JP2014211822A - Contact surface detection system, state change calculation system, connotation determination system, contact surface detection method and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To more properly determine contact relation between surfaces.SOLUTION: A contact surface detection system includes, a coordinates data acquisition part which acquires coordinate data of apex of a first polyhedron and coordinate data of apex of a second polyhedron, a surface selection part which selects a first surface from the surface forming the first polyhedron, and selects a second surface from the surface forming the second polyhedron, a connotation determination part which determines whether or not at least one apex among apexes of the first polygon forming the first surface is connoted in the second polygon forming the second surface, and a contact surface detection part which, according to determination result of the connotation determination part, detects a surface contacting to the surface forming the second polyhedron among the surfaces forming the first polyhedron.

Description

  The present invention relates to a contact surface detection system, a state change calculation system, an inclusion determination system, a contact surface detection method, and a program.

Several techniques have been proposed for determining the positional relationship between a plurality of figures. For example, in the hidden line / hidden surface calculation processing method described in Patent Document 1, a plane forming a figure model is divided into triangles. Then, using a 4 × 4 determinant, it is determined whether the point is inside or outside the plane including the triangle, and whether the side and the side intersect is determined. The part where the triangle is hidden by other triangles is determined.
According to Patent Document 1, this makes it possible to uniformly determine the coherence between complex figures by determinant calculation of 4 rows and 4 columns.

JP-A 61-265777

By the way, the aging deterioration of each member which comprises a building can change with the positional relationship with another building. In particular, when the surface of the building is in contact with the surface of another building, the aging of the member is affected. In the prediction of the aging deterioration of such a member, the contact relationship between the faces is more important than the context of the building.
On the other hand, the technique described in Patent Document 1 relates to interference between figures caused by the context of figures, and when applied to the determination of contact relation between faces, there is a possibility that inconvenience may occur. For example, Patent Document 1 does not fully show the determination of the contact relationship that does not cause an intersection between sides.

  The present invention has been made in consideration of such circumstances, and the object thereof is a contact surface detection system, state change calculation system, and inclusion determination system that can more appropriately determine the contact relationship between surfaces. Another object is to provide a contact surface detection method and program.

  The present invention has been made to solve the above-described problem, and a contact surface detection system according to an aspect of the present invention is a coordinate system for acquiring coordinate data of vertexes of a first polyhedron and coordinate data of vertexes of a second polyhedron. A data acquisition unit; a surface selection unit that selects a first surface from a surface that forms the first polyhedron; and a second surface that selects a second surface from a surface that forms the second polyhedron; and a first that forms the first surface An inclusion determination unit that determines whether or not at least one vertex of the polygon vertices is included in the second polygon that forms the second surface, and according to the determination result of the inclusion determination unit, And a contact surface detecting unit that detects a surface that contacts the surface that forms the second polyhedron among the surfaces that form the first polyhedron.

  A contact surface detection system according to another aspect of the present invention is the above-described contact surface detection system, wherein the inclusion determination unit determines whether or not a point is included in a convex polygon. And a vertex of the convex polygon having an area of a triangle composed of a line segment connecting each of the two adjacent vertices of the vertex of the convex polygon and a side connecting the two adjacent vertices. An area comparison unit that performs comparison between the total of all the combinations of two adjacent vertices and the area of the convex polygon, and at least one of the vertices of the first polygon; A second polygon or a convex polygon obtained by dividing the second polygon is applied to the area comparison unit, and at least one vertex of the first polygon is changed to the second polygon. It is characterized by determining whether it is included or not.

  A contact surface detection system according to another aspect of the present invention is the above-described contact surface detection system, wherein the second polygon includes one vertex of the second polygon and a vertex adjacent to the vertex. A division unit that divides the triangles into line segments that connect each other vertex, and the inclusion determination unit is obtained by dividing the at least one vertex among the vertices of the first polygon and the division unit. Applying at least one of the triangles to the area comparing unit to determine whether at least one vertex of the first polygon is included in the second polygon; It is characterized by that.

  A contact surface detection system according to another aspect of the present invention is the contact surface detection system described above, and determines whether or not the side of the first polygon intersects the side of the second polygon. And the contact surface detection unit determines the second polyhedron among the surfaces forming the first polyhedron according to the determination result of the inclusion determination unit and the determination result of the intersection determination unit. It is characterized by detecting a surface in contact with the surface to be formed.

  The state change calculation system according to another aspect of the present invention forms the first polyhedron for a first polyhedron corresponding to the shape of the first structure and a second polyhedron corresponding to the shape of the second structure. The surface which contacts the surface which forms the said 2nd polyhedron among the surfaces to perform is detected based on the contact condition which the contact surface detection system as described in any one of Claim 1 to 4 and the said contact surface detection system detected A state change calculating unit that calculates a change in state of a member of the first structure or the second structure over time, at least a part of the first structure or the second structure;

  Further, an inclusion determination system according to another aspect of the present invention includes a coordinate data acquisition unit that acquires coordinate data of a certain point and coordinate data of a vertex of the polygon, the certain point, and the vertex of the polygon About all combinations of two adjacent vertices of the polygonal vertices of a triangular area composed of a line segment connecting each of two adjacent vertices and an edge connecting the two adjacent vertices An inclusion determination unit that determines whether or not the total of the polygon and the area of the polygon are equal, and determines whether the certain point is included in the polygon according to a determination result. It is characterized by doing.

  A contact surface detection method according to another aspect of the present invention is a contact surface detection method of a contact surface detection system, and acquires coordinate data of vertexes of a first polyhedron and coordinate data of vertices of a second polyhedron. A coordinate data acquisition step, a surface selection step of selecting a first surface from the surfaces forming the first polyhedron, selecting a second surface from the surfaces forming the second polyhedron, and a first surface forming the first surface. According to an inclusion determination step for determining whether or not at least one vertex of one polygon vertex is included in the second polygon forming the second surface, and according to a determination result in the inclusion determination step And a contact surface detecting step of detecting a surface in contact with a surface forming the second polyhedron among surfaces forming the first polyhedron.

  According to another aspect of the present invention, there is provided a program according to another aspect of the present invention, wherein a computer provided in a contact surface detection system acquires coordinate data of vertexes of a first polyhedron and coordinate data of vertexes of a second polyhedron, A surface selection step of selecting a first surface from the surfaces forming the first polyhedron and selecting a second surface from the surfaces forming the second polyhedron, and a vertex of the first polygon forming the first surface Forming the first polyhedron according to an inclusion determination step for determining whether or not at least one vertex is included in the second polygon forming the second surface, and a determination result in the inclusion determination step And a contact surface detecting step for detecting a surface in contact with a surface forming the second polyhedron among the surfaces to be performed.

  According to this invention, it is possible to more appropriately determine the contact relationship between surfaces.

