JP2002328959A - Cube development creating method, device, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a cube development creating method, device, and a computer program which enables automatic creation using a computer. SOLUTION: This system is provided with the first process, which extracts coordinates 1, 2, and 3 which compose a cube; the second process which extracts side A and C, which consist of greater or equal to three apexes and are associated with the apexes; the third process which extracts an edge line E3, which is on the boundary of adjoining two sides A and C and forms an edge and is associated with each side, the fourth process which develops the side by transforming the coordinates 1, 2, and 3, which composes the side A to be developed, to two dimensional coordinates 1', 2', and 3'; and the fifth process which decides a side C', which is adjoins the developed side and is to be developed next, according to the edge line E3' which composes an edge of side A' developed by the forth process. The forth and fifth processes are repeated in this order until all the developable sides are developed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for creating a two-dimensional development from a three-dimensional solid, and a computer program.

[0002]

2. Description of the Related Art Conventionally, it has been widely practiced to print an original three-dimensional model from a three-dimensional solid by printing a two-dimensional developed view on paper or the like, cutting out the developed view as appropriate, and assembling it. Have been done. For example, in the construction industry, there are companies that specialize in creating models that show the expected completion of buildings, and each construction company requests these companies to create models every time a house or the like is designed.

[0003]

In the conventional model making, however, the work of creating a two-dimensional development from the original solid is manually performed, and there are problems in efficiency, delivery time and cost. Was. In particular, when the three-dimensional shape is complicated, it is very difficult to create a development view, and there has been a problem that a model cannot be created unless some skilled person is used.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned problems, and has as its object to provide a method and apparatus for creating a three-dimensional development view which can be automatically created by using a computer, and a computer program.

[0005]

In order to achieve the above object, according to the first aspect of the present invention, there is provided a method for creating a development view of a solid, comprising: a first step of extracting coordinates of vertices constituting a target solid; A second step of extracting a face composed of three or more vertices and associated with the vertices, forming an edge of each face at a boundary between two adjacent faces, 2
A third step of extracting a ridge line associated with one of the faces, and a fourth step of developing the face by converting the coordinates of vertices constituting the face to be developed among the faces into two-dimensional coordinates And a fifth step of determining, based on a ridge line forming an edge of the surface developed in the fourth step, a surface adjacent to the developed surface and to be developed next, The fourth and fifth steps are repeated in this order until all possible planes are developed. In this way, when the vertex coordinates of a predetermined surface are converted into two-dimensional coordinates and expanded, the adjacent surface is determined as the next surface to be expanded based on the information of the ridge line belonging to the surface.
By repeating these processes until a developable surface is developed, a developed view can be automatically created on a computer.

According to a second aspect of the present invention, there is provided a method for creating a three-dimensional development view, comprising a sixth step of extracting an undeployable face, and the fourth and the fourth steps only for the face extracted in the sixth step. Step 5 is repeated in this order. In this way, another unfolded view can be created for a surface that cannot be unfolded. By combining the solids created by these unfolded views, the entire solid can be assembled from the unfolded views.

According to a third aspect of the present invention, there is provided a method for creating a three-dimensional developed view, wherein a surface which cannot be developed, a ridge line which forms an edge of the surface when a surface to be developed next is converted into two dimensions, and a surface which has already been developed. A seventh step of determining whether or not a ridge forming the edge of the surface intersects. In this way, it is easy and accurate to determine whether or not deployment is possible.

According to a third aspect of the present invention, in the method of developing a three-dimensional developed view, when a surface temporarily determined to be developed and two or more surfaces adjacent to the surface are on the same plane, the temporary It is characterized in that the determined surface is not a surface on which the expansion in the fourth or fifth step is performed. In this way, a developed view is easy to assemble based on experience.

According to a fifth aspect of the present invention, in the method of creating a three-dimensional developed view, a surface having the largest angle with the developed surface among the surfaces adjacent to the developed surface in the fourth step is defined as: The ninth step is characterized in that a ninth step of determining the surface to be developed in the fifth step is performed. In this case, it is empirically difficult to generate an undeployable surface.

