JP5878907B2 - Interference determination apparatus, interference determination method, and interference determination program - Google Patents

Description

  The present invention relates to an interference determination device, an interference determination method, and an interference determination program.

  Conventionally, a simulation is performed in which a plurality of objects are arranged in a three-dimensional virtual space, and interference and proximity verification between the objects are performed. In this specification, interference means that a plurality of objects occupy the same space, and proximity means that a plurality of objects approach within a predetermined distance. Such verification of interference and proximity is used in a wide range of applications such as determination of gripping of an object by a machine and determination of an optical sensor, in addition to prevention of a collision between equipment and a robot.

  The shape of the surface of an object in the three-dimensional virtual space may be expressed by connecting polygons (polygons) such as triangles. One of the methods for determining such interference between objects is whether or not a polygon indicating the shape of the surface of one object intersects with a polygon side indicating the shape of the surface of the other object. Is to perform a geometric calculation. In addition, a technique for determining interference between objects at higher speed is disclosed (Patent Document 1).

JP 11-250122 A

  However, in the conventional technique, there are cases where the amount of calculation required for the determination of the interference and proximity of objects is large. For example, when a curved surface is expressed by connecting triangles, the number of necessary triangles increases dramatically as the precision increases. Therefore, if interference or proximity determination is performed using the geometric calculation as described above, the amount of calculation becomes enormous. As described above, there are cases where it is not possible to determine interference or proximity between a plurality of objects with a small amount of calculation.

  The present invention has been made in view of the above points, and provides an interference determination apparatus, an interference determination method, and an interference determination program for determining interference and proximity between a plurality of objects with a small amount of calculation.

  SUMMARY An advantage of some aspects of the invention is that at least one of a plurality of polygons indicating a shape of a surface of a first object among the plurality of objects is selected. A selection unit that selects a polygon as a polygon to be determined; and a closed curved surface that includes the selected polygon to be determined, the point corresponding to the polygon to be determined or the determination target Interference between the closed curved surface having a constant distance from the first line segment corresponding to the polygon and the second line segment indicating the shape of the surface of the second object among the plurality of objects is defined as the distance. An interference determination apparatus comprising: a determination unit configured to perform determination based on the determination unit.

  According to another aspect of the present invention, in the interference determination apparatus, the second line segment is one of a plurality of polygons indicating a shape of a surface of the second object. It is an edge.

  According to another aspect of the present invention, in the interference determination apparatus, at least one of the polygons to be determined is a triangle.

  Further, according to one aspect of the present invention, in the interference determination apparatus, the first line segment is a line segment that passes through a midpoint of each of two sides of the three sides of the determination target triangle.

  According to another aspect of the present invention, in the interference determination apparatus, the length of the first line segment is a length of one side of the determination target triangle.

  Further, according to one aspect of the present invention, in the interference determination apparatus, the certain point is an outer center of the determination target triangle.

  Further, according to one aspect of the present invention, in the interference determination apparatus, the selection unit includes a plurality of polygons that indicate a shape of a surface of a first object among the plurality of objects, and the determination unit includes the first At least one polygon that is not included in the first closed curved surface as the closed curved surface for determining interference with the two line segments is selected as the polygon to be determined, and the determining unit includes the closed curved surface The interference between the second closed curved surface and the second line segment is determined.

  One embodiment of the present invention is the above-described interference determination device, wherein at least one of the plurality of polygons indicating the shape of the surface of the first object is converted into a plurality of polygons based on the distance. The selection unit selects at least one polygon among the plurality of polygons after the division by the division unit as the determination target.

  Further, according to one aspect of the present invention, in the interference determination apparatus, the division unit uses at least one polygon among a plurality of polygons indicating the shape of the surface of the first object based on the distance. Divide into 2 to 5 polygons.

  Further, according to one aspect of the present invention, in the interference determination apparatus, at least one of the plurality of polygons before division by the division unit is a triangle, and the division unit is before the division. Are divided into two triangles as a plurality of polygons after the division by one middle line of the triangles.

  According to another aspect of the present invention, in the interference determination apparatus, the determination unit includes a distance between the certain point or the first line segment and the closed curved surface, and the certain point or the first point. The interference is determined based on a comparison of the distance between the line segment and the second line segment.

  One aspect of the present invention is a selection process in which the selection unit selects, as a determination target, at least one of the plurality of polygons indicating the shape of the surface of the first object among the plurality of objects. The determination unit is a closed curved surface including the selected determination target polygon, and a certain point corresponding to the determination target polygon or a first line segment corresponding to the determination target polygon And a determination process for determining interference between the closed curved surface having a constant distance to the second line segment indicating the shape of the surface of the second object among the plurality of objects based on the distance. This is an interference determination method.

  According to one aspect of the present invention, a selection procedure for causing a computer to select at least one polygon among a plurality of polygons indicating a shape of a surface of a first object among a plurality of objects as a determination target; A closed curved surface including the selected polygon to be determined, and a distance from a certain point corresponding to the polygon to be determined or a first line segment corresponding to the polygon to be determined is constant. And a determination procedure for determining, based on the distance, an interference between the closed curved surface and the second line segment indicating the shape of the surface of the second object among the plurality of objects. It is a program.

  According to the present invention, interference and proximity between a plurality of objects can be determined with a small amount of calculation.

It is a schematic diagram explaining an example of the use environment of the interference determination apparatus which concerns on the 1st Embodiment of this invention. It is a block diagram which shows an example of a function structure of the interference determination apparatus which concerns on 1st Embodiment. It is a flowchart which shows an example of the process of the interference determination which the interference determination apparatus which concerns on 1st Embodiment performs. It is a schematic diagram which shows an example of the closed curved surface containing the triangle of the determination target which shows the shape of the surface of the object in the three-dimensional virtual space which concerns on 1st Embodiment. It is a flowchart which shows an example of the process in which the closed surface setting part of the determination part which concerns on 1st Embodiment sets a closed surface in the polygon of determination object. It is a block diagram which shows an example of a function structure of the interference determination apparatus which concerns on the 2nd Embodiment of this invention. It is a schematic diagram which shows an example of the division | segmentation method of the polygon of the determination target which shows the shape of the surface of the object in the three-dimensional virtual space which concerns on 2nd Embodiment. It is a flowchart which shows an example of the process in which the interference determination apparatus which concerns on 2nd Embodiment sets a closed curved surface in the polygon of determination object. It is a block diagram which shows an example of a function structure of the interference determination apparatus which concerns on the 3rd Embodiment of this invention. It is a table | surface which shows an example of the closed surface setting table which concerns on 3rd Embodiment.

<First Embodiment>
[Usage environment of interference judgment device]
Hereinafter, a first embodiment of the present invention will be described in detail with reference to the drawings. FIG. 1 is a schematic diagram illustrating an example of an environment in which the interference determination apparatus 100 according to the first embodiment of the present invention is used. The interference determination apparatus 100 in the present embodiment is a production line simulator related to the design of a production line. The object for which the interference determination apparatus 100 determines interference or proximity is polygon data 200 that reproduces a production line in a three-dimensional virtual space. For example, the polygon data 200 includes equipment on a production line whose surface shape is represented by polygons (polygons), robots 210 (A) to 210 (B), products 220 (A) to 220 (B), and the like. Is described in a virtual space. The interference determination apparatus 100 can correctly operate / move / place each element constituting the production line by determining the interference and proximity of the objects arranged in the virtual space with respect to the polygon data 200. .

  In an actual production line, each element is required to continuously operate or move at an appropriate timing. The interference determination apparatus 100 determines interference and proximity for a simulation of a production line with such movement. Therefore, the interference determination apparatus 100 can determine whether the arrangement of each component of the production line 300 is appropriate, and can determine whether the control program for operating and moving the component is appropriate.

[Constitution]
FIG. 2 is a block diagram illustrating an example of a functional configuration of the interference determination apparatus 100. The interference determination apparatus 100 includes a polygon acquisition unit 110, a selection unit 120, a determination unit 140, and an output unit 150. Furthermore, the determination unit 140 includes a closed curved surface setting unit 142, an interference calculation unit 144, and an interference determination unit 146. Although not shown, the interference determination apparatus 100 includes a CPU (Central Processing Unit), a storage unit, an input unit, an output unit, and the like that are generally included in a computer. The proximity determination value 400 is stored in the storage unit and used for the processing of the determination unit 140.

