JPH1063873A - Octal tree generating method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate the octal tree representation of a body in a nonprojection shape fast from polygon representation by generating a polygonally-sectioned voxel with some plane of a three-dimensional body and generating the octal tree by using a voxel decided to have a representative point inside. SOLUTION: A straight line Mr crosses the outline (r) or an (n)-gon at Mr1 -Mr3 on one side and at Mr4 -Mr6 on the other side each even-number of times, so it is judged that the point (r) is in an (n)-gon P. A straight line Ms passing a point (s) in a plane Q, on the other hand, crosses the outline of the (n)-gon P at Ms1 and Ms2 on one side of the point (s) and at Ms3 and Ms4 on the other hand each odd-number of times T, so it is judged that the point (s) is outside the (n)-gon. A voxel having the point (r) inside is called a black voxel and a voxel having it outside is called a white voxel. Then an octal tree is generated by using voxes having representative points inside. Consequently, this method is applicable even to a nonprojection body and the octal tree can be generated fast from polygon representation.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to an octree generating method, and more particularly to an octree generating method for generating an octree from a polyhedral representation of a three-dimensional object.

[0002]

2. Description of the Related Art Although shape data of a three-dimensional object is used in various fields, in recent years, it has been demanded that interactive and efficient processing be performed particularly in a wide variety of applications. However, since one shape representation method usually has only a limited function, it has been necessary to carefully select a shape representation method that can make maximum use of the function according to the application. For example, a polyhedral representation of an object is often used to generate a realistic image at high speed using computer graphics.

[0003] In addition, the shape expression using a super quadratic function or another parametric method can easily express the deformation of an object, and the interference between objects can be reduced at a high speed by utilizing the inside / outside judgment by the function. Can be found in
Octagon is also one of the three-dimensional representation methods widely used in many fields such as computer vision, graphics, and robotics.

FIG. 9 is a view for explaining the representation of the shape of an object by an octree. An object based on an octree is represented by a tree obtained by sequentially dividing the entire space into eight nodes. Each node is labeled a white node and a black node. The white node completely represents the space outside the object, and the black node completely represents the space inside the object. Nodes that represent a space that spans both inside and outside the object that is not are gray nodes and are divided into eight child nodes until they reach a predetermined minimum size. For example, as shown in FIG. 9 (a), the root node is divided into child nodes labeled as 0, 1, 2,. Each child node is similarly subdivided. An octree representation of the object shown in FIG. 9 (b) is shown in FIG. 9 (c).

[0005]

The octree can efficiently access a specific subspace by making use of the characteristic as a hierarchical representation of a three-dimensional space. There is a problem that it is difficult to directly generate or deform the deformed object shape.

The simplest method of generating an octree from a polyhedral representation of an object is to divide the space by a plane containing each face of the polyhedron and determine whether each octree node is inside them. However, there is a drawback that the shape of the object is limited to a convex object.

Therefore, a main object of the present invention is to provide an octree generating method which can be applied to non-convex objects and can generate an octree at high speed from a polyhedral representation.

[0008]

The invention according to claim 1 is
An octree generating method for generating an octree from a polyhedral representation of a three-dimensional object, comprising: a first step of generating a cross-sectional polygon on a plane of the three-dimensional object; The method includes a second step of determining a voxel, and a third step of generating an octree using the voxel determined to have a representative point inside.

According to the second aspect of the present invention, the second aspect of the first aspect is provided.
The step of passing through the representative point and intersects with the outline of the polygonal cross section, the representative point is inside when the number of intersections with the outline on one side and the other side of the representative point is odd, and It is determined that the point is outside.

In the invention according to claim 3, the first to third steps are processed using a parallel computer.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a diagram for explaining a voxel interior point determination according to an embodiment of the present invention, and FIG. 2 is a diagram for explaining a polygon interior point determination.

In FIG. 1, it is assumed that an object 1 is given as a polyhedral representation composed of a face list. In the world coordinate system, the space where the object is placed is M ³ , M = 2
Divide into ^{l + h} voxels. Here, l is the depth of the octree to be created, and h is a natural number. It is determined whether or not each of these voxels exists inside the object, and an octree is created based on this. In order to simplify the problem, the center of each voxel is set as a representative point, and the inside / outside determination of the voxel with respect to the object is determined based on the inside / outside determination of the point with respect to the object.

As shown in FIG. 1, a given polyhedron is cut along a plane Q passing through a representative point r, and the inside and outside of the section polygon P appearing there and the point r are determined. The cross section when the object 1 in FIG. 1 is cut along the plane Q is a polygon P in cross section shown in FIG. In a two-dimensional plane, a simple polygon is divided into two disjoint regions inside and outside the plane. Using this, for a simple n-gon P and a point r given in a plane, it can be determined by O (n) whether the point r is inside the n-gon P. As shown in FIG. 2, considering a straight line m passing through a point r, if the straight line m does not intersect the contour of the n-sided polygon P, the point r is outside the n-sided polygon P. If the straight line m intersects the n-sided polygon P, the number of times the straight line m intersects the contour of the n-sided polygon P on one side of the point r is counted. If it is an even number, it can be determined that it is outside. That is, in the example shown in FIG. 2, the straight line m _r intersects with Mr ₁ ~Mr ₃ on one side of the contour point r of the n-gon P, intersect with Mr ₄ ~Mr ₆ on the other side, respectively Since the number of intersections T is an odd number, it can be determined that the point r is inside the n-sided polygon P.

