JPH1074215A - Inter-object distance computing unit and inter-object distance computing program storage medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate the distance between two convex objects at a high speed by providing a first closest approach vector computing means for obtaining a closest approach vector and a second closest approach vector computing means for correcting the closest approach vector. SOLUTION: A closest approach vector obtained in the first closest approach vector computing means 15 is the closest approach vector when both objects are regarded to be convex polyhedrons and is the closest approach vector of insufficient precision for a convex curved surface object. The closest approach vector obtained in such a manner is inputted to the second closest approach vector computing means 16 along with the shape information (including curved surface batch information) of the two convex objects to be the object. In the second closest approach vector computing means 16, based on the principle that a plane in contact with a convex curved surface object and the closest approach vector for connecting the closest approach points of the two convex objects with each other are orthogonal at the closest approach point of the convex curved surface object, the obtained closest approach vector is corrected to the new closest approach vector of high precision further.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] The present invention relates to an object (CG (computer graphics)) constructed on a computer.
The present invention relates to an inter-object distance calculation device for calculating a closest-contact distance of a model, and an inter-object distance calculation program storage medium storing such an inter-object distance calculation program for calculating such a closest-contact distance.

[0002]

2. Description of the Related Art For example, a CAD system for designing a mechanism, planning by a robot, offline teaching,
Furthermore, in the field of virtual reality systems such as games, animations, walk-throughs, etc. using high-speed graphics WS (workstation) / PC (personal computer), the latest contact points between CG models constructed on computers. Calculate the distance and calculate them C
It is desired to determine whether the G models are separated from each other or interfere with each other, or to know a margin to interference when the G models are separated.

[0003] The interference check methods conventionally performed to meet this demand are classified as follows. (A) Method using coating with a sphere. An object is covered with a set of spheres, and the interference state between the objects is determined by repeating the interference check between the spheres. U.S. Pat. No. 4,578,757 (Stark), U.S. Pat. No. 4,922,430 (Wavish), U.S. Pat. No. 5,056,231.
Publication (Nakano et al.), JP-A-6-8
The methods disclosed in JP-A-3422, JP-A-2-224004, JP-A-6-259506, JP-A-7-100733, etc. correspond to this.

(B) A space is divided into a set of fine lattices, and a space map is created in which codes are assigned to a region occupied by an obstacle and other regions. By searching where the target object on the other side is located on the spatial map,
Determine the interference state. This includes the octree method. U.S. Pat. No. 5,150,452 (Poll
ack), U.S. Pat. No. 5,347,459 (Gr.
eenspan et al. The method proposed in (1) corresponds to this. In particular, U.S. Pat. No. 5,347,459 also uses the sphere coating method (a) described above in order to facilitate search.

(C) A map of the interfering region and the other region is stored in a “configuration space (Configurat) well known in the field of robotics.
ion space) ", and a system in which interference determination is performed in this space. The system disclosed in U.S. Pat. No. 5,047,916 (Kondo) corresponds to this system.
In the method disclosed in this publication, the configuration space is divided into a lattice shape, and a map for interference determination is created.

(D) "EG Gilbert,
D. W. Johnson, andS. S. Kee
rthi, IEEE Journal of Rob
otics and Automation, Vo
l. 4, No. 2, pp. 193-203, 198
No. 8 "proposes a method in which the object is limited to a convex polyhedron, and a distance between nearest points of contact between the convex polyhedrons is obtained.

This method connects the nearest points of two convex polyhedrons to each other, and a vector (nearest neighbor vector) in a direction from one convex polyhedron (self) of the two convex polyhedrons to the other convex polyhedron (partner). ) And the inner product of each of the position vectors of the vertices that constitute oneself, the inner product of one of the vertices closest to the closest point to the opponent is the inner product of the vertex far from the closest point to one's own. Based on the principle that the convex polyhedron has a larger value, a nearest vector connecting the nearest points of these two convex polyhedrons is obtained.

[0008]

The objects of the above methods (a) to (c) are not limited to convex polyhedrons, and are not limited to convex objects, and may be objects having any shape. In this respect, the application range is wider than the method (d), but the methods (a) to (c) have the following disadvantages as compared with the method (d).

That is, in the method using the sphere covering of the above (a), extra processing is required compared with the above method (d) when a convex polyhedron is required, which requires preprocessing of covering an object with a sphere. There is a problem that the required distance is not calculated, and it is not possible to measure how much margin is left before the interference. The above (b)
In the method of (1), it takes time to perform preprocessing for creating a map in which the workspace is divided into lattices. In addition, when the environment moves, it is necessary to re-create the map, and it is not possible to respond in real time to environmental changes. Since the space is divided into lattices, there is a problem that information with an accuracy higher than a unit lattice cannot be calculated.

Further, in the method (c), it takes time to create a configuration space. Also,
As in (b) above, if the environment moves, it is necessary to recreate the map, and it is not possible to respond to environmental changes in real time. No. 5,047, mentioned above.
In the case of a method of dividing the configuration space into a lattice as proposed in Japanese Patent No. 916,
Information with a precision higher than the unit lattice cannot be calculated.

Compared with these methods (a) to (c), the method (d) can calculate the distance between moving objects without any special preprocessing at a very high speed. However, the object is limited to a convex polyhedron. Therefore, when checking the interference state between objects having free-form surfaces, which is widely used in design design, etc., processing is performed by approximating an object having a free-form surface with a set of a large number of polyhedral patches bonded together. Need to be done. However, in this method, the number of polyhedral patches becomes extremely large, the speed of graphically displaying the object is reduced, and the distance calculation or interference check is performed by reducing the number of polyhedral patches representing the object to increase the display speed. There are drawbacks such as an increase in error if performed.