  Each functional unit of the interference determination apparatus 100 is, for example, a software function unit that functions when a CPU included in the interference determination apparatus 100 executes a program stored in a storage unit. In addition, some or all of these functional units may be hardware functional units such as LSI (Large Scale Integration) and ASIC (Application Specific Integrated Circuit). The storage unit is, for example, a RAM (Random Access Memory), a ROM (Read Only Memory), a flash memory, a register, or the like, and may be a drive device such as an HDD (Hard Disk Drive) or an external memory. In addition to the proximity determination value 400, the storage unit stores processing results of each functional unit, temporary data generated during the processing, a program executed by the CPU, and the like.

[Process overview]
The outline of processing by each functional block will be described below. The polygon acquisition unit 110 acquires polygon data 202 in which a plurality of objects represented by polygons are arranged in a three-dimensional space, and outputs the polygon data 202 to the selection unit 120. The selection unit 120 selects two objects for performing interference and proximity determination from a plurality of objects described in the polygon data input from the polygon acquisition unit 110. Next, the selection unit 120 sets at least one polygon as a polygon to be determined among a plurality of polygons indicating the shape of the surface of one of the two selected objects (first object). select. That is, the selection unit 120 selects at least one polygon as a polygon to be determined from among a plurality of polygons indicating the shape of the surface of the first object among the plurality of objects. Then, the selection unit 120 outputs information indicating the selected polygon to be determined to the closed surface setting unit 142 of the determination unit 140. Further, the selection unit 120 selects a line segment (second line segment) indicating the shape of the surface from another object (second object) of the two objects that perform interference and proximity determination. The information indicating the second line segment is output to the interference calculation unit 144 of the determination unit 140.

  The information indicating the polygon to be determined is, for example, an identifier (described later) that is uniquely determined for the polygon, coordinates of the vertex of the polygon, and the like. The second line segment is, for example, a ridge line indicating the shape of the surface of the second object. The information indicating the second line segment is, for example, the coordinates of the two end points of the line segment.

  The closed curved surface setting unit 142 first acquires information indicating the polygon to be determined from the selection unit 120 and the proximity determination value 400 stored in the storage unit. Next, the closed curved surface setting unit 142 sets a closed curved surface including the selected polygon to be determined. In addition, the distance between the closed curved surface and a point corresponding to the polygon to be determined or a line segment (first line segment) corresponding to the polygon to be determined is a distance indicated by the proximity determination value 400. Is set to be That is, the closed surface setting unit 142 of the determination unit 140 is a closed surface including the selected determination target polygon, and corresponds to a certain point corresponding to the determination target polygon or the determination target polygon. A closed curved surface having a constant distance from the first line segment is set. Then, the closed curved surface setting unit 142 outputs information indicating the set closed curved surface to the interference calculating unit 144. Here, the information indicating the closed surface is, for example, the coordinates of a certain point located at the center of the closed surface, the coordinates of two end points of the first line segment located at the center of the closed surface, or the like. .

  The interference calculation unit 144 acquires information indicating the second line segment from the selection unit 120 and information indicating the closed curved surface from the closed curved surface setting unit 142. Next, the interference calculation unit 144 calculates the distance between the second line segment and a certain point corresponding to the polygon to be determined or the first line segment. The interference calculation unit 144 outputs the calculated distance to the interference determination unit 146.

  The interference determination unit 146 acquires the distance calculated by the interference calculation unit 144 from the interference calculation unit 144, and acquires the proximity determination value 400 from the storage unit. Next, the interference determination unit 146 compares the distance calculated by the interference calculation unit 144 with the distance indicated by the proximity determination value 400. If the calculated distance is equal to or less than the distance indicated by the proximity determination value 400, the interference determination unit 146 determines that the closed curved surface corresponding to the determination target triangle and the second line segment “interfere”. If the calculated distance is larger than the distance indicated by the proximity determination value 400, the interference determination unit 146 determines that the closed curved surface corresponding to the determination target triangle and the second line segment do not interfere.

  That is, the determination unit 140 is a closed curved surface including the selected determination target polygon, and a certain point corresponding to the determination target polygon or a first line segment corresponding to the determination target polygon Is determined based on the distance indicated by the proximity determination value 400. The interference between the closed curved surface having a constant distance and the second line segment indicating the shape of the surface of the second object among the plurality of objects is determined. Further, the determination unit 140 determines interference based on a comparison of a distance between a certain point or first line segment and the closed curved surface, and a distance between a certain point or first line segment and the second line segment. To do. The interference determination unit 146 outputs the determination result to the output unit 150.

  The output unit 150 acquires a determination result from the interference determination unit 146. Based on the acquired determination result, the output unit 150 generates and outputs information for notifying the object and its parts that have shown interference. Alternatively, the output unit 150 generates and outputs information for notifying that there is no interference. The output unit 150 may include, for example, a liquid crystal display, an organic EL (Electroluminescence) display, and the like, and visually display the determination result.

  The polygon data 202 acquired by the polygon acquisition unit 110 is prepared by, for example, a CAD (Computer Aided Design) system or a CAM (Computer Aided Manufacturing) system. , Not limited to a particular format. Further, the number of vertices of a polygon indicating the shape of the surface of the object described in the polygon data is not limited to a specific number. Although the present invention can be applied even if the polygon is a quadrangle or a pentagon, a case where the polygon is a triangle will be described below. That is, at least one of the polygons to be determined is a triangle.

  In the polygon data 202, for example, each of a plurality of polygons indicating the shape of an individual object or its surface, or an edge or vertex of the polygon is assigned an identifier. Therefore, each functional unit of the interference determination apparatus 100 can identify and select each object or part thereof and obtain coordinates. Further, after the polygon acquisition unit 110 acquires the polygon data 202, the identifier may be assigned as described above. Moreover, the interference determination apparatus 100 may have a function of converting data of an object expressed by a shape other than a polygon, for example, expressed by a free-form surface into a representation by a polygon. The interference determination apparatus 100 may include a CAD system or a CAM system, and may exchange polygon data 202 and interference determination results within the apparatus to change the contents of the polygon data 202.

  The second line segment only needs to indicate the shape of the surface of the second object. Accordingly, the second line segment is, for example, a line segment connecting two points located inside or near the triangle of the triangle indicating the shape of the surface of the second object, or the midpoint of the triangle It may be a line segment connecting

[Specific processing flow]
Hereinafter, an example of specific processing performed by the interference determination apparatus 100 will be described. FIG. 3 is a flowchart illustrating an example of interference determination processing by the interference determination apparatus 100.
(Step S300) First, the polygon acquisition unit 110 acquires the polygon data 202 and outputs it to the selection unit 120.
(Step S <b> 302) Next, the selection unit 120 is a first object of two objects that are targets for interference / proximity determination from a plurality of objects described in the polygon data input from the polygon acquisition unit 110. And a second object.
(Step S304) Next, the selection unit 120 selects one of the plurality of triangles indicating the shape of the surface of the first object as a determination target. The selection unit 120 outputs the coordinates of the three vertices of the selected determination target triangle to the closed surface setting unit 142. The coordinates of the three vertices of the determination target triangle are examples of information indicating the determination target polygon.

  (Step S306) Next, the closed surface setting unit 142 sets a closed surface based on the coordinates of the three vertices of the determination target triangle input from the selection unit and the proximity determination value 400 acquired from the storage unit. To do. The setting of the closed curved surface will be described later. Then, the closed curved surface setting unit 142 outputs the coordinates of the point located at the center of the set closed curved surface or the coordinates of the two end points of the first line segment to the interference calculating unit 144. The coordinates of the point located at the center of these closed surfaces or the coordinates of the two end points of the first line segment are examples of information indicating the above-described closed surface.

  (Step S308) Next, the selection unit 120 selects one of the ridge lines of the second object as the second line segment. That is, in this example, the second line segment is one side of one polygon among a plurality of polygons indicating the shape of the surface of the second object. Then, the selection unit 120 outputs the coordinates of the two end points of the selected second line segment to the interference calculation unit 144. The coordinates of the two end points of the second line segment are an example of information indicating the second line segment.

  (Step S310) Next, the interference calculation unit 144 performs the first operation based on the information indicating the second line segment input from the selection unit 120 and the information indicating the closed curved surface input from the closed curved surface setting unit 142. The distance between the second line segment and a certain point or the first line segment located at the center of the closed curved surface is calculated. The calculation of the distance will be described later. The interference calculation unit 144 outputs the calculated distance between the second line segment and the closed curved surface to the interference determination unit 146.