On the other hand, a straight line Ms passing through the point s in the plane Q is n
Since the outline of the polygon P intersects Ms ₁ and Ms ₂ on one side of the point s and Ms ₃ and Ms ₄ on the other side, and the number of intersections T is even, the point s is an n-gon. It can be determined that it is outside P. The voxel inside this point r is a black voxel, and the outside voxel is a white voxel.

As described above, the center of each voxel is used as a representative point, and the inside / outside of the voxel with respect to the object is determined by determining the inside / outside of the point with respect to the object. According to this, as shown in FIG. , Even if some of the nodes are inside the object, they become white voxels 3. However, depending on the application, it may be preferable that the leaf node partially occupied inside the object is the black voxel 2. For example, when considering a collision between objects represented by an octree, the object shape may be required to approximate the safe side. Therefore, in the present invention, first, as shown in FIG.
Then, by tracing the octree and trimming the branches, an octree having a depth 1 as shown in FIG. 5 is created. Therefore, the found black node is read in the form of an octree having a depth of l + h with the entire space as a root. If all eight child nodes are black voxels 2 as shown in FIG.
These child nodes are removed as shown in FIG. As for the nodes having a depth of l + 1 or less, if at least one of the child nodes is a black voxel 2 as shown in FIG. Exclude nodes. As a result, the basic algorithm can be realized as an independent and relatively simple repetition of calculation, so that an effect of speeding up by parallel processing can be expected.

FIG. 8 is a diagram for explaining the concept of parallel processing according to the present invention. In general, in a parallel computer, there are two methods, a method using a shared memory and a message passing method, depending on the difference in communication means between processors.
In the former case, it is said that communication between the processors is performed by reading and writing data in a shared memory that can be equally accessed from all the processors via a path, so that it takes time. On the other hand, in the latter case, each processor has a local memory (distributed memory) and transmits and receives necessary data via a communication path. In the present invention, parallel processing is performed using a parallel computer having such a distributed memory. In that case, two parallelization methods are conceivable.

The first method is to execute the inside / outside determination of a plurality of voxels in the same section by a plurality of processors in parallel. Before executing the parallel algorithm, the voxels in the section are evenly distributed to all processors as preprocessing. That is, the section Q shown in FIG.
_Assuming that N processors are used for the inside / outside determination in _k , the i-th processor is i, i + N, i + 2N,.
The next voxel will be received and processed. After being distributed, each processor performs the above-described procedure on the received voxels and determines whether the voxels are inside or outside the polygon _Pk . When outside judgment of all voxels on the section Q _k completed, the polygonal section P _{k + 1} by the following section Q _{k + 1} is generated and processed similarly.

A second method of parallelization is to allocate one processor to each section, and to execute the inside / outside determination of voxels in a plurality of sections in parallel by the same number of processors. In this case, using M processors,
Assuming that the slices are examined simultaneously, the j-th processor processes the voxels in the j, j + M, j + 2M,...

It is of course conceivable to use these two methods in combination. In this case, N processors are used to determine the inside and outside of voxels in the same plane, and M
Assuming that M processors are to be examined simultaneously by using a plurality of processors, a total of M × N processors are always used. And the voxels in the cross section Q _{k + p} are pN + 1, p
N + 2,..., (P + 1) Nth processor (0 <p <
M).

[0020]

As described above, according to the present invention, a voxel having a polygonal cross section is generated on a plane where a three-dimensional object exists, and it is determined whether or not there is a representative point inside the voxel. Since octrees are generated using voxels determined to have representative points, it is possible to quickly create an octree representation of a non-convex object from a polyhedral representation using a parallel computer. it can.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining determination of voxel interior points according to an embodiment of the present invention;

FIG. 2 is a diagram for explaining determination of an interior point of a polygon;

FIG. 3 is a diagram for explaining an approximation method of an octree at a depth 1;

FIG. 4 is a diagram showing an octree having a depth of l + h.

FIG. 5 is a diagram showing a state where a branch is pruned by tracing an octree having a depth of l + h.

FIG. 6 is a diagram illustrating a state where child nodes are excluded when all child nodes are black voxels.

FIG. 7 is a diagram illustrating a state where a parent is a black voxel and a child node is excluded when at least one of the child nodes is a black voxel.

FIG. 8 is a diagram for explaining the concept of parallel processing in the present invention.

FIG. 9 is a diagram for explaining the shape representation of an object by an octree.

[Explanation of symbols]

 Reference Signs List 1 object 2 black voxel 3 white voxel Q plane P section polygon m straight line

Claims (3)

[Claims] 1. An octree generating method for generating an octree from a polyhedral representation of a three-dimensional object, the method comprising generating a cross-section polygon on a plane of the three-dimensional object.
A second step of determining a voxel of a representative point inside the polygonal cross section; and a third step of generating an octree using the voxel determined to have a representative point inside. An octree generation method, including: 2. The method according to claim 1, wherein the second step intersects with the contour of the polygonal cross section through the representative point, and the number of times of intersection with the contour on one side and the other side of the representative point is an odd number. 2. The octree generating method according to claim 1, wherein the representative point is inside, and when the number is even, it is determined that the representative point is outside. 3. The method according to claim 1, further comprising the step of:
~ An octree generating method, characterized by processing the third step.