In view of the above circumstances, the present invention expands the object to any convex object that may have a convex curved surface, thereby greatly improving the application range, and further increasing the distance between two convex objects at high speed. An inter-object distance calculation device capable of calculating, and an inter-object distance calculation program storage medium storing such an inter-object distance calculation program having an improved application range and capable of calculating a distance at high speed The purpose is to provide.

[0013]

A first inter-object distance calculating device of the inter-object distance calculating device according to the present invention for achieving the above object is intended for a three-dimensional object, and one of them is a convex polyhedron. , And the other or both are composed of a convex curved surface object composed of a set of convex curved surface patches.
An inter-object distance calculating apparatus that calculates a distance between closest points of contact of two three-dimensional convex objects based on shape information including arrangement position information of the two convex objects. The closest vector connecting the contact points, the closest vector in the direction from one of the two convex objects to the other convex object, and the one of the convex objects forming the one convex object A position vector of a vertex when the object is a convex polyhedron, or a position vector of a control point for forming a convex surface patch constituting the convex surface object when one of the convex objects is a convex surface object Of the inner products, the inner product of the one convex object at the vertex or control point near the closest point to the other convex object is the inner product at the vertex or control point away from the closest point of the one convex object. First nearest vector computing means for finding the nearest vector having a value larger than the product (1-2) The nearest vector obtained by the first nearest vector computing means is calculated by using the nearest point of the convex surface object A second closest vector calculating means for correcting a new closest vector orthogonal to a plane tangent to the convex curved object is provided.

[0014] A first inter-object distance calculating apparatus according to the present invention comprises:
In the first nearest-neighbor vector calculating means of (1-1),
By using the principle described in (1-1), for example, the method described in the above-mentioned document (d), a nearest vector when both target two convex objects are regarded as a polyhedron is obtained. However, in addition to the above, the second nearest neighbor vector calculating means of (1-2) calculates the first nearest neighbor vector calculating means of (1-1) based on the principle described in (1-2). The target object does not need to be a convex polyhedron, and is extended to any convex object having a convex surface, since the newest vector is obtained by correcting the nearest vector obtained. Greatly spread.
In addition, the calculations based on the principles described in (1-1) and (1-2) can be performed at a much higher speed than those of the above-described prior arts (1) to (3), and furthermore, there is interference. It is possible to determine not only the presence or absence but also the distance between the closest points between two convex objects.

It is to be noted that there are three or more large convex objects, and it is necessary to determine which two convex objects are likely to interfere with each other, that is, to determine the nearest vector between any two convex objects. When it is not clear whether there is any, instead of finding the nearest vector for all combinations of these many convex objects, each convex object is covered with an envelope sphere, and a plurality of adjacent spheres among those envelope spheres are further Two sets of hierarchical metatrees are constructed by covering with one envelope sphere,
Depth-first search between meta trees
Search) to select a pair of convex objects that are most likely to be approaching (Japanese Patent Application No. 7-174627).
No.) is preferably used.

Here, in the first inter-object distance calculating apparatus according to the present invention, (1-3) based on the new nearest vector obtained by the second nearest vector calculating means, It is preferable to include an interference determination unit that determines whether two convex objects are interfering with each other.

This is because it is often necessary to finally determine whether or not interference occurs. Furthermore, the first inter-object distance calculating apparatus according to the present invention includes the above (1-1), (1-
(1-4) In addition to the means of (2), (1-4) a convex surface constituting the convex curved object including a set of vertices of the convex polygon when one of the two convex objects is a convex polyhedron Shape information storage means for storing shape information comprising a set of control points for forming a curved surface patch (1-5) Vertex or control point of the convex object based on the information indicating movement or deformation of the convex object Shape information updating means for obtaining new shape information by calculating coordinates after movement or deformation of the object (1-6) generating a convex surface patch constituting the convex surface object based on the shape information of the convex surface object It may be provided with a curved surface patch information generating means.

The apparatus for calculating the distance between objects according to the present invention is capable of performing a higher-speed operation than the conventional apparatus. It is suitable for applications in which a convex object is moved or deformed and the distance between the convex objects moving or deformed in such a manner is quickly obtained. In this case, in the first nearest-neighbor vector calculating means of the above (1-1), as disclosed in Japanese Patent Application Laid-Open No. 7-134735, the target convex object is moved to the position before the immediately preceding movement or to the immediately preceding movement. The inner product may be obtained only for each vertex or each control point in the region near the closest point in the state before the deformation. In this way, the first closest vector calculating means can calculate the closest vector for the moved or deformed convex object at a higher speed.

Alternatively, when the moving amount or the deformation amount of the convex object between the adjacent frames is equal to or less than a predetermined amount, the nearest neighbor vector after the movement or the deformation is determined by the first nearest neighbor vector as described below. The calculation of the closest vector by the calculation means may be omitted. In the first inter-object distance calculating apparatus of the present invention, the mode configured as described above is as follows.
The second closest vector calculation means of (1-2), wherein when the convex object is moved or deformed, the first closest vector calculation means obtains the closest vector after movement or deformation. Instead of this, the second closest vector calculating means corrects the new closest vector obtained before the current movement or deformation to a new closest vector.