It is a schematic block diagram which shows the function structure of the contact surface detection system in the 1st Embodiment of this invention. It is explanatory drawing which shows the example of the polyhedron from which the coordinate data acquisition part in the embodiment acquires data. It is explanatory drawing which shows the example of the polygon division | segmentation which the division part in the embodiment performs. It is explanatory drawing which shows the example of the surface which the surface selection part in the embodiment selects. It is explanatory drawing which shows another example of the surface which the surface selection part in the same embodiment selects. It is explanatory drawing which shows the example of the positional relationship of two triangles. It is explanatory drawing which shows the example of the triangle which the area comparison part in the embodiment calculates the total of an area. It is explanatory drawing which shows another example of the triangle which the area comparison part in the embodiment calculates the total of an area. It is explanatory drawing which shows the example of two sides which cross | intersect. It is explanatory drawing which shows the example of two sides which do not cross | intersect. It is explanatory drawing which shows another example of two sides which do not cross | intersect. It is explanatory drawing which shows the example of a display of the determination result of the contact surface detection part by the result output part in the embodiment. In the embodiment, it is explanatory drawing which shows the example of the process sequence which a contact surface detection system detects the contact surface of a polyhedron. In the same embodiment, it is a flowchart which shows the example of the process sequence in which the surface selection part detects the surface contained in the same plane. In the same embodiment, the inclusion determination unit determines whether at least one of the vertices of the polygon forming one of the faces is included in the polyhedron forming the other face with respect to the combination of the two faces. It is a flowchart which shows the example of a process sequence. In the embodiment, the intersection determination unit shows an example of a processing procedure for determining whether or not there is an intersection between a triangle side included in one surface and a triangle side included in the other surface, for a combination of two surfaces. It is a flowchart. It is a schematic block diagram which shows the function structure of the state change calculation system in the 2nd Embodiment of this invention. It is a schematic block diagram which shows the function structure of the inclusion determination system in the 3rd Embodiment of this invention.

<First Embodiment>
Embodiments of the present invention will be described below with reference to the drawings.
FIG. 1 is a schematic block diagram showing a functional configuration of a contact surface detection system according to the first embodiment of the present invention. In FIG. 1, the contact surface detection system 10 includes a coordinate data acquisition unit 110, a division unit 120, a surface selection unit 130, a contact surface detection unit 140, and a result output unit 150. The contact surface detection unit 140 includes an inclusion determination unit 141 and an intersection determination unit 143. The inclusion determination unit 141 includes an area comparison unit 142.

The contact surface detection system 10 detects contact surfaces in a plurality of polyhedrons such as models of a plurality of buildings, for example.
The coordinate data acquisition unit 110 acquires coordinate data of vertices of a plurality of polyhedra. For example, the coordinate data acquisition unit 110 acquires coordinate data of vertexes of a polyhedron as a building model as CAD (Computer Aided Design) data or BIM (Building Information Modeling) data.

FIG. 2 is an explanatory diagram illustrating an example of a polyhedron from which the coordinate data acquisition unit 110 acquires data. In the example shown in the figure, a rectangular parallelepiped ABCD-EFGH and a rectangular parallelepiped abcd-efgh are shown. The coordinate data acquisition unit 110 acquires coordinate data of each vertex of the rectangular parallelepiped. In the example of FIG. 2, part of the surface ABCD is in contact with part of the surface abcd.
Hereinafter, two of the polyhedrons from which the coordinate data acquisition unit 110 acquires data are referred to as a first polyhedron and a second polyhedron, respectively. Accordingly, the coordinate data acquisition unit 110 acquires the coordinate data of the vertices of the first polyhedron and the coordinate data of the vertices of the second polyhedron.
The polyhedron from which the coordinate data acquisition unit 110 acquires data is not limited to a rectangular parallelepiped. Therefore, neither the first polyhedron nor the second polyhedron is limited to a rectangular parallelepiped.

  The dividing unit 120 is a line that connects each of the polygons forming the surface of the polyhedron from which the coordinate data acquisition unit 110 has acquired data to one vertex of the polygon and each vertex other than the vertex adjacent to the vertex. Divide into triangles at minutes (diagonal lines). The polygon that the dividing unit 120 divides includes a second polygon that forms a second surface selected by the surface selection unit 130 described later. Therefore, the dividing unit 120 divides the second polygon into triangles by line segments connecting one vertex of the second polygon and each vertex other than the vertex adjacent to the vertex.

FIG. 3 is an explanatory diagram illustrating an example of polygonal division performed by the dividing unit 120. In the example of the figure, the dividing unit 120 divides the rectangle ABCD into a triangle ABC and a triangle ACD along a diagonal line AC.
The polygon division performed by the dividing unit 120 only needs to divide the polygon into triangles by line segments that do not intersect the sides of the polygon. Therefore, the dividing unit 120 may perform polygon division using a line segment other than a line segment that connects one vertex of the polygon and each vertex other than the vertex adjacent to the vertex. For example, when the polygon to be divided is a concave polygon with a complicated shape, the dividing unit 120 is a figure obtained by dividing the process of dividing the polygon by an arbitrary diagonal line that does not intersect with the sides of the polygon. You may repeat until all become triangles.

  On the other hand, when the dividing unit 120 divides a triangle by a diagonal line connecting one vertex and each vertex other than the adjacent vertex, the intersection of the diagonal lines can be avoided and obtained by the division. An increase in the number of triangles can be prevented. In addition, the dividing unit 120 divides a triangle by a diagonal line connecting one vertex and each vertex other than the vertex adjacent to the vertex so that a line segment used for the division becomes clear, and the processing performed by the dividing unit 120 It becomes easy to automate.

The surface selection unit 130 selects the first surface from the surfaces that form the first polyhedron, and selects the second surface from the surfaces that form the second polyhedron. Specifically, the surface selection unit 130 detects a surface included in the same plane from each surface forming the first polyhedron and each surface forming the second polyhedron. For example, the surface selection unit 130 detects the triangles included in the same plane by calculating the coefficients of the equations of the plane passing through the three vertices of each surface forming each polygon and comparing the coefficients of the obtained equations. To do. As a method for the plane selection unit 130 to obtain a plane equation, a known method such as a method of calculating a unit normal vector of the plane and obtaining a coefficient of the equation can be used.
Hereinafter, the polygon forming the first surface selected by the surface selection unit 130 is referred to as a first polygon, and the polygon forming the second surface selected by the surface selection unit 130 is referred to as a second polygon. .

