JPH0731742B2 - Vector set attribute determination device - Google Patents

Description

DETAILED DESCRIPTION [Outline] Whether or not a plurality of vectors existing in a three-dimensional space, that is, a vector set, exists on only one of the planes passing through a common starting point of the vector set is arbitrarily determined. By combining two vectors and judging from the sign of the determinant having these three vectors as column vectors, the attributes of the vector set can be judged accurately with relatively simple logic.

[Industrial application field]

The present invention relates to an apparatus for determining whether or not a vector set existing in a three-dimensional space exists only on one side of a plane that passes through at their common starting point, and particularly, it is possible to create an arbitrary two vectors in the vector set. The present invention relates to a vector set attribute determination device that determines the positional relationship between a plane to be generated and all other vectors by the determinant code.

In recent years, along with the progress of various technologies, there is a demand for establishment of technology for causing an information processing apparatus to recognize the shape of an object.

For example, the introduction of industrial robots has become popular in the industrial world. The performance of robots has improved remarkably due to the development of semiconductor technology and robot control technology. But,
In order for a robot to perform high-level work, it must have the ability to recognize a robot object and select what it needs.

By the way, in order for a robot to recognize a given object,
The computer system that controls the robot must store a model that matches the shape of the object seen by the robot. In order to create a model stored in this computer system, it is necessary to easily determine that the normal vector of each surface forming the model exists only on one side of a plane.

[Conventional technology]

Conventionally, among the attributes of the vector set existing in the three-dimensional space, as a method for determining whether or not all the vectors pass through a common starting point and only exist on one side of the plane, each vector is a normal vector, By considering the plane corresponding to this normal vector, defining the visible plane when looking at the polyhedron formed by this plane, and checking by the simplex method whether all the vectors have a common visible region , Is being determined.

That is, for example, assuming a convex polyhedron, using the equations of each surface forming the convex polyhedron, create an inequality regarding the combination of visible surfaces, and whether the combination of visible surfaces is possible depending on whether there is an inequality or a solution. Determine whether This determination method will be described using a truncated pyramid, for example.

FIG. 3 is a diagram showing an example of a pentahedron.

The faces F ₁ , F ₂ , F ₃ , F ₄ and F ₅ of the pentahedron are respectively represented by the following equations as is known.

F ₁ : a ₁ x + b ₁ y + c ₁ z + d ₁ = 0 F ₂ : a ₂ x + b ₂ y + c ₂ z + d ₂ = 0 F ₃ : a ₃ x + b ₃ y + c ₃ z + d ₃ = 0 F ₄ : a ₄ x + b ₄ y + c ₄ z + d ₄ = 0 F ₅ : a ₅ x + b ₅ y + c ₅ z + d ₅ = 0 Therefore, if the equation of each surface Fi is aix + biy + ciz + di = 0 (1 ≦ i ≦ 5), for example, only the surfaces F ₁ , F ₂ and F ₃ are visible. The condition that is a surface is Is.

To find out whether the faces F ₁ , F ₂ , F ₃ form a combination of visible faces, one has to look at whether the equation has a solution. Therefore, to check whether or not each surface of the pentahedron shown in FIG. 3 constitutes a combination of visible surfaces, 2n = 32 (however, n
= 5) It is necessary to check whether the simultaneous inequalities have the solution.

[Problems to be solved by the invention]

As described above, conventionally, when investigating the states that form a combination of visible surfaces of an n-sided polyhedron, it is necessary to check whether there are 2n simultaneous inequality solutions, and the amount of calculation becomes enormous. There is a problem that the memory of the arithmetic unit is expanded by the introduction of variables and the numerical accuracy and the processing speed are deteriorated due to repeated transformation of the determinant.

In view of such a problem, the present invention ensures that when all the vectors of a vector set pass through a common starting point and only exist on one side of a plane, a plane created by any two vectors in this vector set is always generated. In particular, paying attention to the geometrical property that all the vectors may exist on only one side of the plane created by the two vectors, the outer product is obtained from the two vectors, and this and other The attribute of the vector set is determined by obtaining the inner product of the two vectors and the sign thereof.

[Means for solving problems]

FIG. 1 is a block diagram of a circuit showing an embodiment of the present invention.

1 is an input unit for inputting a target vector set, 2
Selects three vectors from among the m vectors entered in the input unit 1 and combines them, and for all combinations of vectors, calculates the determinant of a matrix having these three vectors as column vectors The element matrix calculation unit 3 is a memory for storing the determinant calculated by the element matrix calculation unit 2.

