step S324 that the projection images of the first object 52 and the second object 54 do not overlap each other. In addition, it is determined that the projected images of the first object 52 and the second object 54 do not overlap with each other on the first reference plane. Note that, with the e ₃ axis positive direction in the e ₁ e ₂ e ₃ coordinate system as the upper side, “upper surface” and “lower surface” of the main surfaces are distinguished.

  The first partial determination step S320, the second partial determination step S322, and the third partial determination step S324 may all be performed, or the projected image of each region and the first object 52 in any one step. When it is determined that the two overlap each other, other processes that have not yet been performed are stopped, and it is determined that the projected images of the first object 52 and the second object 54 overlap each other on the first reference plane. . In addition, the execution order of 1st partial determination process S320, 2nd partial determination process S322, and 3rd partial determination process S324 is not specifically limited.

The first partial determination step S320 will be described below.
FIG. 11A is a schematic diagram illustrating an example of a projection image of the first object 52 and a projection image of the second object 54 on the first reference plane. In the drawing, a circle 520 is a circle indicating the outline of the projected image of the first object 52 on the first reference plane. The ellipse 540 is an ellipse that shows the outline of the region where the upper surface portion of the second object 54 is projected. In the first part determination step S320, a first projection region that is a projection part of the upper surface of the second object 54 among the projection image of the first object 52 and the projection image of the second object 54 on the first reference plane. Are overlapped with each other. The first projection area is an area having an ellipse 540 as an outline in the drawing.

  FIG. 11B is a schematic diagram for explaining the first partial determination step S320. When a circle 521 having the same shape as the circle 520 is circumscribed to the ellipse 540 and moved without rolling in order to determine whether or not the projection image of the first object 52 and the first projection area overlap. A region having an ellipse 542 drawn by the center of the circle 521 as an outline is defined. Then, based on whether or not the center of the circle 520 that is the projection image of the first object 52 is within the region having the ellipse 542 as an outline, the projection image of the first object 52 and the first projection It is determined whether or not the area overlaps. Specifically, when the center of the projection image of the first object 52 is within a region having an ellipse 542 as an outline, it is determined that the projection image of the first object 52 and the first projection region overlap, When the center of the projection image of the first object 52 is not within the region having the ellipse 542 as an outline, it is determined that the projection image of the first object 52 and the first projection region do not overlap.

  The examination described above does not have to be performed for each determination, and in the present embodiment, the first partial determination step S320 can be performed using the following equation (11). That is, when Expression (11) does not hold, it is determined that the projection image of the first object 52 and the first projection area do not overlap.

Next, 2nd partial determination process S322 is demonstrated below.
In FIG. 11A, an ellipse 541 is an ellipse showing the outline of the region where the lower surface portion of the second object 54 is projected. In the second part determination step S322, a second projection region that is a projection part of the lower surface of the second object 54 among the projection image of the first object 52 and the projection image of the second object 54 on the first reference plane. Are overlapped with each other. The second projection area is an area having an ellipse 541 as an outline in the drawing.

  In the second part determination step S322, as in the first part determination step S320, when the circle 521 having the same shape as the circle 520 is moved without circumscribing the ellipse 541, the ellipse drawn by the center of the circle 521 is drawn. A region having an outline is defined. Then, based on whether or not the center of the circle 520, which is the projection image of the first object 52, is within a region having the ellipse as an outline, the projection image of the first object 52 and the second projection It is determined whether or not the area overlaps. Specifically, when the center of the projection image of the first object 52 is within a region having the ellipse as an outline, it is determined that the projection image of the first object 52 and the second projection region overlap, When the center of the projection image of the first object 52 is not within the region having the ellipse as an outline, it is determined that the projection image of the first object 52 and the second projection region do not overlap.

  The above-described examination need not be performed for each determination, and the second partial determination step S322 according to the present embodiment can be performed using the following equation (12). That is, when Expression (12) does not hold, it is determined that the projection image of the first object 52 and the second projection area do not overlap.

Next, the third partial determination step S324 will be described below.
FIG. 12A is a schematic diagram showing a projected image of the first object 52 and a projected image of the second object 54 on the first reference plane, and corresponds to FIG. In FIG. 12A, a region 543 surrounded by a broken line is a partial region of the projection image of the second object 54 and is not included in the first projection region or the second projection region. An area exists. Therefore, it is necessary to determine whether or not the area and the projection image of the first object 52 do not overlap. Here, the first reference plane includes all of the projection image of the first object 52 and the projection image of the second object 54 that include all of the areas not included in the first projection area or the second projection area. When the three projection areas are defined and the projection image of the first object 52 and the third projection area do not overlap, the first projection image of the first object 52 and the projection image of the second object 54 are the first. It can be confirmed that there is no overlap between the projection area and the area not included in the second projection area.

  FIG. 12B is a diagram illustrating a third region according to the present embodiment. In this figure, an ellipse 544 is an ellipse drawn by the center of the circle 521 when the circle 521 having the same shape as the circle 520 is moved without being rolled by circumscribing the ellipse 541 described in the second part determination step S322. is there. In the drawing, a region 545 corresponds to a third region. The region 545 is a region whose outline is a rectangle whose two sides are the major axis of the ellipse 542 and the major axis of the ellipse 544. In this way, by defining the third region having a simple shape, the region that is not included in the first projection region or the second projection region and the projection image of the first object 52 are less likely to overlap. It can be confirmed by the calculation amount.

  In the third partial determination step S324, it is determined whether or not the projected image of the first object 52 overlaps the region 545 that is the third region. The determination is made based on the relationship between the four vertex coordinates of the region 545 and the center of the projected image of the first object 52.

  The examination described above does not have to be performed for each determination, and the third partial determination step S324 according to the present embodiment can be performed using the following expressions (13) and (14). That is, when at least one of Expression (13) and Expression (14) does not hold, it is determined that the projection image of the first object 52 and the third projection area do not overlap. It should be noted that whether the expressions (13) and (14) are satisfied is sequentially determined, and when it is determined that one does not hold, the projection image of the first object 52 and the third projection area do not overlap. It may be determined that the other determination that has not been performed may be cancelled. Note that the order in which the determinations are made for both mathematical formulas is not particularly limited.

  The determination method in the first reference plane determination step S32 is not limited to the above method. It is only necessary to determine whether or not at least parts of the projected images of the first object 52 and the second object 54 overlap each other. In the present embodiment, the example in which the first projection area, the second projection area, and the third projection area are determined in the first reference plane determination step S32 has been described. However, the present invention is not limited to such a method. Whether the projection images of the first object 52 and the second object 54 overlap each other based on an area defined by arbitrarily dividing the projection image of the first object 52 and the projection image of the second object 54, respectively. It may be determined. Alternatively, it may be determined whether or not the projection images of the first object 52 and the second object 54 overlap each other based on a determination area defined based on each projection image and a mutual relationship such as determination points. .