  (Step S312) Next, the interference determination unit 146 compares the distance indicated by the proximity determination value 400 with the distance calculated by the interference calculation unit 144. When the distance calculated by the interference calculation unit 144 is equal to or smaller than the distance indicated by the proximity determination value 400 (step S312; YES), the interference determination unit 146 determines that the determination target triangle and the second line segment interfere with each other, and the output unit The determination result is output to 150. Then, the process proceeds to step S314. When the distance calculated by the interference calculation unit 144 is larger than the distance indicated by the proximity determination value 400 (step S312; NO), the interference determination unit 146 determines that the determination target triangle and the second line segment do not interfere with each other, and step The process proceeds to S316.

(Step S314) Next, the output unit 150 outputs information indicating that there is interference based on the determination result of the interference determination unit 146. The information may include, for example, a triangle to be determined, an identifier or coordinates of the second line segment, and the degree of interference such as the distance between the center of the closed curved surface calculated by the interference calculation unit 144 and the second line segment. May be included.
(Step S316) Next, the selection unit 120 confirms whether all the ridge lines indicating the shape of the surface of the second object have been checked for interference with the triangle to be determined of the first object. When all the ridge lines indicating the shape of the second surface are being examined (step S316; YES), the process proceeds to step S318. When all the ridge lines indicating the shape of the surface of the second object have not been examined (step S316; NO), the process returns to step S308.

(Step S318) Next, the selection unit 120 confirms whether or not the interference with the second object has been examined for all the triangles indicating the shape of the surface of the first object. When interference is examined for all triangles indicating the shape of the surface of the first object (step S318; YES), the process proceeds to step S320. When interference is not examined for all triangles indicating the shape of the surface of the first object (step S318; NO), the process returns to step S304.
(Step S320) The output unit 150 outputs information notifying that there is no interference based on the determination result of the interference determination unit 146.

  Although not shown in the above flowchart, when the closed curved surface setting unit 142 does not set a closed curved surface for the determination target triangle in step S306, the interference calculating unit 144 follows the conventional technique. Calculate the intersection of the triangle and the second line segment. This will also be described in detail later. Further, the above-described flowchart describes a case where the interference of two objects among a plurality of objects arranged in the virtual space is examined. When determining interference for the entire component in the virtual space, it is only necessary to comprehensively select combinations of two objects to be determined and determine interference for each combination. In this case, the determination result may be output every time interference is detected, or the determination result may be output collectively after determining the interference for all the components.

  When testing a control program that moves a component, first, for example, according to an instruction of the control program, the content of the polygon data 202 is updated to move the component in the virtual space. Next, the interference determination apparatus 100 selects the first object and the second object by the above processing, and determines interference or proximity between the objects. In this way, the control program can be tested by repeating the updating of the polygon data 202 and the determination of interference and proximity.

[Closed surface setting]
Hereinafter, the setting of the closed curved surface will be described in detail. FIG. 4 is a schematic diagram illustrating an example of a closed curved surface including a determination target triangle indicating the shape of the surface of the object in the three-dimensional virtual space. The x-axis, y-axis, and z-axis shown in FIG. 4 are axes that indicate the coordinates of the orthogonal three-dimensional virtual space. The schematic diagrams of FIGS. 4A and 4B are respectively viewed from the z-axis direction. In this example, the normal line of the triangle 230 and the normal line of the triangle 240 coincide with each other in the z-axis direction. ing. d is a distance indicated by the proximity determination value 400. FIG. 4A illustrates a case where the closed curved surface including the determination target triangle is spherical. d2 is the radius of the circumscribed circle of the triangle to be determined. FIG. 4B illustrates a case where the closed curved surface including the determination target triangle is a capsule type. d3 is the length of a perpendicular drawn from the vertex that is not the end point of the longest side (longest side) of the triangle to be judged to the longest side. However, when the triangle has two or more longest sides, one of them is the longest side.

  In FIG. 4A, the determination target triangle 230 is a triangle whose radius d2 of the circumscribed circle of the determination target triangle is equal to or less than the distance d indicated by the proximity determination value 400 (d2 ≦ d). The closed curved surface 234 that includes the triangle 230 is a spherical closed curved surface that is set so that the distance from the outer center 232 of the triangle 230 is d. That is, in this example, a certain point is the outer center of the triangle 230 to be determined.

  In the following description, a certain point corresponding to the triangle to be determined is described as being an outer center of the triangle. However, the certain point may not be an outer center of the triangle. It may be. Also, a certain point corresponding to the triangle to be determined may not be on the same plane as the triangle. However, a closed curved surface in which a certain point corresponding to the triangle to be determined is an outer center under the same proximity determination value 400 is a triangle having a variety of shapes as compared to a spherical closed curved surface set by another method. Therefore, the amount of calculation can be further reduced.

  In FIG. 4B, the determination target triangle 240 has a length d3 of a perpendicular line extending from the vertex that is not the end point of the longest side of the determination target triangle to the longest side, twice the distance d indicated by the proximity determination value 400. The following is a triangle (d3 ≦ 2 × d). The first line segment 242 corresponding to the triangle 240 is a line segment that passes through the midpoint of each of the two sides other than the longest side of the triangle 240. Further, the length of the first line segment 242 is the length of the longest side of the triangle 240. Further, the midpoint of the first line segment 242 exists on the perpendicular bisector of the longest side of the triangle 240. The closed curved surface 244 that includes the determination target triangle 240 is a capsule-type closed curved surface that is set so that the distance from the first line segment 242 is d. That is, in this example, the first line segment 242 is a line segment that passes through the midpoint of each of two sides of the three sides of the triangle 240 to be determined. In this example, the length of the first line segment 242 is the length of one side of the triangle 240 to be determined.

  In the following, the first line segment is a line segment passing through the midpoint of each of two sides of the three sides of the determination target triangle 240, and the length of the first line segment is the longest side of the determination target triangle 240. The first line segment corresponding to the determination target triangle may not be as described above, for example, a line segment that connects the longest side and the midpoint of each other side. It may be. Further, the first line segment may be, for example, a line segment longer than that in the example of FIG. 4B described above. In addition, the first line segment may not be on the same plane as the determination target triangle. However, a closed curved surface in which the first line segment corresponding to the determination target triangle is set as in the above-described example of FIG. 4B under the same proximity determination value 400 is set by another method. Since triangles with various shapes can be included rather than a capsule-type closed curved surface, the amount of calculation can be further reduced. In addition, since the closed curved surface is not excessively large, interference and proximity of the determination target triangle are not excessively evaluated.

Hereinafter, a method for setting a closed curved surface by the interference determination apparatus 100 will be described. This process corresponds to step S306 in FIG. FIG. 5 is a flowchart illustrating an example of processing for setting a closed curved surface to a polygon to be determined by the closed curved surface setting unit 142 of the determination unit 140.
(Step S500) The closed curved surface setting unit 142 acquires the proximity determination value 400 from the storage unit.
(Step S502) Next, the closed surface setting unit 142 calculates the radius d2 of the circumscribed circle of the triangle from the coordinates of each vertex of the determination target triangle selected by the selection unit 120.

(Step S504) Next, the closed curved surface setting unit 142 compares the distance d indicated by the proximity determination value 400 with the calculated circumscribed circle radius d2, and the circumscribed circle radius d2 is the distance d. It is then determined whether (d2 ≦ d). When d2 ≦ d (step S504; YES), the process proceeds to step S506. When d2 ≦ d is not satisfied (step S504; NO), the process proceeds to step S508.
(Step S506) Next, the closed surface setting unit 142 calculates the coordinates of the outer center of the triangle from the coordinates of the vertex of the triangle to be determined. Then, the closed curved surface setting unit 142 associates the identifier of the triangle with the calculated outer-center coordinates, stores them in the storage unit, and outputs them to the interference calculation unit 144.

(Step S508) Next, the closed curved surface setting unit 142 calculates the length d3 of the perpendicular drawn from the vertex that is not the end point of the longest side of the vertices of the triangle to be determined to the longest side.
(Step S510) Next, the closed curved surface setting unit 142 compares the distance d indicated by the proximity determination value 400 with the perpendicular length d3 calculated in Step S508, and the perpendicular length d3 is twice the distance d. It is then determined whether (d3 ≦ 2 × d). When d3 ≦ 2 × d is satisfied (step S510; YES), the process proceeds to step S512. When d3 ≦ 2 × d is not satisfied (step S510; NO), the process proceeds to step S514.