In a continuous movement or a continuous deformation, when the change from the immediately preceding position or the immediately preceding deformation state is slight, instead of re-calculating the approximate nearest vector newly by the first nearest vector calculating means, Before the current movement or deformation, that is, when the convex object is in the position before the immediately preceding movement or in the last deformed state, the nearest nearest vector obtained by the second nearest vector calculation means is roughly approximated to the nearest vector. By using the vector as a vector and correcting the nearest vector immediately before used as the approximate nearest vector, the nearest vector for the convex object after the current movement or deformation can be obtained. By doing so, higher-speed arithmetic processing can be performed as compared with the case where the closest vector is newly calculated with the first closest vector every time the object is moved or deformed.

Further, in the first inter-object distance calculating apparatus according to the present invention, there is provided: (1-7) the shape information stored in the shape information storage means of (1-4) and the shape information of (1-5). It is preferable to include a display unit that displays the convex object drawn based on the new shape information obtained by the information updating unit.

By providing such display means,
The moving state or the deformed state of the convex object can be grasped intuitively. The second inter-object distance calculating device of the inter-object distance calculating device of the present invention that achieves the above object is intended for a two-dimensional convex object. Since the operation of the second inter-object distance calculating device of the present invention described below is the same as the operation of the first inter-object distance calculating device described above, the description of the operation will be omitted.

The second inter-object distance calculating apparatus according to the present invention is characterized in that one of the two polygons is constituted by a convex curved object composed of a set of convex curved patches, one of which is allowed to be a convex polygon. In the inter-object distance calculating device for calculating the distance between the closest points of the two-dimensional convex object based on the shape information including the arrangement position information of the two convex objects, (2-1) the closest points of the two convex objects are And the closest vector in the direction from one of the two convex objects to the other convex object, and one of the convex objects constituting the one convex object, The position vector of a vertex in the case of a convex polygon, or the inner product with the position vector of a control point for forming a convex curve surface patch constituting the convex curve object when one of the convex objects is a convex curve object Out of Of the one convex object,
A first vector for finding a nearest vector whose inner product at a vertex or control point close to the closest point to the other convex object has a larger value than inner product at a vertex or control point away from the closest point of the one convex object. Nearest-neighbor vector calculating means (2-2) calculating the nearest-neighbor vector obtained by the first nearest-neighbor vector calculating means as a new nearest vector orthogonal to a straight line tangent to the convex-curve object at the nearest point of the convex-curve object And a second closest vector calculation means for correcting

Here, in the second inter-object distance calculating apparatus according to the present invention, it is preferable that (2-3) based on the new closest vector obtained by the second closest vector calculating means, It is preferable to include an interference determination unit that determines whether or not the convex objects interfere with each other.

Further, the second inter-object distance calculating apparatus according to the present invention further includes (2-4) one of the two convex objects in addition to the means (2-1) and (2-2). Is a convex polygon, a shape information storage means for storing shape information comprising a set of control points for forming a convex curve patch constituting a convex curve object, including a set of vertices of the convex polygon. 2-5) Shape information updating means for calculating new shape information by calculating coordinates after movement or deformation of vertices or control points of the convex object based on information instructing movement or deformation of the convex object. -6) It may be provided with a curve patch information generating means for generating a convex curve patch constituting the convex curve object based on the shape information of the convex curve object.

In this case, the second closest vector computing means of the above (2-2), when the convex object is moved or deformed, the first nearest vector computing means moves or deforms the convex object after the movement or deformation. Instead of obtaining the closest vector, it is preferable that the second closest vector calculating means corrects the new closest vector obtained before the current movement or deformation to a new closest vector.

Further, the second inter-object distance calculating apparatus according to the present invention further comprises: (2-7) adding the new shape information obtained by the shape information updating means to the shape information stored in the shape information storing means. It is preferable to include a display unit that displays the convex object drawn based on the image.

The first object-to-object distance calculating program storage medium of the present invention for achieving the above object has one of which is allowed to be a convex polyhedron and the other or both of which are convex curved surfaces. Distance calculation for calculating the distance between the closest points of two three-dimensional convex objects composed of a set of patches having a convex surface based on shape information including arrangement position information of the two convex objects (3-1) a closest vector connecting the closest points of the two convex objects, the closest vector in a direction from one convex object to the other convex object of the two convex objects; A tangent vector and a position vector of a vertex when one of the convex objects is a convex polyhedron, or a convex surface when one of the convex objects is a convex curved object Of the inner products with the position vectors of the control points for forming the convex surface patch constituting the object, the inner product of the one convex object, the vertex or the control point near the closest point to the closest point to the other convex object is the inner product. A first closest vector calculating means for obtaining a closest vector having a value larger than an inner product of a vertex or a control point of one of the convex objects away from the closest point thereof (3-2) the first closest vector calculating means A second closest vector calculating means for correcting the closest vector obtained in the above to a new closest vector orthogonal to a plane tangent to the convex surface object at the closest point of the convex surface object. It is characterized by being stored.