<Second reference plane determination step>
The second reference plane determination step S34 will be described below.
FIG. 13A is a schematic diagram illustrating an example of a projected image of the first object 52 and a projected image of the second object 54 on the second reference plane, and FIG. 13B is a first determination region. FIG.
In the second reference plane determination step S34 according to the present embodiment, a first determination area defined by using the projection image of the first object 52 and the projection image of the second object 54 on the second reference plane, By determining whether or not the determination target line determined using the projection image of the target object 54 overlaps, the first target object 52 and the first target object 52 on the second reference plane composed of the e ₂ axis and the e ₃ axis. It is determined whether the projected images of the two objects 54 overlap each other. Details will be described below.

  In FIG. 13A, a quadrangle 522 is a quadrangle that indicates the contour of the projected image of the first object 52 on the second reference plane. The ellipse 546 is an ellipse that shows the outline of the region where the upper surface portion of the second object 54 is projected. The ellipse 547 is an ellipse showing the outline of the region where the lower surface portion of the second object 54 is projected. In the second reference plane determination step S34, in the second reference plane, the first determination area defined by using the projection image of the first object 52 and the projection image of the second object 54 and the second object 54 are determined. It is determined whether the determination target lines overlap.

  The first determination area refers to an ellipse having the same shape as the projected portion of the upper surface of the second object 54 in the projected image of the second object 54 that is circumscribed by the projected image of the first object 52 and does not roll. Is a region having a contour drawn by the center of the ellipse. In FIG. 13B, a graphic 523 corresponds to the contour. The shape of the projected portion on the upper surface of the second object 54 and the shape of the projected portion on the lower surface are the same.

  FIGS. 14A and 14B are diagrams illustrating the determination target line 82 and the determination target point 80. The determination target line 82 is indicated by a dotted line in FIGS. 14 (a) and 14 (b). The projected image of the second object 54 can be regarded as an area formed by translating an ellipse 548 having the same shape as the upper and lower surfaces between the projected portion (ellipse 546) on the upper surface and the projected portion (ellipse 547) on the lower surface. it can. If the ellipse 548 does not overlap the projection image of the first object 52 at all the positions during translation, it can be determined that the projection images of the first object 52 and the second object 54 do not overlap each other. Here, if the center point of the ellipse 548 at each position during translation is not within the first determination region described above, it is determined that the ellipse 548 does not overlap the projected image of the first object 52. The determination target line 82 is a line segment composed of the center points of all ellipses 548 that are being translated. That is, the determination target line 82 includes the lower surface center projection point 840 corresponding to the projection point at the center of the lower surface of the second object 54 in the projection image of the second object 54 on the second reference surface, and the second object. 54 is a line connecting the upper surface center projection point 820 corresponding to the projection point at the center of the upper surface.

  In the second reference plane determination step S34, when at least one point on the determination target line 82 is included in the first determination area, projection images of the first target object 52 and the second target object 54 are displayed on the second reference plane. It is determined that they overlap each other. On the other hand, when any point on the determination target line 82 is not included in the first determination region, it is determined that the projection images of the first object 52 and the second object 54 do not overlap with each other on the second reference plane. Is done.

Here, it is not always necessary to determine whether or not all points on the determination target line 82 are within the first determination region. For example, as shown in FIG. 14 (a), the length L of the determination target line 82, the thickness _l if _p is smaller than the first object 52, the two points of the top surface central projection point 820 and the bottom surface center projection point 840 only If it is determined whether or not the determination target point 80 is within the first determination region, it can be determined whether or not the determination target line 82 and the first determination region overlap. When neither the upper surface center projection point 820 nor the lower surface center projection point 840 is within the first determination region, the line segment between them does not overlap the first determination region. Therefore, it can be determined that the projected images of the first object 52 and the second object 54 do not overlap with each other on the second reference plane.

On the other hand, as shown in FIG. 14 (b), the length L is, if it is the thickness l _p or more first object 52, none of the top central projection point 820 and the bottom surface center projection point 840 is the first determination area Even if not, there may be a case where another point on the determination target line 82 overlaps the first determination region. Therefore, a determination target point 80 is further provided between the upper surface center projection point 820 and the lower surface center projection point 840. Here, the interval L _s is made smaller than the thickness l _p between all two adjacent determination target points 80. However, in order to reduce the amount of calculation, the number of determination target points 80 is preferably the smallest under the condition that the interval L _s is smaller than the thickness l _p . When all the determination target points 80 selected in this way are not within the first determination region, it can be determined that the projected images of the first object 52 and the second object 54 do not overlap with each other on the second reference plane.

In summary, among the projected images of the second object 54 on the second reference plane, a plurality of points on a line segment connecting the lower surface center projection point 840 and the upper surface center projection point 820 are a plurality of determination target points 80. Selected as. The plurality of determination target points 80 include at least the upper surface center projection point 820 and the lower surface center projection point 840, and the distance L _s between the determination target points 80 adjacent to each other is smaller than the thickness l _p of the first object 52. . If none of the determination target points 80 are within the first determination region, it can be determined that the projected images of the first object 52 and the second object 54 do not overlap with each other on the second reference plane. On the other hand, when at least one of the plurality of determination target points 80 is in the first determination region, it can be determined that the projected images of the first object 52 and the second object 54 overlap each other on the second reference plane.

  It should be noted that the determination is performed in order for the plurality of determination target points 80, and when it is determined that any one of the determination target points 80 is within the first determination region, the first target object 52 and the first object 52 on the second reference plane. It may be determined that the projected images of the two objects 54 overlap each other, and the determination of the determination target point 80 that has not yet been performed may be stopped. The order in which the determination is made for the plurality of determination target points 80 is not particularly limited.

  A method for determining whether or not each determination target point 80 is in the first determination region will be described below.

  FIG. 15 is a schematic diagram illustrating three regions included in the first determination region. FIGS. 15A to 15C are diagrams corresponding to FIG. 13B, respectively. In the second reference plane determination step S34 according to the present embodiment, the determination area A, the determination area B, and the determination area C included in the first determination area are defined, respectively, and is the determination target point 80 within the first determination area? It is determined whether or not. 15A shows the determination area A, FIG. 15B shows the determination area B, and FIG. 15C shows the determination area C.

  As shown in FIG. 15A, the determination area A is an area composed of four ellipses 549 having the same shape as the projected portion of the upper surface of the second object 54 in the projected image of the second object 54. Here, the four ellipses 549 are centered on the four vertices of the quadrangle 522, respectively. If the determination target point 80 is inside any ellipse 549, it is determined that the determination target point 80 is in the determination region A.