(Step S512) Next, the closed surface setting unit 142 is a line segment passing through the midpoint of each of the two sides other than the longest side, the length of which is the length of the longest side, and the midpoint is the longest side The coordinates of the two end points of the line segment existing on the vertical bisector are calculated. Then, the closed curved surface setting unit 142 associates the identifier of the triangle with the calculated coordinates of the two end points of the line segment, stores them in the storage unit, and outputs them to the interference calculation unit 144.
(Step S514) Next, the closed surface setting unit 142 determines that there is no closed surface suitable for the triangle to be determined. Then, the closed curved surface setting unit 142 associates the identifier of the triangle with information indicating that the closed curved surface is not set in the storage unit, and outputs the information to the interference calculation unit 144.

  In addition, between step S502 and step S504, as step S503, the closed curved surface setting unit 142 may determine whether the lengths of the three sides of the determination target triangle are twice or less than the distance d. . In step S503 (not shown), if the length of each side is not more than twice the distance d, the process proceeds to step S504. In step S503 (not shown), if the length of each side is not less than twice the distance d, the process proceeds to step S508. By doing in this way, the calculation process of the radius d2 of the circumscribed circle having a large calculation amount may be avoided, and the interference determination apparatus 100 can further reduce the calculation amount.

[Interference calculation]
Hereinafter, calculation of the distance between the second line segment and a certain point located at the center of the closed curved surface or the first line segment in step S310 in FIG. 3 will be described. The interference calculation unit 144 performs any of the following three calculations (A) to (C) based on the processing result (Step S306 in FIG. 3 and FIG. 5) by the closed curved surface setting unit 142.

  In the following equation, the amount of calculation is indicated by the number of multiplications / divisions. This is because when a computer performs a numerical calculation, the load of multiplication and division is much larger than addition and subtraction, and the amount of calculation is often compared by the number of multiplications and divisions. Further, since the value that can be calculated in advance before the calculation of the interference between the closed curved surface and the second line segment (step S310 in FIG. 3) can be omitted by storing the value in the storage unit, Not counted in the number of calculations. Examples of such values include the square of the length of the first line segment, the square of the length of the second line segment, twice the area of the triangle to be determined, and the distance indicated by the proximity determination value 400. There are squares of. Further, when there are multiple multiplications / divisions between the same values in the course of calculation, the result of the multiplication / division is stored in the storage unit, and the calculation can be omitted. Further, in the following expression, vector inner product calculation is used. Since each vector is a three-dimensional vector, one inner product calculation corresponds to three multiplications.

  In the following calculations (a) and (b), the distance between a point and a line segment and the distance between two line segments are calculated. The interference determination unit 146 compares the calculated distance with the distance indicated by the proximity determination value 400, and determines that interference occurs when the calculated distance is equal to or less than the distance indicated by the proximity determination value 400. When the calculated distance is not less than or equal to the distance indicated by the proximity determination value 400, it is determined that there is no interference. Since the square of the distance indicated by the proximity determination value 400 can be calculated in advance, the above distance comparison is performed between the squares of the distances.

(A) When the closed curved surface setting unit 142 sets a spherical closed curved surface as the determination target triangle (step S506 in FIG. 5), the interference calculating unit 144 is based on the following equations (1) to (4). The distance between the second line segment and the outer center of the determination target triangle is calculated. This calculation process corresponds to obtaining a distance between a point and a line segment. Let P ₀ and P _{1 be} vectors of the two end points of the second line segment, and let Q be a vector indicating the outer center of the triangle to be determined. Furthermore, the vector of the second segment and _{P 10.} The perpendicular line extending from the point Q to the extended line of the second line segment is perpendicular to the second line segment. Thus, by using the internal division parameter t of the vector P ₁₀ of the second segment, when the foot of the perpendicular line and P _t, the following equation (1) holds.

  The internal parameter t is calculated by the following formula (2) obtained by expanding the formula (1).

Since the values of P ₁₀ and P ₁₀ in Equation (2) can be calculated in advance, they are not included in the number of calculations as described above. Therefore, the internal division parameter t is calculated by one inner product calculation and one division. Therefore, the number of multiplications / divisions required for calculating the internal parameter t is four. When the internal parameter t is smaller than 0 (t <0), since the point P _t does not exist on the vector P ₁₀ of the second line segment, the distance from the point Q to the closest point P ₀ is This is the distance to the second line segment. Therefore, the square D ^{2 of the} distance is the inner product of the point vector Q and the point vector P _0, and the number of multiplications / divisions based on this calculation is three.

When the internal parameter t is larger than 1 (t> 1), the point P _t does not exist on the vector P ₁₀ of the second line segment, so the distance between the point P ₁ closest to the point Q and the point Q is a point. This is the distance between Q and the second line segment. Therefore, the square D ² of the distance is the inner product of the point vector Q and the point vectors P _1, the number of multiplication and division based on this calculation is 3 times. When the internal parameter t is not less than 0 and not more than 1 (0 ≦ t ≦ 1), the point P _t exists on the second line segment. Vector of the point P _t is calculated by the following equation (3).

The shortest distance between the point Q and the second line segment is the length of the perpendicular drawn from the point Q to the second line segment, and the square D ² of the shortest distance is calculated by the following equation (4). .

The number of multiplication and division applied to the calculation of P _t according to equation (3) is three times. Further, the number of multiplication and division applied to the calculation of the square D ² of the distance based on Equation (4) is 3 times. Therefore, the number of multiplications / divisions for the entire calculation of (a) is 10 when the internal division parameter t is 0 or more and 1 or less, and 7 when the internal division parameter t is less than 0 or greater than 1. is there.

(A) When the closed curved surface setting unit 142 sets a capsule-shaped closed curved surface as a determination target triangle (step S512 in FIG. 5), the interference calculating unit 144 is based on the following equations (5) to (13). The distance between the second line segment and the first line segment associated with the determination target triangle is calculated. This calculation process corresponds to obtaining the distance between two line segments. If P ₀ and P ₁ are vectors indicating the two end points of the second line segment, and Q ₀ and Q ₁ are vectors indicating the two end points of the first line segment, the shortest of the extension lines of the two line segments The line segment connecting the distances is orthogonal to both the vector P ₁₀ of the second line segment and the vector Q ₁₀ of the first line segment. Accordingly, the following equations (5) and (6) are established by using the internal division parameters s and t for the second line segment vector P ₁₀ and the first line segment vector Q ₁₀ .

  When this equation is expanded, the following equations (7) and (8) are obtained.

  Therefore, the internal division parameters s and t are calculated by the following equations (9) and (10).

In the equations (9) and (10), a = P ₁₀ · P _10, b = −P ₁₀ · Q _10, c = (Q ₀ −P ₀ ) · P _10, d = P ₁₀ · Q _10, e = −Q ₁₀ · Q _10, f = (Q ₀ −P ₀ ) · Q ₁₀ , and a to f correspond to the terms of the equations (9) and (10). Of these, a and e can be calculated in advance, and thus are not included in the number of calculations as described above. Further, since b and d include overlapping calculations, as described above, they are combined into one inner product calculation. Therefore, the inner product calculation of a to f is three times, and the number of multiplications and divisions required for the calculation of a to f is nine. Further, since the denominators on the right side of Expressions (9) and (10) overlap, the calculation of the denominator values of Expressions (9) and (10) is counted together as described above. For this reason, the number of multiplications required to calculate the denominator values of the equations (9) and (10) is two times required to calculate bd and ae. Therefore, the total number of multiplications and divisions performed based on equations (9) and (10) is five. From the above, the number of multiplications / divisions required for calculating the internal parameters s, t is 17 in total.

Next, the interference calculation unit 144 performs different calculations depending on the values of the internal parameters s and t. When the internal parameters s and t are both smaller than 0 or larger than 1, the shortest distance between the first line segment and the second line segment is the distance between the end points of the respective line segments. Accordingly, the square D ² of the shortest distance is calculated by calculating the inner product between the point vectors. The number of multiplications / divisions based on this calculation is three.

When the internal division parameter s is 0 or more and 1 or less and t is smaller than 0 or larger than 1, the shortest distance between the first line segment and the second line segment is the end point of the first line segment and the second line segment. The distance from the line segment. Accordingly, the square D ² of the distance between the first line segment and the second line segment can be obtained by performing the same calculation as the above calculation (A). The number of multiplications / divisions based on this calculation is 10 when it is the largest. The same applies when the internal parameter t is 0 or more and 1 or less and s is less than 0 or greater than 1, and the number of multiplications / divisions based on this calculation is 10 when it is the largest.