In the storage medium for the first inter-object distance calculation program according to the present invention, the inter-object distance calculation program stored in the storage medium is the same as that of the first inter-object distance calculation apparatus described above.
In the first nearest-neighbor vector calculating means of 1), (3-
By using the principle described in 1), for example, the method described in the above-mentioned document (d), a nearest vector when both target convex objects are regarded as a polyhedron is obtained. In addition, in the second nearest neighbor vector calculating means of (3-2), based on the principle described in (3-2), the second nearest neighbor vector calculating means of (3-1) Since the tangent vector is corrected to obtain a new nearest vector, the target object does not need to be a convex polyhedron, but is extended to any convex object having a convex curved surface, and the applicable range is greatly increased. spread. In addition, the calculations based on the principles described in (3-1) and (3-2) can be performed at a much higher speed than the above-described prior arts (1) to (3), and furthermore, there is interference. It is possible to determine not only the presence or absence but also the distance between the closest points between two convex objects.

It is to be noted that there are three or more convex objects, and it is necessary to determine which two convex objects are likely to interfere with each other, that is, to determine the nearest vector between any two convex objects. When it is not clear whether there is any, instead of finding the nearest vector for all combinations of these many convex objects, each convex object is covered with an envelope sphere, and a plurality of adjacent spheres among those envelope spheres are further Two sets of hierarchical metatrees are constructed by covering with one envelope sphere,
Depth-first search between meta trees
Search) to select a pair of convex objects that are most likely to be approaching (Japanese Patent Application No. 7-174627).
No.) is preferably used.

Here, in the first medium-to-object distance calculation program storage medium of the present invention, the object-to-object distance calculation program stored therein is obtained by: (3-3) the second closest vector calculation means. It is preferable that the apparatus further includes an interference determination unit that determines whether or not the two convex objects are interfering with each other based on the obtained newest closest vector.

This is because it is often necessary to finally determine whether or not interference occurs. Further, in the storage medium for the first inter-object distance calculation program according to the present invention, the inter-object distance calculation program stored therein is stored in the storage medium.
(3-4) In addition to the means of (1) and (3-2), (3-4) the convex shape including a set of vertices of the convex polygon when one of the two convex objects is a convex polyhedron Based on information indicating the movement or deformation of the convex object, the shape information including the set of control points for forming the convex surface patch forming the curved object is obtained after the movement or deformation of the vertex or control point of the convex object. (3-5) Surface patch information generation for generating a convex surface patch constituting the convex surface object based on the shape information of the convex surface object based on the shape information of the convex surface object It may have a means.

The inter-object distance calculation program stored in the storage medium of the inter-object distance calculation program according to the present invention is capable of performing a higher-speed calculation than the conventional one. 4) to (3-5)
It is suitable for applications in which a convex object is moved or deformed and the distance between the convex objects moving or deformed in such a manner is quickly obtained.

In this case, in the first nearest-neighbor vector calculating means (3-1), as disclosed in Japanese Patent Application Laid-Open No. Hei 7-134735, the target convex object is moved to the position before the previous movement. Alternatively, the inner product may be obtained only for each vertex or each control point in the region near the closest point in the state before the last deformation. In this way, the first closest vector calculating means can calculate the closest vector for the moved or deformed convex object at a higher speed.

Alternatively, when the moving amount or the deformation amount of the convex object between the adjacent frames is equal to or less than a predetermined amount, the nearest neighbor vector after the movement or the deformation is determined by the first nearest neighbor vector as described below. The calculation of the closest vector by the calculation means may be omitted. In the first inter-object distance calculation program stored in the first inter-object distance calculation program storage medium according to the present invention,
(3-2) The second closest vector calculating means in (3-2), wherein when the convex object is moved or deformed, the first closest vector calculating means obtains the closest vector after movement or deformation. Instead of this, the second closest vector calculating means corrects the new closest vector obtained before the current movement or deformation to a new closest vector.

In a continuous movement or a continuous deformation, if the change from the immediately preceding position or the immediately preceding deformation state is slight, instead of re-calculating the approximate nearest vector newly by the first nearest vector calculating means, Before the current movement or deformation, that is, when the convex object is in the position before the immediately preceding movement or in the last deformed state, the nearest nearest vector obtained by the second nearest vector calculation means is roughly approximated to the nearest vector. By using the vector as a vector and correcting the nearest vector immediately before used as the approximate nearest vector, the nearest vector for the convex object after the current movement or deformation can be obtained. By doing so, higher-speed arithmetic processing can be performed as compared with the case where the closest vector is newly calculated with the first closest vector every time the object is moved or deformed.

Next, a description will be given of a second inter-object distance calculation program storage medium of the inter-object distance calculation program storage medium of the present invention which achieves the above object. A second medium for calculating a distance between objects according to the present invention stores a program for calculating a distance between objects targeting a two-dimensional convex object. The operation of the present invention described below with respect to the configuration of the second inter-object distance calculation program storage medium stored in the second inter-object distance calculation program storage medium is similar to that of the first inter-object distance calculation program storage medium described above. Since the operation is the same as that of the distance calculation program, the description of the operation is omitted.

The storage medium for the second program for calculating the distance between objects according to the present invention is constituted by a convex-curve object composed of a set of patches of one of which is allowed to be a convex polygon and the other or both are convex. An inter-object distance calculation program for calculating a distance between closest contacts of two two-dimensional convex objects based on shape information including arrangement position information of the two convex objects, wherein: (4-1) the two convex objects The closest vector connecting the closest points of the two convex objects, the closest vector in the direction from one convex object to the other convex object of the two convex objects, and one of the convex objects constituting one of the convex objects A position vector of a vertex when the convex object is a convex polygon, or a position of a control point for forming a convex curve surface patch constituting the convex curve object when one of the convex objects is a convex curve object Vect Out of the inner product with
A first vector for finding a nearest vector whose inner product at a vertex or control point close to the closest point to the other convex object has a larger value than inner product at a vertex or control point away from the closest point of the one convex object. Nearest vector calculation means (4-2) A newest closest vector orthogonal to a straight line tangent to the convex curve object at the closest point of the convex curve object at the closest point of the convex curve object calculated by the first closest vector calculation means. Wherein a program for calculating the distance between objects having second closest vector calculating means for correction is stored.