Determination area B, as in FIG. 15 (b), a region included in the first determination area, separated first determination area by two straight lines extending in e ₂ axially contains a long axis of the ellipse 549 Is a region 526 including the origin.

Determining region C, as shown in FIG. 15 (c), the a region included in the first determination area, separated first determination area by two straight lines extending in e ₃ axially comprise minor axis of the ellipse 549 Is a region 527 including the origin.

  In the second reference plane determination step S34, when the determination target point 80 is not included in any of the determination area A, the determination area B, and the determination area C, the determination target point 80 is included in the first determination area. It is determined that there is no.

  It should be noted that the determination of whether or not the determination target point 80 is included in the determination region A, the determination region B, and the determination region C may be all performed, or the determination target point 80 is included in any one region. It may be determined that the determination target point 80 is in the first determination region, and determination regarding another region that has not yet been performed is stopped. Note that the order of determination for the fixed region A, the determination region B, and the determination region C is not particularly limited.

FIG. 16 is a flow of a process for determining whether one determination target point 80 is in the first determination region. The above-described examination need not be performed for each determination, and the second reference plane determination step S34 according to the present embodiment can be performed using the following expressions (15) to (22). Here, the coordinates of the plurality of determination target points 80 on the second reference plane are respectively (e _2n , e _3n ) (n = 1, 2,...).

  First, when none of the following Expression (15), Expression (16), Expression (17), and Expression (18) holds for one determination target point 80, the determination target point 80 is within the determination area A. It is determined that it is not.

  Further, when at least one of the following formula (19) and formula (20) does not hold, it is determined that the determination target point 80 is not in the determination region B.

  Further, when at least one of the following formula (21) and formula (22) is not satisfied, it is determined that the determination target point 80 is not in the determination region C.

Note that the coordinates (e _2n , e _3n ) (n = 1, 2,..., N) of the N determination target points 80 are, for example, n = 1,. When n = N, it can be expressed by the following formula (24). Here, N is an integer of 2 or more.

Here, (e ₂₁ , e ₃₁ ) are the coordinates of the lower surface center projection point 840, and (e _2N , e _3N ) are the coordinates of the upper surface center projection point 820, and the following equation (25) is established.

  When it is determined that one determination target point 80 is not included in any of the determination region A, the determination region B, and the determination region C, it is determined that the determination target point 80 is not in the first determination region. When it is determined that all the determination target points 80 are not within the first determination region, it is determined that the projected images of the first object 52 and the second object 54 do not overlap with each other on the second reference plane. The

  Specifically, a step of determining whether or not equation (15) is satisfied, a step of determining whether or not equation (16) is satisfied, a step of determining whether or not equation (17) is satisfied, A step of determining whether or not Expression (18) is satisfied, a step of determining whether or not both of Expression (19) and Expression (20) are satisfied, and any of Expression (21) and Expression (22) At least one of the steps of determining whether or not is established is performed. When it is determined that the expression (15) is satisfied in the step of determining whether or not the expression (15) is satisfied, when it is determined that the expression (16) is satisfied in the process of determining whether or not the expression (16) is satisfied, the expression (17) When it is determined that it is established in the step of determining whether or not is established, when it is determined that it is established in the step of determining whether or not equation (18) is established, the equations (19) and (20) When it is determined that both are satisfied in the step of determining whether or not both are satisfied, or both of the steps of determining whether or not both of the expressions (21) and (22) are satisfied When it is determined that it is established, it can be determined that the determination target point 80 is in the first determination region.

  Alternatively, a step of determining whether or not Expression (15) is satisfied, a step of determining whether or not Expression (16) is satisfied, a step of determining whether or not Expression (17) is satisfied, Expression (18) ) Is satisfied, whether the expressions (19) and (20) are both satisfied, and both the expressions (21) and (22) are satisfied. All of the steps for determining whether or not to do are performed. Then, it is determined that the expression (15) is not satisfied in the step of determining whether or not the expression (15) is satisfied, and is determined not to be satisfied in the process of determining whether or not the expression (16) is satisfied, and the expression ( 17) is determined not to be satisfied in the step of determining whether or not, and it is determined not to be satisfied in the step of determining whether or not Expression (18) is satisfied, and Expression (19) and Expression (19) are determined. A step of determining whether at least one of the equations (20) and (22) is satisfied, and determining whether at least one of the equations (21) and (22) is satisfied. When it is determined that at least one of them is not established, it can be determined that the determination target point 80 is not in the first determination region.

  A step of determining whether or not equation (15) is satisfied, a step of determining whether or not equation (16) is satisfied, a step of determining whether or not equation (17) is satisfied, and equation (18): A step of determining whether or not, a step of determining whether or not both of the equations (19) and (20) are satisfied, and whether or not any of the equations (21) and (22) are satisfied Steps for determining whether or not are performed in order, when it is determined that the expression (15) is satisfied, when it is determined that the expression (16) is satisfied, when it is determined that the expression (17) is satisfied, the expression (18) When it is determined that is satisfied, when it is determined that both Expression (19) and Expression (20) are satisfied, or when it is determined that both Expression (21) and Expression (22) are satisfied, It is determined that the determination target point 80 is in the first determination area and is still performed. Not the rest of the process may be aborted. Note that the order of determination is not particularly limited.

  In addition, the determination method in 2nd reference plane determination process S34 is not limited to said method. It is only necessary to determine whether or not at least parts of the projected images of the first object 52 and the second object 54 overlap each other. In the present embodiment, the example in which the determination is performed for the determination area A, the determination area B, and the determination area C defined from the first determination area in the second reference plane determination step S34 has been described. It is not limited. For example, it may be determined whether or not the projection images of the first object 52 and the second object 54 overlap each other based on areas defined by dividing the first determination area by another method. Alternatively, it may be determined whether or not the projected images of the first object 52 and the second object 54 overlap each other based on a relationship between a determination area different from the first determination area and a determination point.

<Third reference plane determination step>
The third reference plane determination step S36 will be described below. In the first reference surface determining step S32 according to the present embodiment, the third reference plane consisting of a e ₃ axes and e ₁ axis, whether the projected image of the first object 52 and second object 54 overlap each other Is determined.

  In the third reference plane determination step S36 according to the present embodiment, in the second determination area defined by using the projection image of the first object 52 and the projection image of the second object 54 on the third reference plane, It is determined whether or not the center point of the projected image of the two objects 54 is included. Then, when the center point is not included in the second determination region, it is determined that the projected images of the first object 52 and the second object 54 do not overlap with each other on the third reference plane. On the other hand, when the center point is included in the second determination region, it is determined that the projected images of the first object 52 and the second object 54 overlap each other on the third reference plane.