When the internal parameters s and t are both 0 or more and 1 or less, the interference calculation unit 144 calculates vectors P _s and Q _t at both ends of the line segment indicating the shortest distance between the first line segment and the second line segment. It calculates based on the following formula | equation (11) and (12). The number of multiplications / divisions in the calculations of Expressions (11) and (12) is three.

Therefore, the square D ² of the shortest distance between the first line segment and the second line segment is calculated based on the following equation (13).

Number of applied multiplication and division in the calculation of the square D ² of the distance based on Equation (13) is three times. Therefore, when the internal division parameters s and t are both 0 or more and 1 or less, the number of multiplications / divisions in calculations based on the equations (11) to (13) is nine. Accordingly, the number of multiplications / divisions for the entire calculation of (A) is 20 when the internal division parameters s and t are both smaller than 0 or larger than 1 and the largest. When the internal division parameter s is 0 or more and 1 or less and t is smaller than 0 or larger than 1, 27 times. Also, when the internal parameter t is 0 or more and 1 or less and s is less than 0 or greater than 1, it is 27 times. When the internal division parameters s and t are both 0 or more and 1 or less, it is 26 times.

  (C) When the closed curved surface setting unit 142 does not set a closed curved surface for the triangle to be determined (step S514 in FIG. 5), the interference calculating unit 144 is based on the following equations (14) to (16). The plane to which the determination target triangle belongs, the second line segment, and the intersection are calculated, and the coordinates are output to the interference determination unit 146. The interference determination unit 146 determines interference with the determination target triangle by determining whether or not the coordinates of the intersection calculated by the interference calculation unit 144 are a point inside the determination target triangle. This calculation is a general one belonging to the prior art, but an example is shown below.

If the vectors of the vertices of the determination target triangle are Q ₀ , Q ₁ , and Q ₂ and the vectors of the two end points of the second line segment are P ₀ and P ₁ , the plane to which the determination target triangle belongs and the The intersection point P _t with the line segment 2 is expressed by the above-described equation (3) using the internal division parameter t. P _t is present on the determination target of the triangle and the same plane. Therefore, the following equation (14) is established between the normal vector N of the triangle to be determined. Since the value of the normal vector N of the triangle to be determined can be calculated in advance, it is not included in the number of calculations as described above.

  Next, t is calculated from the following equation (15) by solving equation (14) for t.

The number of multiplication and division applied to the calculation of P _t according to equation (3) is three times. Further, the calculation for calculating t based on the equation (15) is two times of inner product calculation and one time of division, and the number of times of multiplication / division combining these is seven. Therefore, the number of applied multiplication and division by the calculation of _{P t,} based on the equation (3) and (15), which is 10 times in total. Next, a triangle (Q ₀ Q ₁ P _t , Q ₁ Q ₂ P _t , Q ₀ Q ₂ P _t ) formed by a set of each vertex Q ₀ , Q ₁ , Q _{2 of} each triangle to be determined and an intersection point P _t The sum of the areas S ₀ , S ₁ , S ₂ is calculated and compared with the area S of the determination target triangle Q ₀ Q ₁ Q ₂ . When the area S is larger than the sum of the areas S ₀ , S ₁ and S ₂ (S> S ₀ + S ₁ + S ₂ ), the interference determination unit 146 causes the determination target triangle and the second line segment to interfere with each other. Judge that not. When the area S is less than or equal to the sum of the areas S ₀ , S ₁ , S ₂ (S ≦ S ₀ + S ₁ + S ₂ ), the interference determination unit 146 determines that the determination target triangle and the second line segment do not interfere with each other. To do.

The area of the triangle is calculated by dividing the outer product of the vector of line segments indicating the two sides of the triangle by 2. Calculation of the outer product of three-dimensional vectors requires 6 multiplications and divisions per time. Moreover, since the interference determination unit 146 compares the areas of the triangles, the process of dividing by 2 in the calculation of the area of the triangles can be omitted. In addition, three triangles (Q ₀ Q ₁ P) excluding the calculation required for calculating twice the area S (2 × S) of the determination target triangle Q ₀ Q ₁ Q ₂ that can be calculated in advance. _t , Q ₁ Q ₂ P _t , Q ₀ Q ₂ P _t ) area S ₀ , S ₁ , S ₂ each double (2 × S ₀ , 2 × S ₁ , 2 × S ₂ ) Since one outer product calculation and one inner product calculation are required, nine multiplications and divisions are required. The calculation of from (c) above, it is necessary to 10 times and 27 times and 37 times of multiplication and division of the combined applied twice the calculation of the area of the three triangles to calculate the P _t.

  As described above, (a) the amount of calculation when using a spherical closed surface is 10 times at the maximum, and (b) the amount of calculation when using a capsule-type closed surface is the largest. In some cases, 27 times. (C) The amount of calculation when using the prior art is 37 times. Therefore, the interference calculation unit 144 determines the interference with a calculation amount of about 1/4 in the case of (a) and about 2/3 in the case of (b) compared with the calculation amount of (c) which is the conventional technique. A necessary value can be calculated. Therefore, the interference determination apparatus 100 can determine the interference and proximity between the first object and the second object with a small amount of calculation.

  Moreover, the interference determination apparatus 100 can further reduce the amount of calculation necessary for determining the interference by including more triangles in the closed curved surface. For this purpose, the proximity determination value 400 may be set large so that a large triangle can be included in the closed curved surface. On the other hand, when the proximity determination value 400 increases, the determination of the interference between the closed curved surface and the ridge line becomes unsatisfactory, and the determination accuracy of the proximity between the first object and the second object decreases. Therefore, even when the proximity determination value 400 is small, the interference determination apparatus 100 is optimal for determining interference and proximity of an object having a surface shape in which many triangles are covered by a closed curved surface.

  Examples of such an object include an object having a curved surface. Equipment and robots in the production line are chamfered in consideration of safety and strength in the event of a collision with a person. When a curved surface with such chamfering is expressed by a polygon, the curved surface portion includes a very large number of small triangles and needle-like elongated triangles as compared with the flat surface portion. Therefore, the interference determination apparatus 100 sets many closed curved surfaces for the triangle indicating the shape of the surface of the object that is chamfered. Therefore, the interference determination apparatus 100 can reduce the amount of calculation required for determining the interference and proximity of the chamfered object. In addition to the equipment and robots listed above, chamfering is generally performed on industrial products in consideration of aesthetics and the like. Therefore, the interference determination apparatus 100 can produce an effect of reducing the amount of calculation even when applied to different technical fields as well as the production line simulator.

  As described above, according to the interference determination apparatus 100 of the first embodiment, the selection unit 120 includes at least one of a plurality of triangles indicating the shape of the surface of the first object among the plurality of objects. The triangle is selected as a determination target triangle, and the determination unit 140 is a closed curved surface including the selected determination target triangle, and corresponds to a certain point corresponding to the determination target triangle or a determination target triangle. Based on the distance indicated by the proximity determination value 400, the interference between the closed curved surface having a constant distance from the first line segment and the second line segment indicating the shape of the surface of the second object among the plurality of objects. judge. Therefore, the interference determination apparatus 100 can determine the interference and proximity between the first object and the second object with a small amount of calculation.

  Further, according to the closed curved surface setting unit 142 of the determination unit 140 of the first embodiment, the first line segment is a line segment that passes through the midpoint of each of the two sides of the three sides of the determination target triangle. . Accordingly, since the closed surface setting unit 142 can set a closed surface including more triangles, the interference determination apparatus 100 can reduce the amount of calculation and the interference and proximity between the first object and the second object. Can be determined.

  In addition, according to the closed curved surface setting unit 142 of the determination unit 140 of the first embodiment, the length of the first line segment is the length of one side of the determination target triangle. Accordingly, since the closed curved surface setting unit 142 does not set an excessively large closed curved surface, the interference determination apparatus 100 can correctly reflect the set proximity distance in the determination of interference or proximity. Moreover, the interference determination apparatus 100 does not need to calculate the length of a 1st line segment anew, and can reduce calculation amount.