According to a sixth aspect of the present invention, in the method of creating a three-dimensional developed view, of the surfaces adjacent to the developed surface in the fourth step, the length of a ridge line serving as a boundary with the developed surface is the shortest. There is provided a tenth step of determining a surface to be enlarged as a surface to be developed in the fifth step. By doing so, the length of the portion (ridge line or the like) at which the developed view is cut can be reduced, so that a developed view that is easy to cut (create) can be obtained. Further, since the size of the mount itself containing the developed view is reduced, a developed view in which the mount can be used effectively can be obtained.

According to a seventh aspect of the present invention, there is provided a method for creating a three-dimensional developed view, wherein a ridge line specified in advance before development is replaced with a ridge line at a boundary between surfaces separated when developed in the fourth step, or an open line. It is characterized by a ridge line at the boundary between the surfaces that are not separated when they are separated.

According to the eighth aspect of the present invention, in the method of generating a three-dimensional developed view, an eighth step of displaying predetermined correspondence information at an edge position corresponding to a plane separated from the adjacent planes when the plane is expanded among the adjacent planes. It is characterized by having. By doing so, when assembling the three-dimensional object, the operator can understand that the correspondence information only needs to connect the end lines of the same surface, thereby facilitating the work.

According to a ninth aspect of the present invention, there is provided a method for creating a three-dimensional developed view, comprising a ninth step of forming a marginal area at any one of the edge positions of the pair of surfaces on which the correspondence information is displayed. And In this case, a "paste" for connecting the separated surfaces is automatically provided on the developed view, so that the assembling work is facilitated.

[0014] The three-dimensional developed view creation device of the present invention comprises: coordinate extraction means for extracting the vertex coordinates; face extraction means for extracting the face; ridge line extraction means for extracting the ridge line; Based on expansion means for expanding the surface by converting the coordinates of vertices constituting the surface to be expanded into two-dimensional coordinates, and a ridge line forming an edge of the expanded surface,
Determining means for determining a surface to be developed next, which is adjacent to the developed surface.

[0015] The computer program of the present invention comprises a first step of extracting the coordinates of the vertices, a second step of extracting the face, a third step of extracting the ridge line, Based on a fourth process of developing the surface by converting the coordinates of the vertices constituting the surface to be developed into two-dimensional coordinates, and a ridge forming an edge of the surface developed in the fourth process, And causing the computer to execute a fifth step of determining the next surface to be developed next to the developed surface, until the fourth expandable surface is developed.
It is characterized in that the computer executes the fifth step repeatedly in this order.

[0016]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing an embodiment of the configuration of a three-dimensional developed view creation apparatus (computer) 100 according to the present invention, and includes a CPU (Central).
A control unit (coordinate extracting means, surface extracting means, ridge line extracting means, expanding means, determining means) 104 comprising a processing unit (central processing unit) and the like; three-dimensional (3D) data 106
a, a display unit (display) 102 for displaying various screens.

FIGS. 2 to 4 visually show the process of creating a developed view from the original solid by the solid view developed apparatus according to the present invention. In the following, a case where the solid is a tetrahedron will be described as an example, but the present invention is applicable to any polyhedron.

In FIG. 2, first, the control unit 104 acquires three-dimensional data of a solid (tetrahedron) for which a development view is to be created (FIG. 2 (1)). Next, the control unit determines, based on the acquired data, vertices (identification number 1
To (4) are extracted (FIG. 2 (2)). Further, the control unit extracts information of a plane which is composed of three or more vertices and is associated with the identification number of each vertex (A to D are respectively assigned as identification numbers) (FIG. 2 (3)). For example, the face A constituted by the vertices 1, 2, and 3 is associated with the identification number of each vertex like the face A (1, 2, 3). The same applies to the other surfaces B to D.

Subsequently, the control unit extracts edge information (Edge) (FIG. 2 (4)). Here, the ridge line is an adjacent 2
It forms the edge of each surface at the boundary of the two surfaces and is associated with these two surfaces. For example, the ridge lines forming the edges of the surface A are E1 to E3, and the ridge line E1 is located at the boundary between the adjacent surfaces A and B. Therefore, the ridge line E1 is divided into the respective surfaces A and B like E1 (A, B).
Associated with the identification number. The same applies to other E2 to E6. Note that specifying the ridge line in this way is equivalent to C
It is known as “Half Edge structure” in the field of G (computer graphics).