  FIG. 17A is a schematic diagram illustrating an example of a projected image of the first object 52 and a projected image of the second object 54 on the third reference plane, and FIG. 17B is a second determination region. FIG. 17C is a diagram illustrating the relationship between the second determination region and the divided regions.

  In FIG. 17A, a quadrangle 524 is a quadrangle that indicates the contour of the projected image of the first object 52 on the third reference plane. A quadrangle 550 is a quadrangle indicating the contour of the projected image of the second object 54 on the third reference plane.

  The second determination region is drawn by the center of the quadrangle 551 when a quadrilateral 551 having the same shape as the projection image of the second object 54 is moved without circumscribing the projection image of the first object 52. This is an area having a line as an outline. In FIG. 17B, an octagon 525 corresponds to the contour. Note that the square center is the intersection of diagonal lines of the square. When the center point of the projected image of the second object 54 is not included in the second determination area, the projected images of the first object 52 and the second object 54 do not overlap with each other on the third reference plane. Determined.

  A method for determining whether or not the center point of the second object 54 is within the second determination region will be described below.

  In the third reference plane determination step S36, the second determination area is divided into a plurality of divided areas consisting of triangles connecting two adjacent vertices of the contour of the area and the origin of the third reference plane. Then, it is determined whether or not each of the plurality of divided areas includes the center point of the projection image of the second object 54, and when the center point is not included in any of the divided areas, the center point is determined. Is not within the second determination region.

  Alternatively, it is determined whether or not the center point of the projected image of the second object 54 is included in at least one of the plurality of divided regions, and the center point is included in at least one of the plurality of divided regions. In addition, it is determined that the center point is within the second determination region.

  For each of the plurality of divided regions, it is determined whether or not the center point of the projection image of the second object 54 is included in order, and the determination is made at the time when it is determined that any one of them is included. The determination on the remaining remaining divided areas may be stopped. The order of determination is not particularly limited.

FIG. 17C is a diagram showing the relationship between the second determination area and the divided areas. The vertices of the octagon 525 are A _{1 to} A ₈ in order, and a triangle OA _i A _j ((i, j) = (1, 2), (2, 3), ( (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 1)) are defined as divided regions. Specifically, the plurality of divided areas obtained by dividing the second determination area are triangle OA ₁ A ₂ , triangle OA ₂ A ₃ , triangle OA ₃ A ₄ , triangle OA ₄ A ₅ , triangle OA ₅ A ₆ , triangle OA ₆ A ₇ , triangle OA ₇ A ₈ , and triangle OA ₈ A ₁ .

FIG. 18 is a diagram illustrating an example of the positional relationship between the triangle OA _i A _j and the center point P of the projection image of the second object 54. When the point P is within the triangle OA _i A _j , the following equations (26) to (29) are established.

Here, the center point P of the projected image of the second object 54 is represented by (e ₁ , e ₃ ) = (a, c), and A _i = (e _1i , e _3i ) and A _j = (e _1j , _e3j ), α and β are expressed by the following equations (30) and (31), respectively, based on equation (26).

The above-described examination need not be performed for each determination, and in the third reference plane determination step S36 according to the present embodiment, expressions α and β expressed by Expression (30) and Expression (31), respectively, When at least one of (27), Expression (28), and Expression (29) does not hold, the center point of the projection image of the second object 54 is not included in the triangle OA _i A _j that is each divided region. It is determined. On the other hand, when all of Expression (27), Expression (28), and Expression (29) hold, the center point of the projection image of the second object 54 is included in the triangle OA _i A _j that is each divided region. It is determined.

  It should be noted that it is determined whether or not Expression (27), Expression (28), and Expression (29) hold in order, and when it is determined that any one does not hold, the second object is included in the divided region. It may be determined that the center of the 54 projection images is not included, and the determination that has not been performed may be stopped. Note that the order in which it is determined whether or not Expression (27), Expression (28), and Expression (29) are satisfied is not particularly limited.

Here, A _i = (e _1i , e _3i ) and A _j = (e _1j , e _3j ), and the vertex A _m = (e _1m , e _3m ) (m = 1 to 8) of the second determination region is These are respectively expressed by the following formulas (32) to (39).

  Note that the determination method in the third reference plane determination step S36 is not limited to the above method. It is only necessary to determine whether or not at least parts of the projected images of the first object 52 and the second object 54 overlap each other. In the present embodiment, the example in which the determination is performed by dividing the second determination region into a plurality of triangular divided regions in the third reference plane determination step S36 has been described, but the present invention is not limited to such a method. For example, it may be determined whether or not the projected images of the first object 52 and the second object 54 overlap each other based on an area defined by dividing the second determination area by another method. Alternatively, it may be determined whether or not the projection images of the first object 52 and the second object 54 overlap each other based on a relationship between a determination area different from the second determination area and a determination point.

  In the present embodiment, when it is not determined that the first object 52 and the second object 54 are “no interference”, for example, the first object 52 and the second object 54 are “interference”. May be determined. In the interference determination step S70 according to the present embodiment, when it is determined that “no interference”, it can be said that the first object 52 and the second object 54 do not interfere in the three-dimensional space. On the other hand, even when it is determined as “interfering” as described above, the case of actually interfering and the case of not interfering are included. However, in the simulation, if the state determined to be “interfering” is prohibited, the state in which the first object 52 and the second object 54 interfere can be avoided. In addition, the frequency of occurrence of no actual interference despite the determination of “interfering” is sufficiently rare, and there is no practical problem. Compared to the determination method based only on the radius and distance of the circumscribed sphere as described above, the percentage of cases where there is no actual interference even though it is determined to be “interfering” is significantly higher. It can be said that this is a small and more accurate determination method.

  Further, since the coordinates defined in the coordinate defining step S20 are orthogonal coordinates, the frequency of occurrence of the case where there is no actual interference even though it is determined as “interfering” is further reduced. Can do. Therefore, more accurate determination is possible.

  According to the interference determination step S70 according to the present embodiment, it can be determined whether or not a plurality of plate-like objects in the three-dimensional space interfere.

  In addition, since each determination step is performed depending on whether or not a simple mathematical relationship is satisfied, determination can be performed with a small amount of calculation.

  Further, since the determination is made in consideration of the shape and orientation of the object, more accurate interference determination is possible.

[Interference judgment between plate-like object and spherical object]
FIG. 19 is a diagram illustrating an example of the arrangement of the plate-like object 57 and the spherical object 58 according to the present embodiment. A method in which the plurality of objects 50 include at least one plate-like object 57 and one spherical object 58, and the interference determination unit 70 determines whether or not the plate-like object 50 and the spherical object 50 interfere with each other. Details are described below.