  Further, according to the closed curved surface setting unit 142 of the determination unit 140 of the first embodiment, the certain point corresponding to the determination target triangle is the outer center of the determination target triangle. Accordingly, since the closed surface setting unit 142 can set a closed surface including more triangles, the interference determination apparatus 100 can reduce the amount of calculation and the interference and proximity between the first object and the second object. Can be determined.

  In order to achieve both the accuracy of proximity determination and the effect of reducing the amount of calculation, the interference determination apparatus 100 may have a function of appropriately setting the proximity determination value 400. For example, the interference determination apparatus 100 checks in advance the size of a triangle (for example, the radius of a circumscribed circle) indicating the shape of the surface of the first object, and, for example, the triangle of 20% to 30% is selected. The proximity determination value 400 may be set so that it can be included. Further, the interference determination apparatus 100 may cluster the triangles based on the size or the like, and set the proximity determination value 400 so that the closed curved surface can include a small triangle class. Further, the proximity determination value 400 may be arbitrarily set by the user of the interference determination apparatus 100, or may be changed for each object, for each triangle, or the like.

<Second Embodiment>
[Constitution]
Hereinafter, the interference determination apparatus according to the second embodiment will be described in detail. FIG. 6 is a block diagram illustrating an example of a functional configuration of the interference determination apparatus 100b according to the second embodiment. When the interference determination apparatus 100b (FIG. 6) according to the present embodiment is compared with the interference determination apparatus 100 (FIG. 2) according to the first embodiment, the difference is that the interference determination apparatus 100b includes a dividing unit 130. In addition, since the interference determination apparatus 100b of the present embodiment includes the dividing unit 130, the selection unit 120b and the process performed by the closed curved surface setting unit 142b of the determination unit 140b are selections corresponding to the functional units of the first embodiment. This is different from the closed surface setting unit 142 of the unit 120 and the determination unit 140. Specifically, the selection unit 120b of the interference determination apparatus 100b has a function of selecting a polygon to be determined and outputting information indicating the polygon to the dividing unit 130. Further, the closed curved surface setting unit 142b of the determination unit 140b has a function of acquiring information indicating the polygon after the division from the dividing unit 130.

  However, the functions of other function units (polygon acquisition unit 110, interference calculation unit 144, interference determination unit 146, and output unit 150) are the same as those in the first embodiment. A description of the same functions as those in the first embodiment is omitted. Moreover, these function parts are software function parts which function when CPU with which the interference determination apparatus 100b is provided executes the program stored in the memory | storage part, for example. In addition, some or all of these functional units may be hardware functional units such as an LSI or an ASIC.

[Process overview]
When setting a closed surface including a polygon to be determined, the interference determination device 100b has a function of setting a plurality of closed surfaces in the polygon. Hereinafter, an outline of processing by the interference determination apparatus 100b will be described. The selection unit 120b selects a polygon to be determined, and outputs information indicating the polygon to the division unit 130. The dividing unit 130 first acquires information indicating the polygon to be determined from the selection unit 120b and the proximity determination value 400 from the storage unit. Next, the dividing unit 130 divides the determination target polygon into a plurality of polygons based on the distance indicated by the proximity determination value 400. That is, the dividing unit 130 divides at least one of a plurality of polygons indicating the shape of the surface of the first object into a plurality of polygons based on the distance. Then, the dividing unit 130 outputs information indicating the polygon after the division to the closed surface setting unit 142b. Note that the information indicating the polygon after division is, for example, the coordinates of each vertex of the polygon after division or an identifier uniquely assigned to the polygon after division.

  The selection unit 120b selects one polygon among a plurality of polygons after division by the division unit as a determination target. That is, the selection unit 120b selects at least one polygon among a plurality of polygons after the division by the division unit 130 as a determination target. The closed curved surface setting unit 142b acquires information indicating the polygon after the division from the dividing unit 130. Then, the closed curved surface setting unit 142b applies a closed curved surface to the polygon selected as the determination target by the selection unit 120b among the divided polygons, similarly to the closed curved surface setting unit 142 in the first embodiment. Set. Subsequent processing is the same as that in the first embodiment, and is therefore omitted.

[Polygon division and closed surface setting]
Hereinafter, polygon division and setting of a closed curved surface will be described in detail. FIG. 7 is a schematic diagram illustrating an example of a method of dividing a polygon to be determined that indicates the shape of the surface of an object in the three-dimensional virtual space. The x-axis, y-axis, and z-axis shown in FIG. 7 are axes that indicate the coordinates of the orthogonal three-dimensional virtual space. The schematic diagrams in FIGS. 7A and 7B are respectively viewed from the z-axis direction. In this example, the normal line of the triangle 250 and the normal line of the triangle 260 coincide with the z-axis direction, respectively. ing. FIG. 7A is a diagram for explaining how the triangle to be determined is divided into two triangles. FIG. 7B is a diagram for explaining how the triangle to be determined is divided into three triangles.

  In FIG. 7A, the determination target triangle 250 has a length of the longest side that is greater than twice and less than or equal to four times the distance d indicated by the proximity determination value 400, and the length of the remaining two sides is the distance d. It is a triangle that is 2 times or less. Since such a triangle does not satisfy the condition for setting a closed surface, the interference determination apparatus 100 according to the first embodiment does not set a closed surface for the triangle. The dividing unit 130 of the interference determination apparatus 100b divides the determination target triangle 250 into two triangles by a line segment 256 that connects a midpoint of the longest side of the triangle 250 and a vertex that is not an end point of the longest side. That is, at least one polygon among the plurality of polygons before division by the division unit 130 is a triangle, and the division unit 130 selects at least one triangle of the polygons before division as the triangle. It is divided into two triangles as a plurality of polygons after division by one central line.

  The length of each side of the two triangles after the division is less than twice the distance d. Therefore, when a closed curved surface centering on the outer centers 258 (A) and 258 (B) of the divided triangles is set, the closed curved surface may include each of the divided triangles. As described above, the amount of calculation performed by the interference calculation unit 144 for a spherical closed curved surface is 10 times in the largest case. Therefore, even if the triangle is divided into two as shown in FIG. 7A, the calculation amount when a spherical closed surface is set for each of the divided triangles is 20 times in the largest case. Therefore, the interference calculation unit 144 can calculate a value necessary for determination of interference with a calculation amount smaller than the calculation amount of 37 times of the prior art.

  In FIG. 7B, the triangle 260 to be determined has a length of two sides that is greater than twice the distance d indicated by the proximity judgment value 400 and not more than four times, and the length of the remaining one side is the distance d. It is a triangle that is 2 times or less. Since such a triangle does not satisfy the condition for setting a closed surface, the interference determination apparatus 100 according to the first embodiment does not set a closed surface for the triangle. The dividing unit 130 of the interference determination apparatus 100b satisfies the closed curved surface setting condition by the line segment 266 that connects the triangle 260 to be determined to the midpoint 269 of the longest side of the triangle 260 and the vertex that is not the end point of the longest side. Divide into two triangles. Further, the dividing unit 130 selects a triangle having a longest side length longer than twice the distance d indicated by the proximity determination value 400 from the two triangles after the division. A line segment 267 is connected to a vertex 269 that is not an end point of the side. That is, the dividing unit 130 divides at least one of a plurality of polygons indicating the shape of the surface of the first object into three of two to five polygons based on the distance.

  The length of each side of the three triangles after the division is not more than twice the distance d. Accordingly, when a closed curved surface centering on the outer centers 268 (A) to 268 (C) of the divided triangles is set, the closed curved surface may include each of the divided triangles. As described above, the calculation amount performed by the interference calculation unit 144 for a spherical closed curved surface is 10 times when it is the largest. Therefore, even if the triangle is divided into three as shown in FIG. 7A, the calculation amount when a spherical closed curved surface is set for each of the divided triangles is 20 times when it is the largest. Therefore, the interference calculation unit 144 can calculate a value related to the determination of interference with a calculation amount smaller than the calculation amount of 37 times of the conventional technique.

[Triangulation and closed surface setting processing]
Hereinafter, a method for dividing a triangle and setting a closed curved surface by the interference determination apparatus 100b will be described. FIG. 8 is a flowchart illustrating an example of processing for setting a closed curved surface to a determination target triangle by the interference determination apparatus 100b. 8, each of steps S800, S802, S804, S806, S820, S822, S824, and S826 corresponds to steps S500, S502, S504, S506, S508, S510, S512, and S514 of FIG. Description is omitted. If the determination in step S804 is no, the process proceeds to step S808.