FIG. 4 is an explanatory diagram illustrating an example of a surface selected by the surface selection unit 130. In the drawing, a rectangular parallelepiped ABCD-EFGH and a rectangular parallelepiped abcd-efgh in the example of FIG. 2 are shown, and a plane P11 is further shown.
In the example of FIG. 4, as in the case of FIG. 2, the rectangle ABCD and the rectangle abcd are on the same plane. Specifically, the rectangle ABCD and the rectangle abcd are both included in the plane P11. The surface selection unit 130 selects a rectangle ABCD and a rectangle abcd on the same plane. As described above, part of the surface ABCD is in contact with part of the surface abcd.

FIG. 5 is an explanatory diagram illustrating another example of the surface selected by the surface selection unit 130. In the same figure, a rectangular parallelepiped ABCD-EFGH, a rectangular parallelepiped Irohani Hohetochi, and a plane P11 are shown. The rectangular parallelepiped ABCD-EFGH and the plane P11 are the same as those shown in the example of FIG.
In the example of FIG. 5, the rectangle ABCD and the rectangle Irohani are on the same plane. Specifically, the rectangle ABCD and the rectangle Irohani are both included in the plane P11. The surface selection unit 130 selects a rectangle ABCD and a rectangle Irohani on the same plane. Note that the rectangle ABCD and the rectangle Irohani in the example of FIG. 5 are not in contact with each other.

As described above, the surfaces selected by the surface selection unit 130 include surfaces that are not in contact with each other. Therefore, the contact surface detection unit 140 detects the surfaces in contact with each other among the surfaces selected by the surface selection unit 130.
Specifically, the contact surface detection unit 140 determines whether or not the triangles obtained by the division of the division unit 120 are in contact with each other with respect to the first surface and the second surface selected by the surface selection unit 130. Then, it is determined whether or not the first surface and the second surface are in contact with each other.

  FIG. 6 is an explanatory diagram showing an example of the positional relationship between two triangles. In the figure, patterns P111, P121, P131, and P141 to P146 are shown as examples of the positional relationship pattern of two triangles. Among these, the pattern P111 indicates a pattern in which two triangles are not in contact with each other, and the other pattern indicates a pattern in which two triangles are in contact with each other.

In the pattern P111, neither vertex of the two triangles is included in the other triangle. Specifically, in the pattern P111, all of the vertices A, B, and C are located outside the triangle abc. In addition, the inclusion here includes the case where the included point overlaps the side or vertex of the included polygon.
Also, neither side of the two triangles intersects the other triangle side. Specifically, none of the sides AB, BC, and CA intersects any of the sides ab, bc, and ca.

The pattern P121 shows a pattern in which two triangles are in contact but none of the vertices are included in the other triangle. Specifically, in the pattern P121, all of the vertices A, B, and C are located outside the triangle abc. In addition, all of the vertices a, b, and c are located outside the triangle ABC. On the other hand, in the pattern P121, the sides of the two triangles intersect. For example, side AB and side ab intersect In this way, if two triangles touch each other, but none of the vertices are included in the other triangle, the intersection of the sides of the two triangles It can be considered that it is determined that two triangles are in contact with each other.

The pattern P131 shows a pattern in which two triangles are in contact but none of the sides intersects the other triangle. Specifically, in the pattern P131, neither side of the two triangles intersects the side of the other triangle. Specifically, none of the sides AB, BC, and CA intersects any of the sides ab, bc, and ca. On the other hand, in the pattern P131, the vertex of one triangle is included in the other triangle. Specifically, all of the vertices a, b, and c are included in the triangle ABC.
In this way, two triangles touch each other, but if neither side intersects the other triangle side, it is determined that the two triangles touch each other by detecting the vertex contained in the other triangle. It is possible.

  The pattern P141 shows a pattern in which one vertex (vertex B) of one triangle is included in the other triangle. The pattern P142 shows a pattern in which two vertices (vertices b and c) of one triangle are included in the other triangle. Pattern P143 shows a pattern in which two triangles contain the other vertex. Specifically, the triangle ABC includes vertices b and c, and the triangle abc includes the vertex B.

  A pattern P144 shows a pattern in which two triangles match. The pattern P145 shows a pattern in which two vertices of two triangles match each other and one of the other vertices is included in the other triangle. The pattern P146 shows a pattern in which two vertices of two triangles match each other, and the other one vertex is not included in the other triangle.

In each of the patterns P141 to P146, two triangles are in contact with each other. In each of the patterns P141 to P146, there are vertices that are included in the other triangle, and there are sides that intersect with the sides of the other triangle.
As described above, both the detection of the intersection of the sides of the two triangles and the detection of the vertices contained in the other triangle are performed, and if the detection is successful in either one, the two triangles are It can be determined that they are in contact with each other.

  In the contact surface detection unit 140, the inclusion determination unit 141 determines whether there is a vertex included in the other triangle. In addition, the contact surface detection unit 140 determines whether or not the two triangle sides intersect each other by the intersection determination unit 143. Then, the contact surface detection unit 140 determines a surface that contacts the surface that forms the second polyhedron among the surfaces that form the first polyhedron according to the determination result of the inclusion determination unit 141 and the determination result of the intersection determination unit 143. To detect.

As described above, the inclusion determination unit 141 determines whether there is a vertex included in the other triangle. By this determination, the inclusion determination unit 141 determines whether at least one vertex of the first polygon that forms the first surface is included in the second polygon that forms the second surface. .
In the inclusion determination unit 141, the area comparison unit 142 determines whether or not the point is included in the convex polygon, and determines the sum of the areas of the triangles obtained by connecting the point and the vertex of the convex polygon, and the convexity The comparison is made with the square area. More specifically, the area comparison unit 142 includes a point, a line segment that connects each of two adjacent vertices among the vertices of the convex polygon, and a side that connects the two adjacent vertices. Calculate the area of each triangle. Then, the area comparison unit 142 calculates the total area of each triangle. That is, the area comparison unit 142 calculates the total area of the triangles for all combinations of two adjacent vertices among the vertices of the convex polygon. Furthermore, the area comparison unit 142 determines whether or not the point is included in the convex polygon by comparing the calculated total area with the area of the convex polygon.

  FIG. 7 is an explanatory diagram illustrating an example of a triangle in which the area comparison unit 142 calculates the total area. In the figure, a point a and a triangle ABC correspond to an example of a point and a convex polygon acquired by the area comparison unit 142, respectively. For example, the area comparison unit 142 acquires one vertex of the first polygon and a triangle obtained by dividing the second polygon by the dividing unit 120.

  In the example of FIG. 7, the area comparison unit 142 first calculates the area of the triangle aAB, the area of the aBC, and the area of the aCA. As a method for calculating the area of the triangle by the area comparison unit 142, a known method such as a method of calculating the area of the triangle from the outer product of the vectors can be used. For example, the area comparison unit 142 calculates the area of the triangle aAB from the outer product of the vector aA and the vector aB.

Next, the area comparison unit 142 calculates the total area of the triangles aAB, aBC, and aCA.
Further, the area comparison unit 142 calculates the area of the triangle ABC. Then, the area comparison unit 142 compares the total area of the triangles aAB, aBC, and aCA with the area of the triangle ABC.