FIG. 19A is a perspective view illustrating an example of an arrangement relationship between the plate-like object 57 and the spherical object 58. FIG. 19B is a cross-sectional view in a plane including the center of the upper surface of the plate-like object 57, the center of the lower surface of the plate-like object 57, and the center of the spherical object 58. In this figure, the point O _d indicates the center of the plate-like object 57, the point O _s indicates the center of the spherical object 58, and N _d indicates the normal vector of the plate-like object 57. Further, the distance between the point O _d and the point O _s is d _ds , the angle between the straight line connecting the point O _d and the point O _s and the normal vector N _d is φ _ds, and the radius of the spherical object 58 is and r _s, the radius of the main surface of the plate-like object 57 as _{r d,} the thickness of the plate-like object 57 and _{l d.}

  When the plate-like object 57 and the spherical object 58 overlap in the plane shown in FIG. 19B, it can be said that the plate-like object 57 and the spherical object 58 interfere with each other in the three-dimensional space. If they do not overlap, it can be said that they do not interfere in a three-dimensional space. Accordingly, a method for determining whether or not the quadrangle 571 that is the cross section of the plate-like object 57 and the circle 581 that is the cross section of the spherical object 58 overlap in the plane will be described below.

  FIG. 20 is a diagram for explaining a method for determining whether or not a cross section of a plate-like object and a cross section of a spherical object overlap. In the plane, when the quadrangle 571 and the circle 581 overlap, the case shown in FIG. 20A, the case shown in FIG. 20B, and the case shown in FIG. 20 (a) to (c), the circle 581 and the quadrilateral 571 overlap each other, that is, the plate-like object 57 and the spherical object 58 Can be said to interfere. In the case illustrated in FIG. 20A, the center of the circle 581 enters the inside of the quadrangle 572. The case shown in FIG. 20B is a case where the center of the circle 581 enters the inside of the quadrangle 573. The case shown in FIG. 20C is a case where the vertex of the quadrangle 571 falls inside the circle 581.

A case where the center of a circle 581 enters the inside of a quadrangle 572 as shown in FIG. The quadrangle 572 is a quadrangle in which the length of the side in the thickness direction of the plate-like object 57 is l _d + 2 × r _s and the length of the side in the direction orthogonal to the side is 2 × r _d . The center of the quadrangle 572 is coincident with the center of the quadrangle 571. The center of the circle 581 enters the inside of the quadrangle 572 when both the following expressions (40) and (41) are satisfied.

A case where the center of a circle 581 enters the inside of a quadrangle 573 as shown in FIG. The quadrangle 573 is a quadrangle in which the length of the side in the thickness direction of the plate-like object 57 is l _d, and the length of the side in the direction orthogonal thereto is 2 × (r _d + r _s ). The center of the quadrangle 573 is coincident with the center of the quadrangle 571. When both the following formulas (42) and (43) are satisfied, the center of the circle 581 enters the inside of the quadrangle 573.

As shown in FIG. 20C, the case where the vertex of the quadrangle 571 falls inside the circle 581 will be described. In this case, the distance between the apex and the center of the square 571 of the circle 581 is equal to or less than _{r s.} When the following expression (44) is satisfied, the vertex of the quadrangle 571 enters the inside of the circle 581.

  The interference determination unit 70 arbitrarily selects a plate-like object 57 and a spherical object 58 from the plurality of objects 50 in the temporary space state data, and the plate-like object 57 and the spherical object 58 interfere as described above. It is determined whether or not.

  Note that “≦” used in each of the above mathematical expressions may be replaced with “<”. When an operation using a floating point number is performed, an operation error occurs. Therefore, in the determination using a computer, it can be said that there is almost no equal sign, and the determination result is the same with or without the equal sign.

  In addition, each said numerical formula is not limited to the form shown by this embodiment, Each can be deform | transformed and used.

  Next, the operation and effect of this embodiment will be described. According to the simulation method according to the present embodiment, a three-dimensional space in which a plurality of objects including a plate-like object are arranged can be simulated.

  As mentioned above, although embodiment of this invention was described with reference to drawings, these are the illustrations of this invention, Various structures other than the above are also employable.