Next, the control unit determines the plane to be developed first by a predetermined method (may be random), and converts the coordinates of the vertices constituting the plane into two-dimensional coordinates (xy coordinates) ( FIG. 3 (5)). For example, if the plane A is the plane to be developed first, the coordinates of the vertices 1, 2, and 3 are converted into two-dimensional coordinates (vertices 1 'to 3'). Thereby, the surface A is x as A '
-Expanded on the y-plane. Here, the control unit associates a flag for identifying the completion of the development with the surface A ′ as appropriate.

Further, the control unit obtains the ridge lines E'1 to E'3 forming the edge of the surface A ', and determines the next surface to be developed next based on these (FIG. 3 (6)). . Here, the ridge lines E′1 to E′3 are obtained by performing coordinate conversion on the xy plane in accordance with the coordinate conversion of the vertices 1, 2, and 3. Since the information on each of the ridgelines E′1 to E′3 specifies the faces B to D adjacent to the face A ′ as described above (for example, the ridgeline E′1 is the boundary between the faces A and B). The ridge E'2 is located at the boundary between the planes A and D, and the ridge E'3 is located at the boundary between the planes A and C). Determined by the method. In addition,
The plane (A ′) to which the above flag is attached is excluded from the candidates for the plane to be developed next.

Next, the control unit moves the surface C as shown in FIG.
The coordinates of the vertices are converted into two-dimensional coordinates (xy coordinates) in the same manner as in FIG. 3 (7). Here, since the vertices 2 and 3 have already been coordinate-converted, the vertex 4 is subjected to coordinate conversion (vertex 4 ′). Then, the control unit generates a ridge line E′4 that forms an edge of the surface C ′ obtained by converting the surface C into xy coordinates (two-dimensional),
It is determined whether E′6 (E′3 is omitted because it is common) and the ridge lines E′1 and E′2 forming the edges of the already developed plane A ′ intersect. Is that the surface C is C '
Is actually developed on the xy plane, and the above-mentioned flag is appropriately associated. In the figure, since each ridge line is a line segment (having a start point and an end point), it does not cross even if it is not parallel. On the other hand, if they intersect, the plane C cannot be developed, and other planes B and D are determined to be the planes to be developed next instead. Note that the coordinates of the vertex 4 ′ are the coordinates of the vertices 2 and 3 ′ that have already been coordinate-converted, and the ridge lines E′3, E′4,
It can be determined geometrically from the length of E'6 (the length of the ridge after the coordinate transformation is the same as the length of the original ridge).

Hereinafter, the control means develops the remaining surfaces B and D. That is, in the same manner as in FIG. 3 (6), a plane to be developed next (for example, plane B) is determined based on the ridge line information forming the edge of the already developed plane A ′ (or C ′). .
Then, the coordinates of the vertices constituting the surface B are converted into two-dimensional coordinates, and the surface B is developed (FIG. 4 (8)). Here, when the surface B is developed as a surface adjacent to the surface A ′ as shown in the figure, since the vertices 1 and 3 have already been coordinate-transformed, the vertex 4
(Vertex 4 ″). When the surface B is developed as a surface adjacent to the surface C ′, since the vertices 3 and 4 have already been subjected to the coordinate conversion, the vertex 1 is subjected to the coordinate conversion. Become.

The same applies to the development of the plane D. The plane D to be developed next is determined based on the ridge line information forming the edge of the already developed plane A '(or B', C '). , Surface D
Are converted into two-dimensional coordinates and the plane D is developed (FIG. 4 (9)). In this way, a developed view is created, and a three-dimensional model is assembled based on the developed view.