In the example of FIG. 7, the point a is included in the triangle ABC. In this case, the triangle ABC is divided into triangles aAB, aBC, and aCA by the line segments aA, aB, and aC. Accordingly, the total area of the triangles aAB, aBC, and aCA is equal to the area of the triangle ABC.
As described above, when the point is included in the triangle, the point is constituted by a line segment connecting each of the two adjacent vertices among the vertices of the triangle, and a side connecting the two adjacent vertices. The area of each triangle is equal to the area of the triangle.
Therefore, if the area comparison unit 142 determines that the total area of the triangles is equal to the area of the convex polygon, the area comparison unit 142 determines that the point is included in the polygon.

  When the area comparison unit 142 calculates the area of the triangle from the outer product of the vectors, an error such as a rounding error in the square root calculation may occur. In order to cope with such an error, the area comparison unit 142 is not limited to a perfect match in the comparison of the total area of the triangle and the area of the convex polygon, and is equal to the case where the difference can be evaluated as sufficiently small. May be determined. For example, when the value obtained by dividing the difference between the total area of the triangles and the area of the convex polygons by the area of the convex polygons is equal to or smaller than a predetermined threshold, the area comparison unit 142 adds the total area of the triangles. And the area of the convex polygon may be determined to be equal.

  FIG. 8 is an explanatory diagram showing another example of a triangle for which the area comparison unit 142 calculates the total area. As in the case of FIG. 7, the point a and the triangle ABC correspond to examples of points and convex polygons acquired by the area comparison unit 142, respectively. As in the case of FIG. 7, the area comparison unit 142 compares the sum of the areas of the triangles aAB, aBC, and aCA with the area of the triangle ABC.

In the example of FIG. 8, the point a is not included in the triangle ABC. The triangle aAB does not overlap the triangle ABC. Also, the triangles aBC and aCA are not partially overlapped with the triangle ABC. For this reason, the total area of the triangles aAB, aBC, and aCA is larger than the area of the triangle ABC.
As described above, when the point is not included in the triangle, the point is constituted by a line segment connecting each of the two adjacent vertices among the vertices of the triangle, and a side connecting the two adjacent vertices. The area of each triangle is larger than the area of the triangle.
Therefore, if the area comparison unit 142 determines that the total area of the triangle is different from the area of the convex polygon, the area comparison unit 142 determines that the point is not included in the polygon.

The inclusion determination unit 141 applies at least one vertex of the vertices of the first polygon and the second polygon or the convex polygon obtained by dividing the second polygon to the area comparison unit 142, It is determined whether or not at least one vertex among the vertices of one polygon is included in the second polygon.
Specifically, the inclusion determination unit 141 applies at least one vertex among the vertices of the first polygon and at least one triangle among the triangles obtained by the division of the division unit 120 to the area comparison unit 142. Then, it is determined whether at least one vertex of the first polygon is contained in the second polygon.

However, the area comparison unit 142 can determine whether a point is included in a convex polygon as well as a triangle. Therefore, the inclusion determination unit 141 may apply a convex polygon to the area comparison unit 142 as well as the triangle obtained by the division of the division unit 120.
For example, when all the polyhedron surfaces from which the coordinate data acquisition unit 110 acquires data are convex polygons, the inclusion determination unit 141 may apply the polyhedron surfaces to the area comparison unit 142. In this case, regarding the determination of whether or not at least one vertex among the vertices of the first polygon is included in the second polygon, the dividing unit 120 does not need to divide the polygon.

The intersection determination unit 143 determines whether or not the sides of the first polygon and the sides of the second polygon intersect. As a method for determining whether or not the intersection determination unit 143 intersects the line segment, a known method such as a method using an outer product of vectors can be used.
FIG. 9 is an explanatory diagram illustrating an example of two intersecting sides. In the figure, a line segment ab corresponds to an example of a side of a first polygon, and a line segment AB corresponds to an example of a side of a second polygon.

In the example of FIG. 9, the point a and the point b are located on the opposite side when viewed from the line segment AB. For this reason, the normal vector obtained by (vector AB) × (vector Aa) is opposite to the normal vector obtained by (vector AB) × (vector Ab). However, “x” indicates an outer product of vectors.
Similarly, the normal vector obtained by (vector ab) × (vector aA) is opposite to the normal vector obtained by (vector ab) × (vector aB).
As described above, when the normal vector is reversed regardless of which side is used as a reference, it can be determined that the two sides intersect.

FIG. 10 is an explanatory diagram illustrating an example of two sides that do not intersect. As in the case of FIG. 9, the line segment ab corresponds to an example of the side of the first polygon, and the line segment AB corresponds to an example of the side of the second polygon.
Similarly to the case of FIG. 9, also in FIG. 10, the point a and the point b are located on the opposite side when viewed from the line segment AB. For this reason, the normal vector obtained by (vector AB) × (vector Aa) is opposite to the normal vector obtained by (vector AB) × (vector Ab).
On the other hand, the point A and the point B are located on the same side when viewed from the line segment ab. For this reason, the normal vector obtained by (vector ab) × (vector aA) and the normal vector obtained by (vector ab) × (vector aB) are in the same direction.
As described above, when one side is used as a reference, the normal vector is reversed, but when the other side is used as a reference, if the direction of the normal vector is the same, it is determined that the two sides do not intersect. be able to.

FIG. 11 is an explanatory diagram showing another example of two sides that do not intersect. As in the case of FIG. 9, the line segment ab corresponds to an example of the side of the first polygon, and the line segment AB corresponds to an example of the side of the second polygon.
In the example of FIG. 11, the point a and the point b are located on the same side as viewed from the line segment AB. For this reason, the normal vector obtained by (vector AB) × (vector Aa) and the normal vector obtained by (vector AB) × (vector Ab) are in the same direction.
Similarly, the normal vector obtained by (vector ab) × (vector aA) and the normal vector obtained by (vector ab) × (vector aB) are in the same direction.
Thus, if the direction of the normal vector is the same regardless of which side is used as a reference, it can be determined that the two sides do not intersect.

  From the above, the intersection determination unit 143 determines that two sides intersect if the normal vector is in the opposite direction with respect to any side, and the direction of the normal vector is in either direction. If they are the same, it is determined that the two sides do not intersect.

The result output unit 150 outputs the determination result of the contact surface detection unit 140. Specifically, the result output unit 150 has a display screen such as a liquid crystal panel, for example, and displays the determination result of the contact surface detection unit 140.
FIG. 12 is an explanatory diagram illustrating a display example of the determination result of the contact surface detection unit 140 by the result output unit 150.
In the figure, the determination result of the contact surface detection unit 140 is displayed in a table format. Both the row and the column correspond to one of the faces of the polyhedron, and the description of the column where the row and the column intersect indicates the presence or absence of contact between the two corresponding surfaces.