Here, in the storage medium for the second inter-object distance calculation program of the present invention, the inter-object distance calculation program stored therein is obtained by (4-3) the second closest vector calculation means. It is preferable that the apparatus further includes an interference determination unit that determines whether or not two convex objects are interfering with each other based on the obtained newest closest vector.

Further, in the second medium for calculating the distance between objects according to the present invention, the program for calculating the distance between objects stored therein is added to the means of (4-1) and (4-2). (4-4) control points for forming a convex curve patch constituting a convex curve object, including a set of vertices of the convex polygon when one of the two convex objects is a convex polygon Is updated to new shape information by calculating coordinates after movement or deformation of vertices or control points of the convex object based on information indicating movement or deformation of the convex object based on information indicating movement or deformation of the convex object Updating means (4-5) It may have a curve patch information generating means for generating convex curve patches constituting the convex curve object based on the shape information of the convex curve object.

In this case, the second closest vector calculating means of the above (4-2), when the convex object is moved or deformed, the first closest vector calculating means moves or deforms the convex object. Instead of obtaining the closest vector, it is preferable that the second closest vector calculating means corrects the new closest vector obtained before the current movement or deformation to a new closest vector.

[0042]

Embodiments of the present invention will be described below. FIG. 1 is an external view of a computer system including an embodiment of an inter-object distance calculating apparatus according to the present invention.

The computer system 100 shown in FIG.
Is an image display unit 1 that displays an image on a display screen 102a in response to an instruction from the main unit 101 in which a CPU, an MO (magneto-optical disk) drive device, and the like are built.
02, a keyboard 103 for inputting various information to the computer system 100, and a mouse 10 for specifying an arbitrary position on the display screen 102a of the image display unit 102
4. A storage unit 105 for storing an embodiment of the inter-object distance calculation program according to the present invention is provided.

The inter-object distance calculation program stored in the storage unit 105 is stored in an MO (magneto-optical disk) 110 which is a portable storage medium, and the MO 110 is loaded into the computer system 100 shown in FIG. Is uploaded to the computer system 100.
Similarly, the object distance program stored in the computer system 100 shown in FIG.
10, and can be transferred to another computer system via the MO 110.

In the following, an embodiment of the inter-object distance calculating device will be described. A program for realizing such a function as the inter-object distance calculating device in the computer 100 shown in FIG. This is an embodiment of a calculation program, and the storage unit 105 in which the program is stored corresponds to an embodiment of a storage medium for calculating a distance between objects calculation program of the present invention. Further, when the program is stored in the MO 110, the MO 110 in a state where the program is stored also corresponds to an embodiment of the storage medium for the distance calculation program between objects according to the present invention.

FIG. 2 is a block diagram of an embodiment of the apparatus for calculating the distance between objects according to the present invention. In this figure, one solid arrow indicates the flow of data for the first time only, two solid arrows indicate the flow of data for the second and subsequent times, and the dashed arrow indicates the flow of the first and second data.
The flow of data common to the second and subsequent times is shown. The inter-object distance calculating device 10 shown in FIG.
1 is provided. The shape information storage means 11 stores shape information including a set of vertices or a set of control points of two convex objects to be calculated for the distance between closest contacts. The shape information consisting of a set of vertices or a set of control points may be a set of information expressing each vertex or each control point independently, or a function for analytically expressing the surface of a convex object. It may be an expression. At least one of the two convex objects to be calculated for the closest contact point distance is formed of a set of convex curved surface patches defined by control points. The shape information storage means 11 may store the convex surface patches including the convex surface patches. Only the control points are stored, and the convex surface patches defined by the stored control points are stored in the surface patch information described later. It may be generated by the generation unit 13. The other convex object of the two convex objects to be calculated for the closest contact point distance may be a convex curved surface object or a convex polyhedron composed of a set of vertices.

The shape information stored in the shape information storage means 11 is read out and input to the shape information updating means 12. The shape information updating means 12 calculates the coordinates of the vertices or control points of the convex object after movement or deformation based on the shape information read from the shape information storage means 11 or the shape information just before movement or deformation. , The shape information of the sequentially moved or deformed convex object is obtained for each frame.

The shape information as the initial state read from the shape information storage means 11 and the shape information updating means 12
Are sequentially input to the curved surface patch information generating means 13. When the shape information read from the shape information storage means 11 or the shape information updated by the shape information updating means is a set of control points of the convex surface object, the curved surface patch information generating means 13 sets these control points. , A convex surface patch that defines the surface of the convex surface object is generated. However, if the shape information representing the initial state of the convex surface object read from the shape information storage unit 11 includes information on the convex surface patch of the initial state of the convex surface object, the shape information is read from the shape information storage unit 11. Generation of a convex surface patch is unnecessary for the convex surface object as the initial state. In this case, the surface patch information generating means 13
Then, a convex surface patch for the convex surface object updated by the shape information updating means 12 is generated.