If the surface to be developed cannot be developed, the surface to be developed next is determined from other surfaces as described above. In this case, the development proceeds as follows. I do. That is, as shown in FIG.
When the plane F adjacent to the plane F is to be developed, the plane F intersects with the ridge line of the developed plane (cross hatched area in the figure), so that it is determined that the plane F cannot be developed. Therefore, another surface G adjacent to the surface E is developed. In this way, the development proceeds in the left direction in the figure, and the surface F becomes adjacent to the surface developed in the left direction. For example, there is a possibility that the surface F can be developed. Then, in the present invention, the surface to be developed is determined randomly or according to a predetermined rule and developed, so that if the development is repeated, it is highly likely that all the surfaces will be developed in due course. Become. Whether or not an undeveloped surface remains can be easily determined by the flag.

It should be noted that the method of judging a non-developable surface according to the present invention can be performed, for example, even if the vertices of the surface F in FIG. Therefore, the method is superior to the method of determining whether or not development is possible based on whether the vertex coordinates of the surface F are included in the developed surface.

On the other hand, even if trials of deployment are repeated, a surface that cannot be deployed may remain. FIG. 6 is a diagram schematically showing such a case. In particular, an undeployable surface often remains in a complicated intricate development surface. In such a case, all the data of the undeployable surface is removed from the data of the developed surface, and a first development view is created only for the developed surface. On the other hand, the data of the removed surface (consisting of the three-dimensional data of the three-dimensional object before expansion) is subjected to expansion processing in the same manner as in FIGS. If a plurality of undeployable surfaces are adjacent to each other, they are regarded as one group, and the unfolding process is performed. In FIG. 6, since there are two non-deployable surfaces (groups) and they are not adjacent to each other, the decompression process is performed separately for each group, and a development view is created for each. After individually assembling the three-dimensional models based on the plurality of development views, the models are connected to complete the entire three-dimensional model.

When assembling a three-dimensional model from the above-described development view, assembling work is facilitated if the correspondence of which end lines of the separated surfaces are connected to each other is displayed. In addition, if a "paste" is provided for connecting the end lines of the separated surfaces, the assembling work is further facilitated. For this reason, in the present invention, the processing shown in FIG. 7 can also be performed.

This figure shows a development of the tetrahedron, and is composed of planes A to D. The plane BD, the plane BC, and the plane CD are separated. Also, each ridgeline E
Among E1 to E6, E1 to E3 are boundaries between two adjacent surfaces, while E4 to E6 are located on separated surfaces (for example, there are two E4). Therefore,
The control unit determines, for each ridge line, whether or not the ridge line is located at the boundary between two adjacent surfaces based on the position information of the surface and the ridge line, and determines whether the ridge line is not located at the boundary between the two adjacent surfaces (E4 To E6). And these ridgelines E4
The predetermined symbols (corresponding information) assigned to .about.E6 are displayed at the edge positions of the surface to which each ridge line belongs. For example, since the ridgeline E5 forms the upper edge of the surfaces B and D, a symbol (E5) is displayed on the edge. By doing so, when assembling the three-dimensional model, the worker can understand that it is only necessary to join the end lines of the surfaces B and D so that the same symbols E5 match each other, thereby facilitating the work. It should be noted that the correspondence information may be anything such as a numeral or a character.

Further, the control means includes a marginal area 20, 21, 2 on one of the edges displaying the same symbol.
2 can be performed. The margin region may be formed, for example, such that the margin length is equal to the length of the edge of the target surface with a predetermined margin width w. Alternatively, the side end of the marginal area may have a predetermined angle (45 ° in the figure) so as to become narrower toward the open end. These processes are automatically executed according to a predetermined program.

In the present invention, as shown in FIG. 8, the plane to be developed first can be determined.
FIG. 8 shows a plane to be developed first when a development view of a hexagonal prism is created.

In this figure, it is assumed that each surface is composed of a triangle composed of three vertices, and that development starts from a hexagonal portion. The hexagonal portion includes four surfaces G to J formed of triangles, and the developed view may be different depending on which surface is selected as the first developed surface. FIG. 9 shows the developed view, and in the case of FIG. 9 (1), each face G to J of the hexagonal portion is not separated, and is most preferable because no seam is formed in this portion. On the other hand, in the case of FIG. 9 (2), the plane GH is cut off,
At the time of assembly, a seam is formed at this portion (on the same plane), which is not preferable. The conditions under which a development view as shown in FIG. 9B is created are known from empirical rules.