  For example, in the row of the surface ABCD of the solid I, the result output unit 150 indicates that each surface of the same solid I is not subject to determination on whether there is contact by hatching. Further, the surface ABCD and the surface abcd are in contact with each other, and the result output unit 150 displays “abcd” in a column that intersects the column of the surface abcd in the row of the surface ABCD to indicate that there is contact. On the other hand, the surface ABCD is not in contact with the other surface, and the result output unit 150 indicates that there is no contact by leaving a column that intersects the column of the other surface in the row of the surface ABCD as blank.

Next, the operation of the contact surface detection system 10 will be described with reference to FIGS.
FIG. 13 is an explanatory diagram illustrating an example of a processing procedure in which the contact surface detection system 10 detects a contact surface of a polyhedron.
In the process shown in FIG. 5, first, the coordinate data acquisition unit 110 acquires coordinate data of vertices of a plurality of polyhedrons as contact surface detection targets (step S101).
Next, the dividing unit 120 divides each of the polygons forming the surfaces of the plurality of polyhedrons from which the coordinate data acquisition unit 110 has acquired data into triangles (step S102).
Further, the surface selection unit 130 detects a surface included in the same plane among the surfaces of the plurality of polyhedrons from which the coordinate data acquisition unit 110 has acquired data (step S103).

FIG. 14 is a flowchart illustrating an example of a processing procedure in which the surface selection unit 130 detects surfaces included in the same plane. The surface selection unit 130 performs the process of FIG. 14 in step S103 of FIG.
In the processing of FIG. 14, the surface selection unit 130 first starts a loop L <b> 21 that performs processing on each surface of the plurality of polyhedrons for which the coordinate data acquisition unit 110 has acquired data (step S <b> 201).
Then, the surface selection unit 130 calculates two vectors included in the surface to be processed in the loop L21 (step S202). For example, the surface selection unit 130 calculates a vector corresponding to two sides for one of the triangles obtained by dividing the surface to be processed in the loop L21 by the dividing unit 120.

Next, the surface selection unit 130 calculates the outer product of the two vectors obtained in step S202 (step S203). This outer product represents a normal vector of a plane including two vectors.
Then, the surface selection unit 130 calculates the coefficient of the plane equation based on the outer product calculated in step S203 (step S204). Specifically, the surface selection unit 130 divides the outer product calculated in step S203 by the size of the outer product to calculate a unit normal vector. Then, the surface selection unit 130 sets the obtained coordinate value of the unit normal vector as a coefficient indicating the slope of the plane equation. Furthermore, the surface selection unit 130 sets the intercept coefficient so that the equation is established with respect to the coordinate values of the points included in the plane for which the equation is to be obtained.

For example, when the coordinate value of the unit normal vector is (v _x , v _y , v _z ), the surface selection unit 130 calculates the coefficient of the plane equation shown in Expression (1) as a: = v _x , Set b: = v _y and c: = v _z .

Here, “·” indicates a scalar product. Further, when the point (P _x , P _y , P _z ) is included in the plane, the plane selection unit 130 sets the coefficient of the plane equation as d: = − (a · P _x + b · P _y + c · P _z ).

  After step S204, the surface selection unit 130 determines whether or not the process of the loop L21 has been performed for all the surfaces of the plurality of polyhedrons for which the coordinate data acquisition unit 110 has acquired data, and performs branching based on the determination result. (Step S205). If it is determined that there is a surface that has not yet been processed by the loop L21, the process returns to step S201, and the processing of the loop L21 is continued for the unprocessed surface. On the other hand, when it is determined that the process of the loop L21 has been performed on all the surfaces, the loop L21 is terminated.

When the loop L21 ends, the surface selection unit 130 starts a loop L22 that performs processing for each combination of one surface included in two polyhedrons among the plurality of polyhedrons for which the coordinate data acquisition unit 110 has acquired data (step) S211).
Then, the surface selecting unit 130 determines whether or not the absolute values of the coefficients (| a |, | b |, | c |, and | d |) are all equal for the combination of surfaces that are the processing target in the loop L22. Is determined (step S212).

When it is determined that the absolute values of the coefficients are all equal (step S212: YES), the surface selection unit 130 further determines whether the coefficients (a, b, c, and d) are the same or opposite. It is determined whether or not (step S213). If the coefficient values are both zero, it is assumed that both the positive and negative coefficients are the same, and vice versa.
When it is determined that both the positive and negative coefficients are the same or opposite (step S213: YES), the surface selection unit 130 includes the two surfaces to be processed in the loop L22 included in the same plane. Determination is made (step S221).

Next, the surface selection unit 130 determines whether or not the processing of the loop L22 has been performed for all combinations of one surface included in two polyhedrons of the plurality of polyhedrons for which the coordinate data acquisition unit 110 has acquired data. Then, branching is performed based on the determination result (step S241). If it is determined that there is a combination that has not yet been processed in the loop L22, the process returns to step S211 to continue the processing in the loop L22 for the unprocessed combination. On the other hand, when it is determined that the processing of the loop L22 has been performed for all the combinations, the loop L22 is terminated.
When the loop L22 ends, the surface selection unit 130 ends the process of FIG.

On the other hand, when it is determined in step S212 that there are coefficients whose absolute values are not equal (step S212: NO), the surface selection unit 130 includes two surfaces to be processed in the loop L22 in the same plane. It is determined that there is not (step S231).
Thereafter, the process proceeds to step S241.
In Step S213, when it is determined that both positive and negative are the same or neither is reversed (Step S213: NO), the process proceeds to Step S231.

  An error such as a rounding error in the square root calculation when the surface selection unit 130 calculates the size of the outer product may occur. In order to deal with such an error, the surface selection unit 130 determines that the absolute values of the coefficients in step S212 are equal not only when they are completely coincident, but also when the magnitude of the difference can be evaluated to be sufficiently small. May be. For example, when the magnitude of the difference between the absolute values of the coefficients is equal to or smaller than a predetermined threshold, the surface selecting unit 130 may determine that the absolute values of the coefficients are equal.

  Further, the surface selection unit 130 can perform the process of FIG. 14 if the coordinate values of three points included in each of the surfaces to be determined are obtained. Accordingly, in the process of FIG. 13, step S103 may be executed before step S102, or step S102 and step S103 may be executed in parallel.

  Returning to the processing of FIG. 13, after step S <b> 103, the inclusion determination unit 141 includes a combination of two surfaces selected by the surface selection unit 130 in step S <b> 103 (a combination of two surfaces determined to be included in the same plane). About each, the presence or absence of inclusion relation is determined (step S104). Specifically, for each of the combinations of the two surfaces selected by the surface selection unit 130 in step S103, the inclusion determination unit 141 determines that at least one of the vertices of the polygon forming one of the surfaces is the other surface. It is determined whether or not it is included in the polyhedron to be formed.