  (Step S808) The dividing unit 130 compares the distance d indicated by the proximity determination value 400 with the length of each side of the triangle to be determined, and the length of the longest side of the triangle is larger than twice the distance d. It is determined whether or not the length is less than twice (2 × d <longest side ≦ 4 × d), and the length of one side is less than or equal to twice the distance d (1 side ≦ 2 × d). When 2 × d <longest side ≦ 4 × d and 1 side ≦ 2 × d (step S808; YES), the process proceeds to step S810. When 2 × d <longest side ≦ 4 × d and 1 side ≦ 2 × d are not satisfied (step S808; NO), the process proceeds to step S814.

  (Step S810) Next, the dividing unit 130 divides the determination target triangle into two triangles by a line segment connecting the midpoint of the longest side of the triangle and the vertex that is not the end point of the longest side, and each triangle is divided. Assign an identifier to. The dividing unit 130 stores the coordinates of the vertices of each divided triangle and the identifier in the storage unit in association with each other. The selection unit 120b selects each of the two divided triangles as a determination target.

(Step S812) Next, the dividing unit 130 compares the distance d indicated by the proximity determination value 400 with the length of the longest side of the triangle to be determined after the division, and the length of the longest side of the triangle is the distance d. It is determined whether or not it is greater than twice and less than or equal to 4 times (2 × d <longest side ≦ 4 × d). When 2 × d <longest side ≦ 4 × d (step S812; YES), the process returns to step S810. When 2 × d <longest side ≦ 4 × d is not satisfied (step S812; NO), the process proceeds to step S814.
(Step S814) Next, the closed surface setting unit 142b calculates the size d2 ′ of the radius of the outer center of the triangle from the coordinates of the vertex of the triangle to be determined.

(Step S816) Next, the closed curved surface setting unit 142b compares the distance d indicated by the proximity determination value 400 with the radius d2 ′ of the circumscribed circle of the determination target triangle calculated in Step S814, and It is determined whether the radius d2 ′ of the circumscribed circle of the triangle is smaller than the distance d (d2 ′ ≦ d). When d2 ′ ≦ d (step S816; YES), the process proceeds to step S818. When d2 ′ ≦ d is not satisfied (step S816; NO), the process proceeds to step S820.
(Step S818) Next, the closed curved surface setting unit 142b associates the identifier with the calculated coordinates of the outer center, stores them in the storage unit, and outputs them to the interference calculation unit 144.

  The polygon dividing method is not limited to the above method. If it is a triangle, for example, it may be divided by a middle line, or may be divided by a perpendicular drawn from the center of gravity to each side. Moreover, you may set the closed curved surface from which a shape differs to each of the some polygon after a division | segmentation. For example, when the amount of calculation performed by the interference calculation unit 144 for the spherical closed surface is the largest, it is 10 times, and when the amount of calculation performed by the interference calculation unit 144 for the closed capsule surface is the largest, 27 is calculated. Since the polygon is divided into two, and the divided polygon is included by a spherical closed surface and a capsule closed surface, respectively, the calculation amount is 37 times at the maximum. Therefore, there are cases where interference can be determined with a smaller calculation amount than the conventional 37 times.

  Further, the dividing unit 130 may divide the polygon more finely. For example, the amount of calculation performed by the interference calculation unit 144 for a spherical closed curved surface is 7 times when it is the smallest. For this reason, the calculation amount when the triangle divided into five is included by a spherical closed curved surface is the smallest 35 times, and a reduction in the calculation amount may be expected. Therefore, the interference determination apparatus 100b can set closed surfaces for more polygons by dividing the polygon from two to five, and can reduce the amount of calculation. Moreover, the conditions for performing the division may be appropriately set according to the division method.

[Summary]
As described above, according to the interference determination apparatus 100b of the second embodiment, the dividing unit 130 determines at least one polygon among the plurality of polygons indicating the shape of the surface of the first object as the distance. The selection unit 120b selects at least one polygon among the plurality of polygons after the division by the division unit 130 as a determination target. Therefore, since the interference determination apparatus 100b can set a closed curved surface for a large triangle as compared with the interference determination apparatus 100 in the first embodiment, the interference between the first object and the second object can be reduced with a smaller amount of calculation. Proximity can be determined.

<Third Embodiment>
[Usage environment of interference judgment device]
Hereinafter, the interference determination apparatus according to the third embodiment will be described in detail. The interference determination apparatus 100c according to the present embodiment is a production line simulator that performs interference determination on polygon data acquired in the same manner as the interference determination apparatuses 100 and 100b according to the first and second embodiments. Is different. For example, the interference determination apparatus 100c according to the present embodiment is synchronized with the movement of the production line, and simulates the movement of the components of the production line. For example, in the production line shown in FIG. 1, it is assumed that the robot 310 (A) rotates to the right and the robot 310 (B) rotates to the left. Since the robot 310 (A) and the robot 310 (B) are close in position, there is a risk of collision depending on the timing of rotation. If this movement can be simulated with a simulator prior to the actual movement of the production line and interference can be determined, the movement of the robot 310 (A) or the robot (B) can be slowed or stopped, Collisions between robots can be avoided. Thus, the interference determination apparatus 100c according to the third embodiment performs real-time interference determination in a simulation performed in synchronization with the movement of the production line.

  In such a use environment, the interference determination apparatus 100c is required to complete the determination of interference in a shorter time. Therefore, it is desirable to complete in advance processing that can be performed in advance. Therefore, the interference determination apparatus 100c sets a closed curved surface in advance for a polygon indicating the shape of the surface of the first object.

[Constitution]
FIG. 9 is a block diagram illustrating an example of a functional configuration of the interference determination apparatus 100c according to the third embodiment. The interference determination device 100c (FIG. 9) according to the present embodiment includes functional units corresponding to the interference determination device 100b (FIG. 6) according to the second embodiment, and the selection unit 120c includes the selection unit 120b. The determination unit 140c corresponds to the determination unit 140b, the closed surface setting unit 142c corresponds to the closed surface setting unit 142b, and the interference calculation unit 144c corresponds to the interference calculation unit 144. Moreover, the interference determination apparatus 100c includes, for example, a movement vector acquisition unit 160 and a coordinate conversion unit 170. The closed curved surface setting table 410 is stored in the storage unit. The functions of each function unit (polygon acquisition unit 110, division unit 130, interference determination unit 146, and output unit 150) of the interference determination apparatus 100c are the same as the functions of each function unit in the first and second embodiments. Yes, the description of the same function is omitted. These functional units are, for example, software functional units that function when a CPU included in the interference determination apparatus 100c executes a program stored in the storage unit. In addition, some or all of these functional units may be hardware functional units such as an LSI or an ASIC.

[Process overview]
Hereinafter, processing by the interference determination apparatus 100c will be described. The interference determination device 100c sets a closed curved surface corresponding to the polygon to be determined, similarly to the processing in the second embodiment. However, the interference determination apparatus 100c does not perform interference calculation for a polygon when another polygon is included in the closed curved surface already set for the certain polygon in order to reduce overlapping processing. Has function. This process will be described later. The closed surface setting unit 142c associates the identifier of the polygon to be determined with the corresponding closed surface setting information, and stores it in the storage unit as a closed surface setting table 410 (described later). The selection unit 120c selects the determination target and the second line segment of the first object with reference to the closed curved surface setting table 410, and outputs information indicating the determination target to the interference calculation unit 144c. The interference calculation unit 144c performs the calculation shown by the equations (1) to (15) of the first embodiment for the determination target.

  In the real-time interference determination synchronized with the movement of the production line, the movement vector data regarding each component in the virtual space and a part of the movement is updated as needed, and the updated movement vector data is acquired by the movement vector acquisition unit 160. Is done. The movement vector acquisition unit 160 stores the acquired movement vector data in the storage unit and outputs it to the coordinate conversion unit 170. The coordinate conversion unit 170 converts the coordinates of the closed curved surface and the coordinates of the triangle stored in the closed curved surface setting table based on the movement vector indicated by the movement vector data acquired from the movement vector acquisition unit 160, and moves the production line. Is reflected in the arrangement of the components of the virtual space. The selection unit 120c refers to the updated closed surface setting table and selects a determination target. By repeating the above, the interference determination apparatus 100c can perform real-time interference determination.