In other words, returning to FIG. 8, if the initial development surface is a plane where at least two of the surfaces adjacent to the surface are on the same plane, a preferable development diagram as shown in FIG. It is more likely to be obtained. For example, since the plane G forms an angle of 90 ° with the adjacent planes K and L and is on the same plane (180 °) only as the plane I, it is a candidate for the first development plane.
On the other hand, since the plane H is on the same plane as the two adjacent planes G and I, it is excluded from the first developed plane. Note that an angle between a certain surface and an adjacent surface is obtained from information on each surface.

Further, in the present invention, a surface to be developed next can be determined as shown in FIG. According to this determination method, experience has shown that an undeployable surface is unlikely to occur.

In this figure, it is assumed that the plane K has been developed. Surfaces L, M, and N are candidates for the surface to be developed next. Here, angles formed by the surfaces L, M, and N and the developed surface K are 180 °, −90 °, and 90 °, respectively. Note that the angle between the valley-folded surfaces is represented by "-". In such a case, when the plane L having the largest angle with the developed plane K is selected as the next developed plane, a plane that cannot be expanded hardly occurs.

Further, when a solid (long triangular pyramid) as shown in FIG. 11 is developed, it is preferable to determine a plane to be developed next by the following method. According to this determination method,
From experience, it has been found that the developed view can be cut out of the backing sheet without waste, and that the cutout operation is facilitated. In particular, it is effective when developing an elongated solid body. This long triangular pyramid is composed of planes PS.

FIG. 12 shows a developed view of the long triangular pyramid of FIG. 11. In the case of FIG. 12 (1), since the entire developed view is small, it can be cut out from the mount without waste. In addition, since the cutout length is minimized, the cutout operation is facilitated. On the other hand, in the case of FIG. 12 (2), the size of the whole developed view becomes large, a larger backing sheet is required, and the cutout length becomes long.

FIG. 13 shows a method for obtaining the developed view shown in FIG. 12 (1). If the plane P is developed, planes Q, R and S are candidates for the next development. Becomes
Here, focusing on the length of the ridge line located between each of the surfaces Q, R, and S and the developed surface P, the length of the ridge line between the surfaces Q (R) is longer. In such a case, if the plane Q (R) having the longest ridge line is set as the next development plane, a preferable development view shown in FIG. 12A is easily obtained.

The present invention is not limited to the above embodiments. For example, a ridge line for separating two adjacent faces or a ridge line not to be separated can be designated in advance. In the former case, the surface adjacent to the specified edge is excluded from the candidates for the next expandable surface. In the latter case, the surface adjacent to the specified edge is preferentially selected as the next expandable surface candidate. This is selected, and the subsequent development process of the development diagram proceeds.

Note that the three-dimensional developed view creating apparatus of the present invention
The present invention can be realized by a computer and a software program executed by the computer, and the software program executed in the device can be distributed via a computer-readable storage medium or a communication line.

[0041]

As described above, according to the present invention,
When the vertex coordinates of a predetermined surface are converted into two-dimensional coordinates and expanded, the adjacent surface is determined as the next surface to be expanded based on the information of the ridge line belonging to the surface, so that these processes can be expanded. By repeating this process until a particular surface is developed, a development view can be created automatically on the computer.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a three-dimensional developed view creation device of the present invention.

FIG. 2 is a schematic diagram visually illustrating a process of creating a development view from an original solid.

FIG. 3 is a diagram following FIG. 2;

FIG. 4 is a view following FIG. 3;

FIG. 5 is a diagram illustrating a positional relationship between a surface to be developed and a developed surface.

FIG. 6 is a diagram schematically showing a state where an undeployable surface remains.

FIG. 7 is a diagram showing a mode in which correspondence information and a margin are added to a development view.

FIG. 8 is a diagram illustrating a method of determining an initial development plane.

FIG. 9 is a developed view of the solid shown in FIG. 8;

FIG. 10 is a diagram showing a method for determining a plane to be developed next.

FIG. 11 is a diagram showing a solid to be developed.