  In FIG. 15, the inclusion determination unit 141 determines whether at least one of the vertices of the polygon forming one of the surfaces is included in the polyhedron forming the other surface for the combination of the two surfaces. It is a flowchart which shows the example of a process sequence. The inclusion determination unit 141 performs the process of FIG. 15 for each combination of the two surfaces selected by the surface selection unit 130 in step S104 of FIG.

In the processing of FIG. 15, the inclusion determination unit 141 first starts a loop L31 that performs processing for each combination in which the triangles obtained by the division of the dividing unit 120 are selected one by one for two surfaces (step S301). ).
Further, the inclusion determination unit 141 starts a loop L32 for performing processing for each of the two triangles selected in step S301 for each vertex of the triangle and the other triangle (step 302).

Then, the inclusion determination unit 141 applies the triangles and vertices to be processed in the loop L32 to the area comparison unit 142, and the area comparison unit 142 calculates the area of the triangle (step S303).
Next, as described with reference to FIGS. 7 and 8, the area comparison unit 142 is formed by a vertex that is a processing target in the loop L32 and an adjacent vertex among the vertices of the triangle. The area of each triangle is calculated, and the total area is calculated (step S304).

Then, the area comparison unit 142 determines whether or not the total area obtained in step S304 is equal to the area obtained in step S303 (the area of the original triangle) (step S305).
When it is determined that the total area is equal to the area of the original triangle (step S305: YES), the area comparison unit 142 has a vertex whose processing target is the loop L32 as a processing target in the loop L32. (Step S311).

  Next, the inclusion determination unit 141 determines whether or not the processing of the loop L32 has been performed for all combinations of the triangle and the vertex of the other triangle for any of the two triangles selected in step S301. Branching is performed based on the result (step S331). If it is determined that there is a combination that has not yet been processed in the loop L32, the process returns to step S302, and the processing in the loop L32 is continued for the unprocessed combination. On the other hand, when it is determined that the process of the loop L32 has been performed for all the combinations, the loop L32 is terminated.

  When the loop L32 ends, the inclusion determination unit 141 determines whether or not the processing of the loop L31 has been performed for all combinations in which the triangles obtained by the division of the division unit 120 are selected one by one for the two surfaces. Then, branching is performed based on the determination result (step S332). If it is determined that there is a combination that has not yet been processed in the loop L31, the process returns to step S301, and the processing in the loop L31 is continued for the unprocessed combination. On the other hand, when it is determined that the processing of the loop L31 has been performed for all the combinations, the loop L31 is terminated.

  When the loop L31 ends, the inclusion determination unit 141 determines the inclusion relationship between the faces (step S333). If it is determined that any one of the combinations of the triangle and the vertex in the processing of the loop L32 is included (step S311), it is determined that there is an inclusion relationship. That is, the inclusion determination unit 141 includes, for a combination of two surfaces to be determined, at least one of the vertices of a polygon that forms one of the surfaces included in a polyhedron that forms the other surface. judge.

On the other hand, if it is determined that all the combinations of triangles and vertices in the processing of the loop L32 are not included (step S321), it is determined that there is no inclusion relationship. That is, the inclusion determination unit 141 determines that, for the combination of two surfaces to be determined, the vertexes of the polygon that forms any surface are not included in the polyhedron that forms the other surface.
After step S333, the process of FIG.

On the other hand, if it is determined in step S305 that the total area is different from the area of the original triangle (step S305: NO), the area comparison unit 142 determines that the vertex targeted for processing in the loop L32 is the loop L32. It is determined that it is not included in the triangle to be processed (step S321).
Thereafter, the process proceeds to step S331.

  Returning to the processing in FIG. 13, after step S104, the intersection determination unit 143 determines, for each combination of the two surfaces selected by the surface selection unit 130 in step S103, the triangle side included in one surface and the other side. It is determined whether or not there is an intersection with a triangle side included in the surface (step S105).

  FIG. 16 illustrates an example of a processing procedure in which the intersection determination unit 143 determines whether or not there is an intersection between a triangle side included in one surface and a triangle side included in the other surface for a combination of two surfaces. It is a flowchart. The intersection determination unit 143 performs the process of FIG. 16 for each combination of two surfaces selected by the surface selection unit 130 in step S105 of FIG.

In the processing of FIG. 16, the intersection determination unit 143 first starts a loop L41 that performs processing for each combination in which the triangles obtained by the division of the division unit 120 are selected one by one for two surfaces (step S401). ).
Furthermore, the intersection determination unit 143 starts a loop L42 that performs processing for each combination in which one side is selected from each of the two triangles selected in step S401 (step 402).

Next, the intersection determination unit 143 calculates two normal vectors in the same manner as described with reference to FIGS. 9 to 11 with one of the two sides to be processed in the loop L42 as a reference. (Step S403).
Then, the intersection determination unit 143 determines whether or not the directions of the two normal vectors obtained in step S403 are opposite (step S404).

If it is determined that the direction of the normal vector is opposite (step S404: YES), the intersection determination unit 143 will be described with reference to FIGS. 9 to 11 on the basis of a different side from that in step S403. Similarly to the above, two normal vectors are calculated (step S411).
Then, the intersection determination unit 143 determines whether or not the directions of the two normal vectors obtained in step S411 are opposite (step S412).
When it is determined that the direction of the normal vector is opposite (step S412: YES), the intersection determination unit 143 determines that the two sides intersect (step S421).

  Next, the intersection determination unit 143 determines whether or not the processing of the loop L42 has been performed for all combinations that select one edge from each of the two triangles selected in step S401, and branches based on the determination result. (Step S441). If it is determined that there is a combination that has not yet been processed in the loop L42, the process returns to step S402, and the processing in the loop L42 is continued for the unprocessed combination. On the other hand, when it is determined that the processing of the loop L42 has been performed for all the combinations, the loop L42 is terminated.

  When the loop L42 ends, the intersection determination unit 143 determines whether or not the processing of the loop L41 has been performed for all combinations that select the triangles obtained by the division of the division unit 120 one by one for the two surfaces. Then, branching is performed based on the determination result (step S442). If it is determined that there is a combination that has not yet been processed in the loop L41, the process returns to step S401, and the processing in the loop L41 is continued for the unprocessed combination. On the other hand, when it is determined that the processing of the loop L41 has been performed for all the combinations, the loop L41 is terminated.