The shape information including the convex surface patch information via the surface patch information generating means 13 is sent to the display means 14, and the display means 14 displays a convex object in the initial state (including the arrangement position), and Thereafter, the sequentially moved or changed convex object is continuously displayed. The shape information representing the initial state among the shape information that has passed through the curved surface patch information generating means 13 is input to the first closest vector calculating means 15. As described later, since the shape information representing the state after moving or deforming from the initial state does not need to be calculated by the first closest vector calculating means 15,
It is directly input to the second closest vector calculating means 16.

In the first closest vector calculating means 15,
Based on the input shape information in the initial state, a closest vector connecting the closest points of two target convex objects is obtained. This first closest vector calculating means 1
In the step 5, in calculating the closest vector, a direction connecting the closest points of two target convex objects to each other, and a direction from one convex object (self) to the other convex object (partner) of the two convex objects. Is the inner product of the vertex or control point of the vertex or control point that is closest to the opponent of the inner product of the closest vector of The principle of having a value larger than the inner product of the vertex or control point away from the contact point is adopted. A specific example of this principle will be described later.

The nearest vector obtained by the first nearest vector calculation means 15 is a nearest vector when both target objects are regarded as convex polyhedrons.
This is the nearest vector with insufficient accuracy for a convex curved object. In this way, the first closest vector calculating means 1
The closest vector obtained in step 5 is input to the second closest vector calculation means 16 together with the shape information (including the surface patch information) of the two target convex objects. The second closest vector calculating means 16 is based on the principle that the plane closest to the convex surface object at the closest point of the convex surface object is orthogonal to the closest vector connecting the closest points of the two convex objects. First closest vector computing means 15
Is corrected to a new closest vector with higher accuracy. A specific example of this principle will be described later.

The nearest vector obtained by the second nearest vector calculating means 16 is input to the interference determining means 17 and the length of the nearest vector is a small amount ε (for example, 10
If the length is shorter than ^-10 ), it is determined that the target two convex objects are in an interference state, and if the length is longer than the target, the two convex objects are determined to be apart from each other. The result of this determination is sent to the display means 14, which displays information indicating the presence or absence of the interference state together with the two target convex objects.

As described above, it is necessary for the first nearest vector computing means 15 to obtain the nearest vector when the two convex objects of interest are in the initial state. The shape information of the second and subsequent frames, which have been moved or deformed, are directly bypassed or passed by the first nearest neighbor vector calculating means 15,
It is input to the second closest vector calculation means 16. Second
The closest vector calculating means 16 regards, for each frame after the second frame, the closest vector obtained by itself for the immediately preceding frame as the approximate closest vector for the current frame. Is corrected to a highly accurate nearest vector for the current frame based on the principle described above.

As described above, the display means 14 displays in real time the state in which the two convex objects of interest are moving or deformed and whether or not the two convex objects are in the interference state. Is done. Note that, here, with reference to FIG. 2, the description has been made on the assumption that the two convex objects to be processed are three-dimensional objects. However, the same applies to the case where two-dimensional objects are the target. The description of the two-dimensional object will be omitted.

FIG. 3 is a block diagram showing a hardware configuration of an embodiment when the inter-object distance calculating device of the present invention is expressed in a computer system. In the inter-object distance calculating device 20 shown in FIG. 3, the CPU 23 performs a basic algorithm for calculating a closest vector, an operation for displaying a calculation result, an operation for graphically displaying the motion of an object, and any other logical operation. Perform

The storage device 27 has a work environment and shape data of members, their initial position, an execution module of an algorithm for realizing the inter-object distance calculating device according to the present invention, and a graphical display of the motion of the object. An execution module and other data and an execution module necessary for realizing the function as the inter-object distance calculating device are stored.

The RAM 26 stores a work environment read out from the storage device 27 by the CPU 23 and a shape data memory 26a for storing shape data of members, for example, a member movement command input via the data input device 21 such as a mouse. The CPU 23 uses a coordinate conversion data memory 26b for storing coordinate conversion data calculated in the CPU 23 based on the data, the shape data stored in the shape data memory 26a, and the coordinate conversion data stored in the coordinate conversion data memory 26b. Using the surface patch data memory 26c for storing the work environment and the surface patch data of the member calculated in the basic algorithm for calculating the closest vector and the surface patch data stored in the surface patch data memory 26c. The closest vector data calculated in the CPU 23 ( The nearest-neighbor vector data memory 26d that stores the proximity point, the distance between the objects, the interference determination result, and the like), the shape data stored in the shape data memory 26a, and the coordinate conversion data stored in the coordinate conversion data memory 26b. Each memory is provided with a shape conversion data memory 26e for storing shape conversion data representing a member shape after movement calculated in the CPU 23 when used.

The data input device 21 sends the work environment and the position data and movement data of the members to the CPU 23 via the interface 22. Graphic display 25
Is the RA sent through the interface 24.
An image drawn based on the closest vector data stored in the closest vector data memory 26d in the M26 and the shape conversion data stored in the shape conversion data memory 26b is graphically displayed.

In the following, when two target objects are three-dimensional convex objects and both of the two convex objects are convex curved objects (case 1), the two target objects are three-dimensional convex objects. If one of the two convex objects is a convex curved object and the other is a convex polyhedron (case 2), the two convex objects of interest are two-dimensional convex objects and both of the two convex objects Is a convex curved object (case 3), and two target convex objects are two-dimensional convex objects, one of the two convex objects is a curved object and the other is a convex polygon (case 3). The algorithm for calculating the closest vector will be described separately for 4).