Hereinafter, examples of the reference form will be added.
1. A simulation method of a three-dimensional space in which a plurality of objects are arranged,
A moving object selection step of acquiring space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selecting at least one moving object to be moved among the plurality of objects;
A movement information generating step for generating movement information indicating how to move the moving object;
An object moving step of generating temporary space state data, including information on an arrangement state of at least the moving object in the three-dimensional space after moving the moving object based on the movement information;
An interference determination step for determining whether or not the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after moving the moving object based on the movement information when it is determined in the interference determination step that the plurality of objects do not interfere with each other Information indicating a state is the new space state data, and when it is determined that there is interference, the next state determination step that does not change the space state data; and
Repeat the state change process to perform
In the object moving step, at least one of parallel movement and rotational movement of the moving object is performed,
At least one of the plurality of objects is a plate-like object;
Simulation method.
In the simulation method described in 2.1,
The plurality of objects include at least the first plate-like object and the second plate-like object,
The interference determination step includes
A determination object selection step of selecting, from the plurality of objects, a first object that is the first plate-like object and a second object that is the second plate-like object;
A coordinate defining step of defining one orthogonal coordinate system for the first object and the second object;
A projected image determination step of determining whether or not the projected images of the first object and the second object projected on the reference plane of the orthogonal coordinate system overlap each other;
A solid determination step of determining whether or not the first object and the second object interfere in the three-dimensional space,
The orthogonal coordinate system includes an e ₁ axis, an e ₂ axis, and an e ₃ axis that are orthogonal to each other.
The projected image determination step includes
a first reference plane determination step for determining whether or not projection images of the first object and the second object overlap each other on a first reference plane composed of an e ₁ axis and an e ₂ axis;
In the second reference plane consisting of e ₂ axes and e ₃ axes, the second reference surface determining step of determining whether the projected image overlap each other of the first object and the second object, and e ₃ axes And at least one of a third reference plane determination step for determining whether or not the projected images of the first object and the second object overlap with each other on a third reference plane consisting of the e ₁ axis,
In the solid determination step, the projection image of the first object and the second object on at least one of the first reference surface, the second reference surface, and the third reference surface in the projection image determination step. Are determined not to overlap with each other, it is determined that the first object and the second object do not interfere with each other.
Simulation method.
In the simulation method according to 3.1,
The plurality of objects include at least the first plate-like object and the second plate-like object,
The interference determination step includes
A determination object selection step of selecting, from the plurality of objects, a first object that is the first plate-like object and a second object that is the second plate-like object;
A coordinate defining step of defining one orthogonal coordinate system for the first object and the second object;
A projected image determination step of determining whether or not the projected images of the first object and the second object projected on the reference plane of the orthogonal coordinate system overlap each other;
A solid determination step of determining whether or not the first object and the second object interfere in the three-dimensional space,
The orthogonal coordinate system includes an e ₁ axis, an e ₂ axis, and an e ₃ axis that are orthogonal to each other.
The projected image determination step includes
a first reference plane determination step for determining whether or not projection images of the first object and the second object overlap each other on a first reference plane composed of an e ₁ axis and an e ₂ axis;
In the second reference plane consisting of e ₂ axes and e ₃ axes, the second reference surface determining step of determining whether the projected image overlap each other of the first object and the second object, and e ₃ axes And a third reference plane determination step for determining whether or not the projected images of the first object and the second object overlap with each other on a third reference plane consisting of e ₁ axis,
In the three-dimensional determination step, the projection images of the first object and the second object overlap each other on the first reference surface, the second reference surface, and the third reference surface in the projection image determination step. It is determined that the first object and the second object do not interfere with each other,
Simulation method.
In the simulation method according to 4.2 or 3,
In the coordinate defining step, the center of the first object matches the origin, the a major surface and e ₃ axis of the first object is orthogonal, e of the normal vector of the principal surface of the second object Define the Cartesian coordinate system so that the _two components are 0,
The first object and the second object are disk-shaped,
Simulation method.
In the simulation method according to any one of 5.2 to 4,
Including at least the first reference plane determination step;
The first reference plane determination step includes
In the first reference plane, it is determined whether or not a projection image of the first object overlaps a first projection area that is a projection portion of the upper surface of the object in the projection image of the second object. A first partial determination step to perform,
In the first reference plane, it is determined whether or not a projection image of the first object overlaps a second projection region that is a projection portion of the lower surface of the object in the projection image of the second object. A second partial determination step, and a projection image of the first object and a projection image of the second object included in the first projection area and the second projection area in the first reference plane. Including at least one of the third partial determination steps of determining whether or not the third projection region including all of the regions that are not overlapped,
When it is determined that at least one of the first part determining step, the second part determining step, and the third part determining step is overlapped, the first object and the first part on the first reference plane Determining that the projected images of the two objects overlap each other;
Simulation method.
In the simulation method according to any one of 6.2 to 4,
Including at least the first reference plane determination step;
The first reference plane determination step includes
In the first reference plane, it is determined whether or not a projection image of the first object overlaps a first projection area that is a projection portion of the upper surface of the object in the projection image of the second object. A first partial determination step to perform,
In the first reference plane, it is determined whether or not a projection image of the first object overlaps a second projection region that is a projection portion of the lower surface of the object in the projection image of the second object. A second partial determination step to perform,
In the first reference plane, the first reference plane includes a projection image of the first object and a projection image of the second object that includes all areas not included in the first projection area or the second projection area. A third partial determination step of determining whether or not the three projection areas overlap,
In the first reference plane, when it is determined that they do not overlap in all of the first part determination step, the second part determination step, and the third part determination step, the first object and the second part Determining that the projected images of the objects do not overlap each other;
Simulation method.
In the simulation method according to 7.5 or 6,
When the first partial determination step is included, the first partial determination step determines that the projection image of the first object and the first projection region do not overlap when Expression (11) does not hold. And
When the second partial determination step is included, the second partial determination step determines that the projection image of the first object and the second projection region do not overlap when Equation (12) does not hold. And
When the third part determining step is included, in the third part determining step, when at least one of Expression (13) and Expression (14) does not hold, the projected image of the first object and the third projection A simulation method for determining that an area does not overlap.
However, r _p is the radius of the first object, r _c is the radius of the second object, l _c is the thickness of the second object, the coordinates (a, b, c) is The center coordinate of the second object in the orthogonal coordinate system, and the angle θ is an angle formed by a normal vector of the main surface of the first object and a normal vector of the main surface of the second object And θ is 0 rad or more and π / 2 rad or less.
In the simulation method according to any one of 8.2 to 7,
Including at least the second reference plane determination step;
In the second reference plane determination step,
In the second reference plane, at least one point on the determination target line of the second object is included in the first determination area defined using the projection image of the first object and the projection image of the second object. And determining that the projected images of the first object and the second object overlap each other on the second reference plane,
The first determination area moves an ellipse having the same shape as the projected portion of the upper surface of the second object out of the projection image of the second object without circumventing the projection image of the first object and rolling it. Is a region whose outline is a line drawn by the center of the ellipse,
The determination target line includes a lower surface center projection point corresponding to a projection point at the center of the lower surface of the target object and a center of the upper surface of the target object in the projected image of the second object on the second reference plane. A line segment connecting the upper surface center projection point corresponding to the projection point,
Simulation method.
In the simulation method according to any one of 9.2 to 7,
Including at least the second reference plane determination step;
In the second reference plane determination step,
On the second reference plane, any point on the determination target line of the second object is within a first determination region defined using the projection image of the first object and the projection image of the second object. If not included, it is determined that the projected images of the first object and the second object do not overlap each other on the second reference plane;
The first determination area moves an ellipse having the same shape as the projected portion of the upper surface of the second object out of the projection image of the second object without circumventing the projection image of the first object and rolling it. Is a region whose outline is a line drawn by the center of the ellipse,
The determination target line includes a lower surface center projection point corresponding to a projection point at the center of the lower surface of the target object and a center of the upper surface of the target object in the projected image of the second object on the second reference plane. A line segment connecting the upper surface center projection point corresponding to the projection point,