When the loop L41 ends, the intersection determination unit 143 determines whether or not the triangle side included in one surface intersects the triangle side included in the other surface for the combination of the two surfaces to be determined. Determination is made (step S443). If any one of the combinations of sides in the processing of the loop L42 is determined to intersect (step S421), the sides of the triangle included in one surface and the triangle included in the other surface It is determined that there is an intersecting side.
On the other hand, if it is determined that all the combinations of sides in the processing of the loop L42 do not intersect (step S431), it is determined that none of the sides intersect.
After step S443, the process of FIG. 16 ends.

On the other hand, when it is determined in step S404 that the directions of the normal vectors are the same (step S404: NO), the intersection determination unit 143 determines that the two sides do not intersect (step S431).
Thereafter, the process proceeds to step S441.
On the other hand, if it is determined in step S412 that the directions of the normal vectors are the same (step S412: NO), the process proceeds to step S431.

Note that in step S401, the intersection determination unit 143 may exclude the combination of the surfaces that the inclusion determination unit 141 has determined to have an inclusion relationship from the processing target.
In the processing of FIG. 13, step S104 and step S105 may be executed in parallel, or step S104 may be executed after step S105 is executed. When step S104 is executed after step S105 is executed, the inclusion determination unit 141 excludes the combination of faces that have been determined by the intersection determination unit 143 as having side intersections in step S301 of FIG. 15 from being processed. It may be.

Returning to the processing of FIG. 13, after step S105, the contact surface detection unit 140 extracts a combination of two surfaces in contact with each other (step S106). Specifically, the contact surface detection unit 140 is a combination that is detected by the surface selection unit 130 and corresponds to any of the combinations of two surfaces included in the same plane and having an inclusion relationship or a side intersection. Are extracted as combinations in contact with each other.
On the other hand, the contact surface detection unit 140 determines that the combinations that have no inclusion relationship and no side intersection are not in contact with each other.

Next, the result output unit 150 outputs the combination extracted by the contact surface detection unit 140 in step S106 as the determination result of the contact surface detection system 10 (step S107). For example, as described with reference to FIG. 12, the result output unit 150 displays the presence / absence of contact between surfaces.
Thereafter, the process of FIG. 13 is terminated.

As described above, the inclusion determination unit 141 converts at least one vertex of the first polygon forming the first surface of the first polyhedron into the second polygon forming the second surface of the second polyhedron. It is determined whether or not it is included. And the contact surface detection part 140 detects the surface which contact | connects the surface which forms a 2nd polyhedron among the surfaces which form a 1st polyhedron according to the determination result of the inclusion determination part 141. FIG.
Thereby, the contact surface detection part 140 can detect the contact relationship which does not produce the intersection of a side based on an inclusion relationship. In this respect, the contact surface detection system 10 can more appropriately determine the contact relationship between the surfaces.

Further, the area comparison unit 142 determines whether or not the point is included in the convex polygon, a line segment connecting the point and each of two adjacent vertices among the vertices of the convex polygon, Comparison of the area of the triangle formed by the sides connecting the two adjacent vertices with respect to the total of all the combinations of the two adjacent vertices among the vertices of the convex polygon and the area of the convex polygon To do.
Thereby, the area comparison part 142 can determine whether a point is included in a convex polygon by calculating the area of a triangle. The area of the triangle can be calculated by a simple calculation, for example, by calculating from an outer product of vectors. Therefore, the area comparison unit 142 can determine whether or not the point is included in the convex polygon by a simple calculation.

Further, the dividing unit 120 divides the second polygon into triangles by line segments connecting one vertex of the second polygon and each vertex other than the vertex adjacent to the vertex. Then, the inclusion determination unit 141 applies at least one vertex among the vertices of the first polygon and at least one triangle among the triangles obtained by the division of the division unit 120 to the area comparison unit 142, It is determined whether or not at least one vertex among the vertices of one polygon is included in the second polygon.
Thereby, the area comparison part 142 should just calculate the area of a triangle also about the calculation of the area of a convex polygon. Therefore, the area comparison unit 142 can determine whether or not the point is included in the convex polygon by a simple calculation.

In addition, the intersection determination unit 143 determines whether or not the sides of the first polygon and the sides of the second polygon intersect. Then, the contact surface detection unit 140 detects a surface that contacts the surface that forms the second polyhedron among the surfaces that form the first polyhedron, according to the determination result of the inclusion determination unit 141 and the determination result of the intersection determination unit 143. To do.
Thereby, the contact surface detection unit 140 has a contact relationship that does not cause the intersection of the sides and a contact relationship that does not cause an inclusion relationship between the polygon that forms the surface and the vertex of the polygon that forms the other surface. Any of these can be detected, and the contact relationship between the surfaces can be detected without omission.

<Second Embodiment>
FIG. 17 is a schematic block diagram illustrating a functional configuration of the state change calculation system according to the second embodiment of the present invention. In the figure, the state change calculation system 20 includes a contact surface detection system 11, a state change calculation unit 210, and a result output unit 250. The contact surface detection system 11 includes a coordinate data acquisition unit 110, a division unit 120, a surface selection unit 130, and a contact surface detection unit 140. The contact surface detection unit 140 includes an inclusion determination unit 141 and an intersection determination unit 143. The inclusion determination unit 141 includes an area comparison unit 142.
In the figure, parts having the same functions corresponding to the respective parts in FIG. 1 are denoted by the same reference numerals (110, 120, 130, 140, 141, 142, 143), and description thereof is omitted.

The state change calculation unit 210 is based on the contact state between the surfaces detected by the contact surface detection unit 140, and at least a part of the structure modeled by the polyhedron from which the coordinate data acquisition unit 110 acquires data. , The change with time of the members constituting the structure is calculated.
As a method for the state change calculation unit 210 to calculate the state change of the members constituting the structure over time, for example, an area defined corresponding to the member described in JP2013-037321A is representative. It is possible to use a technique in which a point is provided and the influence acting between members is defined by a variable indicating the degree of influence.
The result output unit 250 displays the calculation result of the state change calculation unit 210.

As described above, the state change calculation unit 210 calculates the state change over time of the members constituting the structure based on the contact state of the surface of the structure detected by the contact surface detection system 11. Further, as in the case of the contact surface detection system 10, in the contact surface detection system 11, the inclusion determination unit 141 determines the inclusion relationship between polygons forming the surface of the structure. And the contact surface detection part 140 detects the contact condition of the surface which forms a structure according to the determination result of the inclusion determination part 141. FIG.
Thereby, the contact surface detection unit 140 can detect the contact relationship that does not cause the intersection between the sides based on the inclusion relationship, and the state change calculation unit 210 does not cause the intersection between the sides. It is possible to calculate the change in the situation of the member over time more accurately in accordance with the contact relationship.

<Third Embodiment>
FIG. 18 is a schematic block diagram illustrating a functional configuration of an inclusion determination system according to the third embodiment of the present invention. In the figure, the inclusion determination system 30 includes a coordinate data acquisition unit 310, an inclusion determination unit 141, and a result output unit 350. The inclusion determination unit 141 includes an area comparison unit 142.
In the figure, portions having the same functions corresponding to the respective portions in FIG. 1 are denoted by the same reference numerals (141, 142), and description thereof is omitted.