(Case 1: Case of Three-Dimensional Convex Object and Both Convex Curved Objects) FIG. 4 is a flowchart showing the flow of processing executed by the CPU 23 of FIG. First, Step 3_
At 1, the shapes of the members and the working environment and their initial positions are read from the storage device 27 of FIG. In step 3_1, the members and the working environment are initially arranged on the graphic display 25 in FIG. 3 according to the information on the initial position at the same time as the input. In step 3_2, an object to be checked for interference is picked up and selected from the members displayed on the graphic display 25 and the work environment using the data input device 21 such as a mouse. In step 3_3, the picked-up target object is moved using a mouse or the like, and the movement data is input to the CPU 23 in FIG. Step 3_
In step 4, a transformation matrix representing the movement from the absolute coordinate space is calculated based on the movement data input in step 3_3, and based on the calculated transformation matrix, the shapes of the members and the working environment representing the movement of each member and the working environment are calculated. Create conversion data. Step 3
In _5, the surface patch data of the selected interference determination target object is created based on the shape conversion data created in step 3_4. In step 3_6, the nearest neighbor vector calculation algorithm is activated in response to the result of step 3_5. The closest vector calculation algorithm will be described later. In step 3_7, an image based on the result of step 3_6 and the result of the shape conversion data in step 3_4 is displayed on the graphic display 25 in FIG. In step 3_8, the value of the distance d between the objects of interference determination calculated in step 3_7 is compared with a threshold ε,
If d <ε, it is determined that there is an interference state, and step 3
The interference point is displayed at _9. Step 3_1
At 0, it is determined whether or not to continue the processing from step 3_3 to step 3_8 and step 3_9, and if so, the process returns to step 3_3 to input the movement data of the next frame. If the process is not to be continued, the entire process is exited.

FIG. 5 is a flow chart showing details of the nearest neighbor vector calculation algorithm in step 3_6 in FIG. FIG. 6 is a diagram exemplifying the flow of steps 4_1 to 4_9 in FIG. 5, and is an explanatory diagram of one embodiment of the first closest vector calculating means according to the present invention. FIG.
FIG. 6 is a diagram exemplifying a flow of steps 4_10 to 4_12 in FIG. 5, and is an explanatory diagram of one embodiment of a second closest vector calculating means according to the present invention.

First, in step 4_1 in FIG. 5, the respective centers of gravity of the two target objects are connected to each other and set to ν ₀ (FIG. 6 (a)).
reference). As the center of gravity, the average of the position vector set {Q _i } that defines the curved surface is usually taken. In the case of a polyhedron, the average of the vertex vectors is taken. Next, in step 4_2, an inner product of −ν ₀ and a position vector set X = {Q _i } defining the left object in FIG. 6 is obtained, and a position vector representing the maximum value is defined as p ₀ . Similarly, an inner product of ν ₀ and a position vector set Y = {Q ′ _i } defining the right object in FIG. 6 is obtained, and a position vector representing the maximum value is defined as q ₀ .

In step 4_3, ν _{0 is changed} to ν ₁ = p
₀ is updated to -q ₀ (see Figure 6 (b)). Step 4_
In step 4, as in step 4_2, the inner product of −ν ₁ and the position vector set X = {Q _i } defining the left object in FIG. 6 is calculated, and the position vector representing the maximum value is defined as p ₁
And Further, an inner product of ν ₁ and a position vector set Y = {Q ′ _i } defining the right object in FIG. 6 is obtained, and a position vector representing the maximum value is defined as q ₁ . In general, p ₁
Is a position vector different from p ₀ , and q ₁ is q ₀
Is a different position vector.

In step 4_5, ν _{1 is changed} to ν ₂ = p
Updated to ₁ -q _1. As shown in steps 4_6 and 4_7 in FIG. 5, the same operation is repeated to update ν _i , and in step 4_8, the convergence vector ν _final of ν _i is calculated. Here, ν _i is updated exactly as follows. ν _i is the closest vector to the convex hull spanned by the vector set Y _i , and the vector set Y _i is updated in the form of Y _{i + 1} = {subY _i , p _{i + 1} −q _{i + 1} } Where subY _i is a subset of Y _i , where ν _i is represented as follows:

[0065]

(Equation 1)

Here, m is a maximum of 4 in the three-dimensional Euclidean space, and ν _i is from the origin, to the vertex when m = 1, to the line segment when m = 2, and to m = 3 The case is represented as the closest vector to the triangle patch. When m = 4, the inside of the tetrahedron, that is, ν = 0. "EG.
Gilbert, D.A. W. Johnson, andS.
S. Keerthi, "A Fast Proced
ure for Computing the Dis
tance Between ComplexObje
cts in Three-Dimensional
Space, "IEEE Journal of Rob
otics and Automation, Vo
l. 4, No. 2, pp. 193-203, 198
8 ”, an algorithm for efficiently calculating the coefficient λ _k is presented. The updating process of the vertices p _i , q _i , and vector ν _i shown in FIG.
It has been confirmed that the convergence takes place three times. The amount of calculation until ν _final is calculated is mainly the inner product calculation

[0067]

(Equation 2)

And its load is therefore proportional to the total number of position vectors, M = M ₁ + M ₂ . Next, an embodiment of the second closest vector calculating means according to the present invention will be described with reference to FIG. 7 together with FIG. Step 4_9 in FIG.
Then, the expression of ν _final

[0069]

(Equation 3)

From the above, one set of curved surface patches having the position vectors p _i and q _i as control points is selected. In general,
A plurality of surface patches having the position vector set {p _i } at the control point exist around p _i for m = 1 and 2; however, any of these surface patches may be selected. In step 4_10, on the selected surface patch, ν _fina
ν _final is updated as follows with _l as the initial value.