  FIG. 10 is a table showing an example of a closed curved surface setting table. In FIG. 10, a column t100 is a triangular identifier, a column t102 is a type of a closed surface, a column t104 is a coordinate of the center of the closed surface, a column t106 is a pre-calculated value for reducing interference calculation, and a column t108 is performing interference determination. Indicates whether or not In this example, the triangle indicated by the identifier “1” has a spherical closed surface set in step S806 in FIG. At this time, for example, coordinates of the outer center of the triangle are stored in the corresponding item in the column t104. For the triangle indicated by the identifier “2”, a capsule-type closed curved surface is set in step S824 in FIG. At this time, for example, the coordinates of the two end points of the first line segment of the closed curved surface are stored in the corresponding item of the column t104. In addition, the corresponding item in the column t106 stores the square of the length of the first line segment of the closed curved surface. By using this value, the interference determination unit 146 can determine the interference between the determination target triangle “2” and the second line segment with a small amount of calculation.

  The triangle indicated by the identifier “3” is divided into two in step S810 of FIG. 8, and a spherical closed surface corresponding to each is set in step S818 of FIG. In this embodiment, identifiers “3-1” and “3-2” are newly assigned to each of the two divided triangles, and a closed surface is associated with each of the triangles. Therefore, for example, the coordinates of the outer centers of the two triangles after being divided into the same identifier “3” are stored in the corresponding item in the column t104.

  The triangle indicated by the identifier “4” is a triangle for which a closed curved surface has not been set in step S826 in FIG. For example, the coordinates of the three vertices of the triangle are stored in the corresponding item of the column t104. In addition, a value twice the area of the triangle is stored in the corresponding item in the column t106. By using this value, the determination unit 140c can determine the interference between the triangle “4” to be determined and the second line segment with a small amount of calculation. Since the triangle indicated by the identifier “5” is included in the closed curved surface already set for a certain polygon, it is a triangle determined not to determine interference or proximity.

  For example, when determining whether or not the triangle indicated by the identifier “5” is included in the closed surface corresponding to the triangle indicated by the identifier “1”, the closed surface setting unit 142c closes the triangle “1”. The distance between the coordinate (t104) of the curved surface and each vertex of the triangle “5” is calculated. The closed curved surface setting unit 142c compares the calculated distance with the distance indicated by the proximity determination value 400, and if any of them is smaller than the distance indicated by the proximity determination value 400, the triangle “5” indicates “1”. It is determined to be included in the closed curved surface corresponding to the triangle. Similarly, in the case of a capsule-type closed curved surface such as “2”, the distance between the first line segment corresponding to the closed curved surface and each vertex of the triangle to be determined is calculated, and the calculated distance is used as the proximity determination value. By comparing with the distance indicated by 400, it can be determined whether or not the determination target triangle is included in the already set closed curved surface.

  As described above, in the third embodiment, the triangle included in the closed curved surface set to the triangle that has already been selected as the determination target is not determined. That is, the selection unit 120c is a first unit for the determination unit 140c to determine the interference with the second line segment among the plurality of polygons indicating the shape of the surface of the first object among the plurality of objects. At least one polygon not included in the closed curved surface is selected as a polygon to be determined, and the determination unit 140c determines interference between the second closed curved surface including the polygon and the second line segment. Therefore, since the interference determination device 100c can reduce the number of triangles that are subject to interference and proximity determination compared to the interference determination device 100b in the second embodiment, the first object, the second object, and the like. It is possible to further reduce the amount of calculation performed for the determination of interference and proximity.

  Moreover, the interference determination apparatus 100c may narrow down the polygon used as the object which performs interference determination previously. For example, the interference determination apparatus 100c analyzes the acquired movement vector, identifies an object or a part thereof that may cause interference, and then interferes only with the identified object or a polygon that forms the part. Or proximity determination may be performed. In addition, the interference determination apparatus 100c specifies, for example, an object or a part of the object to be determined in more detail by simply determining interference or proximity on a closed curved surface covering the entire object or a part of the object, and the specified object. Alternatively, interference or proximity may be determined only for a polygon that forms a part of the polygon. Such narrowing down of polygons to be determined may be used without being limited to a specific method.

  As described above, the embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to the above, and various design changes and the like can be made without departing from the scope of the present invention. It is possible to For example, the interference determination apparatus of the present invention can be applied to various fields using computer graphics such as a mechanism design system, industrial product design, three-dimensional map, and game software in addition to a production line simulator. Moreover, you may combine each function of three embodiment demonstrated above. For example, the method for presetting the closed curved surface described in the third embodiment can also be applied to the first embodiment. Further, for example, interference or proximity may be determined between closed curved surfaces.

  DESCRIPTION OF SYMBOLS 100, 100b, 100c ... Interference determination apparatus, 110 ... Polygon acquisition part, 120, 120b, 120c ... Selection part, 130 ... Dividing part, 140, 140b, 140c ... Determination part, 142, 142b, 142c ... Closed curved surface setting part, 144, 144c ... interference calculation unit, 146 ... interference determination unit, 150 ... output unit, 160 ... movement vector acquisition unit, 170 ... coordinate conversion unit, 202 ... polygon data, 204 ... movement vector data, 400 ... proximity determination value, 410 ... Closed surface setting table

Claims (12)

A selection unit that selects, as a polygon to be determined, a polygon of a part of the plurality of polygons indicating the shape of the surface of the chamfered first object among the plurality of objects;
A closed curved surface including the selected polygon to be determined, and a distance from a certain point corresponding to the polygon to be determined or a first line segment corresponding to the polygon to be determined is constant. A determination unit that determines interference between the closed curved surface and a second line segment indicating the shape of the surface of the second object among the plurality of objects based on the distance;
An interference determination device comprising: The interference determination apparatus according to claim 1, wherein the second line segment is one side of one polygon among a plurality of polygons indicating the shape of the surface of the second object. Based on the polygonal shape to be determined, either a closed curved surface having a constant distance to the certain point or a closed curved surface having a constant distance to the first line segment, A closed surface setting unit for setting as a closed surface including a polygon to be judged,
The interference determination apparatus according to claim 1, further comprising: The closed curved surface setting unit includes a closed curved surface having a constant distance from the certain point and a closed curved surface having a constant distance from the first line segment based on a proximity determination value representing the distance. The interference determination apparatus according to claim 3, wherein either one is set as a closed curved surface including the polygon to be determined. The selection unit is a polygon that is not included in the closed curved surface used for the determination of the interference by the determination unit among the plurality of polygons indicating the shape of the surface of the first object among the plurality of objects. The interference determination device according to any one of claims 1 to 4, wherein a polygon is selected as the polygon to be determined. A dividing unit that divides some of the plurality of polygons indicating the shape of the surface of the first object into a plurality of polygons based on the distance;
The interference determination according to any one of claims 1 to 5, wherein the selection unit selects at least one of a plurality of polygons after division by the division unit as the polygon to be determined. apparatus. The division unit determines, based on the distance, whether or not to divide a part of the plurality of polygons indicating the shape of the surface of the first object into a plurality of polygons. 6. The interference determination device according to 6. The division unit divides a part of a plurality of polygons indicating the shape of the surface of the first object into two to five polygons based on the distance. The interference determination apparatus described in 1. Some polygons of the plurality of polygons before division by the division unit are triangles,
9. The division unit divides a part of the polygons before the division into two triangles as a plurality of polygons after the division by one middle line of the triangles. The interference determination apparatus according to any one of claims. The determination unit is based on a comparison between a distance between the certain point or the first line segment and the closed curved surface, and a distance between the certain point or the first line segment and the second line segment. The interference determination apparatus according to any one of claims 1 to 9, wherein the interference is determined. A selection process in which the selection unit selects, as a determination target, a part of the plurality of polygons indicating the shape of the surface of the chamfered first object among the plurality of objects;
The determination unit is a closed curved surface including the selected determination target polygon, and a certain point corresponding to the determination target polygon or a first line segment corresponding to the determination target polygon A determination process for determining an interference between a closed curved surface having a constant distance and a second line segment indicating a shape of a surface of a second object of the plurality of objects based on the distance;
An interference determination method. On the computer,
A selection procedure for selecting a part of the plurality of polygons indicating the shape of the surface of the chamfered first object among the plurality of objects as a determination target;
A closed curved surface including the selected polygon to be determined, and a distance from a certain point corresponding to the polygon to be determined or a first line segment corresponding to the polygon to be determined is constant. A determination procedure for determining interference between the closed curved surface and a second line segment indicating the shape of the surface of the second object among the plurality of objects based on the distance;
Interference determination program for executing