Simulation method.
10. The simulation method according to any one of 10.2 to 7,
Including at least the second reference plane determination step;
In the second reference plane determination step,
Does the second reference plane include a plurality of determination target points of the second object in a first determination region defined using the projection image of the first object and the projection image of the second object? Determine whether or not
When none of the plurality of determination target points is within the first determination region, it is determined that the projected images of the first object and the second object do not overlap with each other on the second reference plane;
The first determination area moves an ellipse having the same shape as the projected portion of the upper surface of the second object out of the projection image of the second object without circumventing the projection image of the first object and rolling it. Is a region whose outline is a line drawn by the center of the ellipse,
The plurality of determination target points are:
Of the projected image of the second object on the second reference plane, a lower surface center projection point corresponding to the projection point at the center of the lower surface of the object and an upper surface corresponding to the projection point at the center of the upper surface of the object A plurality of points on a line connecting the central projection point,
Including at least the lower surface center projection point and the upper surface center projection point,
The distance between the determination target points adjacent to each other is smaller than the thickness of the first object.
Simulation method.
In the simulation method according to any one of 11.2 to 7,
Including at least the second reference plane determination step;
In the second reference plane determination step,
Does the second reference plane include a plurality of determination target points of the second object in a first determination region defined using the projection image of the first object and the projection image of the second object? Determine whether or not
When at least one of the plurality of determination target points is within the first determination region, it is determined that the projected images of the first object and the second object overlap each other on the second reference plane;
The first determination area moves an ellipse having the same shape as the projected portion of the upper surface of the second object out of the projection image of the second object without circumventing the projection image of the first object and rolling it. Is a region whose outline is a line drawn by the center of the ellipse,
The plurality of determination target points are:
Of the projected image of the second object on the second reference plane, a lower surface center projection point corresponding to the projection point at the center of the lower surface of the object and an upper surface corresponding to the projection point at the center of the upper surface of the object A plurality of points on a line connecting the central projection point,
Including at least the lower surface center projection point and the upper surface center projection point,
The distance between the determination target points adjacent to each other is smaller than the thickness of the first object.
Simulation method.
12. In the simulation method described in 10 or 11,
The second reference plane determination step includes
When the coordinates on the second reference plane of the plurality of determination target points are respectively (e _2n , e _3n ) (n = 1, 2,...)
A step of determining whether or not formula (15) is satisfied;
A step of determining whether or not Expression (16) is satisfied;
A step of determining whether or not Expression (17) is satisfied,
A step of determining whether or not formula (18) is satisfied;
At least one of the step of determining whether or not both of the equations (19) and (20) are satisfied and the step of determining whether or not both of the equations (21) and (22) are satisfied. Including
When it is determined that the expression (15) is satisfied in the step of determining whether or not the expression (15) is satisfied,
When it is determined that the expression (16) is satisfied in the step of determining whether or not the expression (16) is satisfied,
When it is determined that the expression (17) is satisfied in the step of determining whether or not the expression (17) is satisfied,
When it is determined that the expression (18) is satisfied in the step of determining whether or not the expression (18) is satisfied,
When it is determined that both are satisfied in the step of determining whether or not both of the expressions (19) and (20) are satisfied, or both of the expressions (21) and (22) are satisfied When it is determined that both are established in the step of determining whether or not to do,
Determining that the determination target point is within the first determination region;
Simulation method.
However, r _p is the radius of the first object, l _p is the thickness of the first object, r _c is the radius of the second object, the angle θ, the first object Is an angle formed by the normal vector of the principal surface and the normal vector of the principal surface of the second object, and θ is 0 rad or more and π / 2 rad or less.
13. In the simulation method according to 10 or 11,
The second reference plane determination step includes
When the coordinates on the second reference plane of the plurality of determination target points are respectively (e _2n , e _3n ) (n = 1, 2,...)
A step of determining whether or not formula (15) is satisfied;
A step of determining whether or not Expression (16) is satisfied;
A step of determining whether or not Expression (17) is satisfied,
A step of determining whether or not formula (18) is satisfied;
A step of determining whether or not both of the equations (19) and (20) are satisfied, and a step of determining whether or not both of the equations (21) and (22) are satisfied,
It is determined that the expression (15) is not satisfied in the step of determining whether or not the expression (15) is satisfied, and
It is determined that the expression (16) is not satisfied in the step of determining whether the expression (16) is satisfied, and
It is determined that the expression (17) is not satisfied in the step of determining whether or not the expression (17) is satisfied, and
It is determined that the expression (18) is not satisfied in the step of determining whether the expression (18) is satisfied, and
It is determined that at least one of the expressions (19) and (20) is not satisfied in the step of determining whether or not both of the expressions (19) and (20) are satisfied; and
When it is determined that at least one of the expressions (21) and (22) is not satisfied in the step of determining whether or not both of the expressions (21) and (22) are satisfied,
Determining that the determination target point is not within the first determination region;
Simulation method.
However, r _p is the radius of the first object, l _p is the thickness of the first object, r _c is the radius of the second object, the angle θ, the first object Is an angle formed by the normal vector of the principal surface and the normal vector of the principal surface of the second object, and θ is 0 rad or more and π / 2 rad or less.
14. In the simulation method according to any one of 14.2 to 13,
Including at least the third reference plane determination step;
In the third reference plane determination step,
In the third reference plane, a center point of the projection image of the second object is included in a second determination region defined using the projection image of the first object and the projection image of the second object. Whether or not
When the center point is not included in the second determination region, it is determined that the projected images of the first object and the second object do not overlap with each other on the third reference plane;
The second determination region is a line drawn by the center of the quadrangle when the quadrangle having the same shape as the projection image of the second object is moved without circumscribing the projection image of the first object. Is a region with a contour,
Simulation method.
15. In the simulation method according to any one of 15.2 to 13,
Including at least the third reference plane determination step;
In the third reference plane determination step,
In the third reference plane, a center point of the projection image of the second object is included in a second determination region defined using the projection image of the first object and the projection image of the second object. Whether or not
When the center point is included in the second determination region, it is determined that the projected images of the first object and the second object overlap each other on the third reference plane,
The second determination region is a line drawn by the center of the quadrangle when the quadrangle having the same shape as the projection image of the second object is moved without circumscribing the projection image of the first object. Is a region with a contour,
Simulation method.
16. In the simulation method according to 16.14 or 15,
In the third reference plane determination step,
Dividing the second determination area into a plurality of divided areas composed of triangles connecting two adjacent vertices of the outline of the area and the origin of the third reference plane;
Determining whether at least one of the plurality of divided regions includes a center point of a projection image of the second object;
When the center point is included in at least one of the plurality of divided regions, the center point is determined to be within the second determination region;
Simulation method.
17. In the simulation method according to 14 or 15,
In the third reference plane determination step,
Dividing the second determination area into a plurality of divided areas composed of triangles connecting two adjacent vertices of the outline of the area and the origin of the third reference plane;
It is determined whether each of the plurality of divided regions includes a center point of the projection image of the second object,
When none of the plurality of divided areas includes the center point, it is determined that the center point is not in the second determination area.
Simulation method.
18. In the simulation method according to 16 or 17,
The vertices A _m = (e _1m , e _3m ) (m = 1 to 8) of the second determination region are respectively expressed by equations (32) to (39),
The center point P of the projected image of the second object is represented by (e ₁ , e ₃ ) = (a, c),
The plurality of divided regions are respectively triangles OA _i A _j ((i, j) = (1,2), (2,3), (3,4)), using the origin O of the third reference plane. (4,5), (5,6), (6,7), (7,8), (8,1))
When A _i = (e _1i , e _3i ) and A _j = (e _1j , e _3j ), α and β represented by the equations (30) and (31) are expressed by the equations (27) and ( 28) and when at least one of the expressions (29) does not hold, it is determined that the center point of the projected image of the second object is not included in the triangle OA _i A _j that is each of the divided regions.
Simulation method.
However, r _p is the radius of the first object, l _p is the thickness of the first object, r _c is the radius of the second object, l _c is the second object The angle θ is an angle formed by a normal vector of the main surface of the first object and a normal vector of the main surface of the second object, and θ is 0 rad or more and π / 2 rad or less. is there.
19. In the simulation method according to 19.1,
The plurality of objects include at least the first plate-like object and the second plate-like object,
Selecting a first object and a second object from the plurality of objects;
Determining whether the projected images of the first object and the second object projected on at least one reference plane overlap each other;
Determining whether or not the first object and the second object interfere with each other based on a determination result of whether or not the projected images overlap each other,
Simulation method.