The coordinate data acquisition unit 310 acquires the coordinate data of the vertices of the convex polygon and the coordinate data of the point to be determined whether to be included in the convex polygon.
The result output unit 350 displays the determination result of whether or not the point is included in the convex polygon by the inclusion determination unit 141.

In the inclusion determination system 30, the inclusion determination unit 141 is a triangle composed of a point, a line segment connecting each of two adjacent vertices among polygon vertices, and a side connecting the two adjacent vertices. The total of all the combinations of two adjacent vertices of the polygon vertices and the area of the polygon are equal to each other, and there are many points to be determined according to the determination result. It is determined whether or not it is enclosed in a square.
Thereby, as in the case of the contact surface detection system 10, the inclusion determination unit 141 (area comparison unit 142) determines whether or not the point is included in the convex polygon by calculating the area of the triangle. It can be carried out. The area of the triangle can be calculated by a simple calculation, for example, by calculating from an outer product of vectors. Therefore, the inclusion determination unit 141 can determine whether or not a point is included in a convex polygon by a simple calculation.

Note that a program for realizing all or part of the functions of the contact surface detection system 10, the state change calculation system 20, and the inclusion determination system 30 is recorded on a computer-readable recording medium, and recorded on the recording medium. Each unit may be processed by causing the computer system to read and execute the program. Here, the “computer system” includes an OS and hardware such as peripheral devices.
Further, the “computer system” includes a homepage providing environment (or display environment) if a WWW system is used.
The “computer-readable recording medium” refers to a portable medium such as a flexible disk, a magneto-optical disk, and a compact disk, and a storage device such as a hard disk built in the computer system. Furthermore, the “computer-readable recording medium” dynamically holds a program for a short time like a communication line when transmitting a program via a network such as the Internet or a communication line such as a telephone line. In this case, a volatile memory in a computer system serving as a server or a client in that case, and a program that holds a program for a certain period of time are also included. The program may be a program for realizing a part of the functions described above, and may be a program capable of realizing the functions described above in combination with a program already recorded in a computer system.

  The embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and includes design changes and the like within a scope not departing from the gist of the present invention.

DESCRIPTION OF SYMBOLS 10 Contact surface detection system 20 State change calculation system 30 Inclusion determination system 110,310 Coordinate data acquisition part 120 Dividing part 130 Surface selection part 140 Contact surface detection part 141 Inclusion determination part 142 Area comparison part 143 Intersection determination part 150,250,350 Result output unit 210 State change calculation unit

Claims (8)

A coordinate data acquisition unit for acquiring the coordinate data of the vertices of the first polyhedron and the coordinate data of the vertices of the second polyhedron;
Selecting a first surface from the surfaces forming the first polyhedron and selecting a second surface from the surfaces forming the second polyhedron;
An inclusion determination unit that determines whether at least one vertex of the first polygon forming the first surface is included in the second polygon forming the second surface;
In accordance with the determination result of the inclusion determination unit, a contact surface detection unit that detects a surface that contacts the surface that forms the second polyhedron among the surfaces that form the first polyhedron,
A contact surface detection system comprising: The inclusion determination unit
Whether or not a point is included in a convex polygon is determined by connecting a line segment connecting the point and each of two adjacent vertices of the convex polygon and the two adjacent vertices. The area of the triangle formed by the sides is provided with an area comparison unit that compares the total of all the combinations of two adjacent vertices among the vertices of the convex polygon and the area of the convex polygon. And
Applying at least one vertex among the vertices of the first polygon and the second polygon or a convex polygon obtained by dividing the second polygon to the area comparison unit, the first polygon 2. The contact surface detection system according to claim 1, wherein it is determined whether at least one of the vertices is included in the second polygon. A division unit that divides the second polygon into triangles by line segments connecting one vertex of the second polygon and each vertex other than the vertex adjacent to the vertex;
The inclusion determination unit applies at least one vertex among the vertices of the first polygon and at least one triangle among triangles obtained by the division of the division unit to the area comparison unit, and The contact surface detection system according to claim 2, wherein it is determined whether at least one vertex of one polygon is included in the second polygon. An intersection determination unit that determines whether or not the side of the first polygon intersects the side of the second polygon;
The contact surface detection unit detects a surface in contact with a surface forming the second polyhedron among surfaces forming the first polyhedron according to a determination result of the inclusion determination unit and a determination result of the intersection determination unit. The contact surface detection system according to any one of claims 1 to 3, wherein For the first polyhedron corresponding to the shape of the first structure and the second polyhedron corresponding to the shape of the second structure, a surface in contact with the surface forming the second polyhedron among the surfaces forming the first polyhedron. The contact surface detection system according to any one of claims 1 to 4 to detect,
Based on the contact state detected by the contact surface detection system, a state change calculation for calculating a state change over time of a member constituting the structure of at least a part of the first structure or the second structure. And
A state change calculation system comprising: A coordinate data acquisition unit that acquires coordinate data of a point and coordinate data of a vertex of a polygon;
The vertex of the polygon having a triangular area composed of a line segment connecting the point and each of two adjacent vertices of the polygon and an edge connecting the two adjacent vertices Whether the total of all combinations of two adjacent vertices is equal to the area of the polygon, and whether the certain point is included in the polygon according to the determination result An inclusion determination unit for determining whether or not,
An inclusion determination system comprising: A contact surface detection method for a contact surface detection system, comprising:
A coordinate data acquisition step of acquiring coordinate data of the vertices of the first polyhedron and coordinate data of the vertices of the second polyhedron;
A surface selection step of selecting a first surface from the surfaces forming the first polyhedron and selecting a second surface from the surfaces forming the second polyhedron;
An inclusion determination step for determining whether at least one vertex of the first polygon forming the first surface is included in the second polygon forming the second surface;
According to the determination result in the inclusion determination step, a contact surface detection step of detecting a surface in contact with a surface forming the second polyhedron among surfaces forming the first polyhedron;
A contact surface detection method comprising: In the computer equipped with the contact surface detection system,
A coordinate data acquisition step of acquiring coordinate data of the vertices of the first polyhedron and coordinate data of the vertices of the second polyhedron;
A surface selection step of selecting a first surface from the surfaces forming the first polyhedron and selecting a second surface from the surfaces forming the second polyhedron;
An inclusion determination step for determining whether at least one vertex of the first polygon forming the first surface is included in the second polygon forming the second surface;
According to the determination result in the inclusion determination step, a contact surface detection step of detecting a surface in contact with a surface forming the second polyhedron among surfaces forming the first polyhedron;
A program for running

Images