4 shows the positional relationship of all other vectors with respect to the plane formed by two arbitrary vectors,
The attribute determining unit 5 that determines by the sign of the determinant is an output unit that outputs the result determined by the attribute determining unit 4.

Here, a method of determining the attribute of the vector by the sign of the determinant will be described.

As mentioned above, based on the geometrical property that all the remaining vectors exist on one side of the plane created by one of the two vectors in the vector set, first three of the m vectors are selected. Of the vector (i, j, k), and a determinant det (i, j, k) of a matrix having the vector as a column vector is obtained for all combinations of vectors.

Next, for any i, j, det (i, j, k) where (1 ≤ k ≤
The code of m, k ≠ i, j) is examined by using the value of the determinant previously obtained and the property of the determinant. At this time, if any one of the different codes appears, the search for i, j is stopped, and the code is checked for other combinations.

If all i, j have the same sign, all the remaining vectors exist on one side of the plane formed by i, j.

For example, as shown in FIG. 2, five vectors ₁ , ₂ ,
_{There are three} , _four, and _five , and whether or not these five vectors exist on the same side of the plane P, two vectors out of the five vectors determine the outer product, and another vector and the inner product are determined. It is determined by obtaining the sign. Therefore, the code is examined by converting it into a determinant that is easy to calculate.

That is, It suffices if any of the expressions (2-1) to (2-10) has the same sign. By the way, if the formulas (2-1) to (2-10) are rewritten in the determinant form, the formula becomes as shown below.

Therefore, it is only necessary to calculate the determinants of the equations (3-1) to (3-10) and check the sign. In general, when m vectors are considered, all the vectors are present if i, j such that det (ijk) (1≤k≤m, k ≠ i, j) has the same sign as described above. Exists on one side of the plane P.

Determinant equation det (i, j,
When the attribute determination unit 4 determines the code of k), and when all the same codes are present, it is determined that the input vector set exists only on one side of a plane, and when i and j that have the same code do not exist. , The input vector set is determined to exist uniformly in the space.

[Action]

With the above configuration, a vector determinant that is easy to calculate is calculated, and when there is a combination of two vectors such that all determinants have the same sign, this vector set forms the two vectors. It can be determined that it exists only on one side of the plane.

〔Example〕

In FIG. 1, the target vector set is the input unit 1
to go into. The element matrix calculation unit 2 selects three vectors from among the m vectors input to the input unit 1 and combines them, and for all combinations, the determinant of the matrix having these three vectors as column vectors Calculate and write to memory 3.

In the attribute determination unit 4, from the combination of the vectors given from the element matrix calculation unit 2 and the determinant obtained from the memory 3, for the plane made up of two arbitrary vectors, what are all the other vectors? It is determined by the sign of the determinant whether or not there is a positional relationship.

That is, when two vectors are (i, j), all determinants det (i, j, k) where k ≠ i, j have the same sign, the input vector set is only on one side of a plane. If such a vector (i,
When j) does not exist, it is determined that the input vector exists uniformly in space.

The output unit 5 sends this determination result.

〔The invention's effect〕

As described above, according to the present invention, it is possible to determine whether or not all the vectors pass through a common start point on only one side of a plane by using only the determinant code. The attributes of the vector set can be accurately determined.

[Brief description of drawings]

 FIG. 1 is a block diagram of a circuit showing an embodiment of the present invention, FIG. 2 is a diagram for explaining the relationship between planes and vectors, and FIG. 3 is a diagram showing an example of a pentahedron. In the figure, 1 is an input unit, 2 is an element matrix calculation unit, 3 is a memory, 4 is an attribute determination unit, and 5 is an output unit.

Claims (1)

[Claims] 1. Element matrix calculation means (2) for selecting and combining three vectors from a plurality of vectors and calculating a determinant of each of these three vectors as a column vector for all combinations. ) And the sign of the determinant calculated by the element matrix calculation means (2), the attribute determination means (4) for determining the positional relationship of all other vectors with respect to the plane created by two arbitrary vectors. ) And when the two vectors are (i, j) and k ≠ i, j, if all determinants det (i, j, k) have the same sign, then A vector set attribute determination device characterized by determining that a plurality of vectors exist only on one side of a certain plane.