DESCRIPTION OF SYMBOLS 10 Determination object selection part 100 Simulation apparatus 12 Movement target selection part 14 Movement information generation part 16 Object movement part 18 Next state determination part 20 Coordinate definition part 22 Randomness degree determination part 24 State change process part 26 Storage part 30 Projection image determination Unit 32 first reference surface determination unit 34 second reference surface determination unit 36 third reference surface determination unit 40 solid determination unit 50 object 500 principal surface 504 dotted line 52 first object 521,581 circle 502,522,524,550, 551, 571, 572, 573 rectangle 523 figure 525 octagon 526, 527, 543, 545 area 54 second object 540, 541, 542, 544, 546, 547, 548, 549 ellipse 56 moving object 57 plate-like Object 58 Spherical object 60 Filling area 70 Interference determination unit 80 Determination target point 82 Determination target line 820 Upper surface center projection point 84 0 Bottom center projection point

Claims (8)

A simulation method of a three-dimensional space in which a plurality of objects are arranged,
A moving object selection step of acquiring space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selecting at least one moving object to be moved among the plurality of objects;
A movement information generating step for generating movement information indicating how to move the moving object;
An object moving step of generating temporary space state data, including information on an arrangement state of at least the moving object in the three-dimensional space after moving the moving object based on the movement information;
An interference determination step for determining whether or not the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after moving the moving object based on the movement information when it is determined in the interference determination step that the plurality of objects do not interfere with each other Information indicating a state is the new space state data, and when it is determined that there is interference, the next state determination step that does not change the space state data; and
Repeat the state change process to perform
In the object moving step, at least one of parallel movement and rotational movement of the moving object is performed,
At least one of the plurality of objects is a plate-like object;
Simulation method. The simulation method according to claim 1,
After the next state determination step, based on the spatial state data, generate randomness data indicating the randomness of the plurality of objects in the three-dimensional space, and whether the randomness satisfies a predetermined criterion Further including a randomness determination step of determining
If the messiness does not meet the criteria, continue to repeat the state change process,
When the degree of randomness satisfies the criterion, the state change process is repeated at that time, or after the state change process is performed a specific number of times.
Simulation method. In the simulation method according to claim 1 or 2,
The plate-like object is a disk-like object,
Simulation method. In the simulation method according to any one of claims 1 to 3,
The plurality of objects further includes a spherical object;
Simulation method. In the simulation method according to any one of claims 1 to 4,
All of the plurality of objects are disposed in a filling region having a finite volume;
In the interference determination step, it is further determined whether or not an area outside the filling area interferes with at least one of the objects,
In the next state determination step,
In the interference determination step, when it is determined that the plurality of objects do not interfere with each other, and it is not determined that an area outside the filling area and at least one of the objects interfere with each other, Information indicating the arrangement state of the plurality of objects in the three-dimensional space after moving the moving object based on movement information is the new space state data,
In other cases, the space state data is not changed.
Simulation method. In the simulation method according to any one of claims 1 to 5,
The plurality of objects include at least the first plate-like object and the second plate-like object,
The interference determination step includes
A determination object selection step of selecting, from the plurality of objects, a first object that is the first plate-like object and a second object that is the second plate-like object;
A coordinate defining step of defining one orthogonal coordinate system for the first object and the second object;
A projected image determination step of determining whether or not the projected images of the first object and the second object projected on the reference plane of the orthogonal coordinate system overlap each other;
A solid determination step of determining whether or not the first object and the second object interfere in the three-dimensional space,
The orthogonal coordinate system includes an e ₁ axis, an e ₂ axis, and an e ₃ axis that are orthogonal to each other.
The projected image determination step includes
a first reference plane determination step for determining whether or not projection images of the first object and the second object overlap each other on a first reference plane composed of an e ₁ axis and an e ₂ axis;
In the second reference plane consisting of e ₂ axes and e ₃ axes, the second reference surface determining step of determining whether the projected image overlap each other of the first object and the second object, and e ₃ axes And at least one of a third reference plane determination step for determining whether or not the projected images of the first object and the second object overlap with each other on a third reference plane consisting of the e ₁ axis,
In the solid determination step, the projection image of the first object and the second object on at least one of the first reference surface, the second reference surface, and the third reference surface in the projection image determination step. Are determined not to overlap with each other, it is determined that the first object and the second object do not interfere with each other.
Simulation method. A three-dimensional simulation apparatus in which a plurality of objects are arranged,
A moving object selection unit that acquires space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selects at least one moving object to be moved among the plurality of objects;
A movement information generating unit that generates movement information indicating how to move the moving object;
An object moving unit that generates temporary space state data including at least information regarding an arrangement state of the moving object in the three-dimensional space after moving the moving object based on the movement information;
An interference determination unit that determines whether or not the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after the movement target is moved based on the movement information when the interference determination unit determines that the plurality of objects do not interfere with each other Information indicating a state is the new space state data, and when it is determined that there is interference, the next state determination unit that does not change the space state data;
Including a state change processing unit including
The state change processing unit repeatedly performs a state change process that operates the moving object selection unit, the movement information generation unit, the object movement unit, the interference determination unit, and the next state determination unit,
The object moving unit performs at least one of a parallel movement and a rotational movement of the moving object,
At least one of the plurality of objects is a plate-like object;
Simulation device. A computer program for realizing a three-dimensional space simulation apparatus in which a plurality of objects are arranged,
Computer
Moving object selection means for acquiring space state data indicating an arrangement state of the plurality of objects in the three-dimensional space, and selecting at least one moving object to be moved among the plurality of objects;
Movement information generating means for generating movement information indicating how to move the moving object;
An object moving means for generating temporary space state data including information on an arrangement state of at least the moving object in the three-dimensional space after moving the moving object based on the movement information;
Interference determining means for determining whether the plurality of objects interfere with each other in the three-dimensional space based on the temporary space state data;
Arrangement of the plurality of objects in the three-dimensional space after moving the moving object based on the movement information when the interference determination unit determines that the plurality of objects do not interfere with each other Information indicating a state is used as the new space state data, and when it is determined that there is interference, a next state determination unit that does not change the space state data;
Function as a state change processing means including
The state change processing means repeatedly performs a state change process for operating the moving object selecting means, the movement information generating means, the object moving means, the interference determining means, and the next state determining means,
The object moving means performs at least one of a parallel movement and a rotational movement of the moving object,
At least one of the plurality of objects is a plate-like object;
Computer program.

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