FIG. 12 is a developed view of the solid shown in FIG. 11;

13 is a diagram illustrating a method of determining a plane to be developed next in the solid illustrated in FIG. 11;

[Explanation of symbols]

1-4 Coordinates of vertices 1'-4 'Coordinates of vertices after coordinate transformation A-S plane A'-S' Surface after development E1-E6 Edge line 20-22

Continued on the front page F term (reference) 5B046 AA03 BA10 CA04 DA08 FA16 GA01

Claims (11)

[Claims] 1. A first step of extracting coordinates of vertices forming a target solid, and a second step of extracting a face composed of three or more vertices and associated with the vertices. A third step of forming an edge of each surface at a boundary between two adjacent surfaces and extracting a ridge line associated with the two adjacent surfaces; The coordinates of the vertices that make up the surface are 2
A fourth step of developing the surface by converting it into dimensional coordinates; and, based on a ridge forming an edge of the surface developed in the fourth step, adjoining the developed surface and then developing And a fifth step of determining a surface on which the expansion is performed. The fourth and fifth steps are repeated in this order until all expandable surfaces are expanded. Diagram creation method. 2. A method according to claim 1, further comprising a sixth step of extracting an undeployable surface, wherein the fourth and fifth steps are repeatedly performed in this order only on the surface extracted in the sixth step. The method for creating a developed view of a solid according to claim 1. 3. A surface that cannot be expanded and a surface that is to be expanded next are 2
And a seventh step of determining whether the ridge forming the edge of the surface intersects with the ridge forming the edge of the already developed surface when converted to the dimension. The method for creating a developed view of a solid according to claim 1. 4. When a surface temporarily determined to be unfolded and two or more surfaces adjacent to the surface are on the same plane, the temporarily determined surface is moved to the fourth or fifth step. 4. The method according to claim 1, wherein the surface is not developed. 5. The surface adjacent to the surface developed in the fourth process and having the largest angle with the developed surface is determined as the surface to be developed in the fifth process. The method for creating a developed view of a solid according to any one of claims 1 to 4, wherein: 6. A development method according to claim 5, wherein, of the surfaces adjacent to the surface developed in the fourth step, a surface having the largest ridge length as a boundary with the developed surface is developed in the fifth step. The method according to any one of claims 1 to 5, wherein the surface is determined as a surface on which to perform (3). 7. A ridge line specified in advance before development is set to a ridge line at a boundary between surfaces separated when developed in the fourth step, or a boundary between surfaces not separated at development. 7. The method according to claim 1, wherein a certain ridge line is set. 8. The method according to claim 1, further comprising the step of displaying predetermined correspondence information at corresponding edge positions of the surfaces separated from each other when the surface is unfolded among the adjacent surfaces. The method for creating a developed view of a solid according to any one of the above. 9. The developed view of the solid according to claim 8, further comprising a ninth step of forming a marginal area at any one edge position of the pair of surfaces on which the correspondence information is displayed. How to make. 10. A coordinate extracting means for extracting coordinates of vertices constituting a target solid, a face extracting means constituted by three or more vertices and extracting a face associated with the vertices, Ridge line extracting means for forming an edge of each surface at a boundary between two surfaces and extracting a ridge line associated with the two adjacent surfaces; and forming a surface to be developed among the surfaces Vertex coordinates 2
Expansion means for expanding the surface by converting it to dimensional coordinates; and determining, based on a ridge line forming an edge of the expanded surface, a surface adjacent to the expanded surface and to be developed next. And a means for creating a three-dimensional developed view. 11. A first step of extracting coordinates of vertices forming a target solid, and a second step of extracting a face composed of three or more vertices and associated with the vertices. A third step of forming an edge of each surface at a boundary between two adjacent surfaces and extracting a ridge line associated with the two adjacent surfaces; The coordinates of the vertices that make up the surface are 2
A fourth step of developing the surface by converting it into dimensional coordinates; and, based on a ridge forming an edge of the surface developed in the fourth step, adjoining the developed surface and then developing And a fifth step of determining a surface on which to perform the operation. A computer program for causing a computer to execute the fourth and fifth steps in this order until all expandable surfaces are expanded. A computer program to be executed by a computer.