In the following, the surface patch is a spline (B-
spline) curved surface

[0072]

(Equation 4)

Is assumed to be represented by First, the initial value of the vector ν _curve is ν _final obtained in step 4_8 in FIG. When updating the vertices p _i and q _i ,

[0074]

(Equation 5)

U and w that satisfy the conditions are obtained by an iterative method. That is,

[0076]

(Equation 6)

[0077]

(Equation 7)

As follows:

[0079]

(Equation 8)

As described above, u and w are updated. Here, as an initial value of u and w, u = w = １ ／ as an example. The above operation is performed for both two convexly curved objects as shown in FIG. Points on two convexly curved objects obtained by substituting the converged values of u and w, u ₁ w _1, into the equation of the curved surface are connected to form a ν _curve . ν _curve to ν
Update to _{curve, l} and repeat the above calculation in the same way.
At this time, u ₁ and w ₁ are taken as initial values of u and w. Ν _curve obtained from converged u and w is ν _{curve, 2}
And

The ν _curve finally obtained by the above iterative calculation is defined as ν _{curve, final} . If the values of u and w exceed the range of 0 ≦ u, w ≦ 1 during the repetitive calculation, the process proceeds to a curved surface patch in the exceeded direction, and the above calculation is repeated. Steps 4_10 and 4 in FIG.
_11. In step 4_12 in FIG. 5, the thus obtained ν _{curve, final} is set as the nearest vector ν _{closes t} finally obtained. The convergence process described above is as shown in FIG.

(Case 2: Three-dimensional convex object, one of which is a convex curved object and the other is a convex polyhedron) Differences from case 1 will be described. In the process of obtaining the closest vector between two target objects, if one is a convex curved surface object and the other is a convex polyhedron, the process of steps 4_1 to 4_8 is performed on the convex polyhedron in the process shown in FIG. Step 4_1 to Step 4 for a convex curved object
By repeating the process of _11, finally ν
Calculate _closest .

(Case 3: Two-dimensional convex object and both are convex
In the case of a curved object) The above-described method for calculating the closest vector is quadratic.
The same applies to the following. Below,
H is considered as a spline curve (B-spline curve).
You. Process of step 4_1 to step 4_8 in FIG.
Is just a two-dimensional component, even in the two-dimensional case
Holds as it is. Step 4_9 of FIG.
“Selection of a switch” is “selection of a curved patch”. In FIG.
Ν of step 4_10_{curve , i}The update process is as follows
become.

Now, one of the two B-spline curves respectively selected for the two target objects is

[0085]

(Equation 9)

Assume that: Here, Q _i is B-Spline
This is the control point of the curve. The following equation J (t) where the inner product between the derivative of the B-spline curve by t and ν _{curve , i} is set to zero
A real root that satisfies 0 ≦ t ≦ 1 for = 0 is obtained. The same procedure is performed for the other selected B-spline curve, and the obtained points are connected to each other to obtain ν _{curve , i} in the next step. Subsequent processing is the same as in the three-dimensional case.

[0087]

(Equation 10)

(Case 4: Two-dimensional convex object and one is a convex curved object and the other is a convex polygon) In the process of obtaining the nearest vector between two target objects, one is a convex curved object and the other is a convex curved object In the case of a convex polygon, for a convex polygon, steps 4_1 to 4_8 in the process of FIG. Step 4_1 to Step 4_ in the process
By repeating the process of _converting 11 into two dimensions in the same manner as in Case 3, ν _closest is finally calculated.

Next, a method of obtaining a nearest vector when two convex objects move or deform with time will be described. Here, it is assumed that the two target convex objects are three-dimensional objects, and both are convex curved objects. In other cases, as described above, it can be applied by a simplified algorithm. When continuously calculating the closest vector between two convex curved objects with respect to time, the process of FIG. 5 is replaced with FIG.

First, in step 71, the first closest vector is obtained by the same process as that of FIG.
In step 7_2, the _closest vector obtained in step 7_1 is substituted into v _final as ν _{closest, previous} . In step 7_3, the surface patch of the previous frame is replaced with the surface patch of the current frame. 7 to 6_6, the same processing as steps 4_10 to 4_12 in FIG. 5 is performed. In step 7_7, it is determined whether or not to calculate the closest vector of the next frame.
_—2, and the process is repeated with ν _{closest, previous} obtained this time.

If one of the objects is a convex polyhedron, the process of step 7_4 performs the inner product calculation shown in FIG. 6 for the convex polyhedron and the update calculation shown in FIG. 7 for the convex curved object. The two-dimensional case is similarly extended to a continuous type.

[0092]

As described above, according to the present invention,
For any convex object in which both or one of the two convex objects is represented by a convex curved surface patch, the closest contact point distance between the two convex objects is determined with high accuracy and high speed. While displaying and moving or deforming the two convex objects, it is possible to calculate the distance between the closest points or the interference state of the two convex objects in real time.

[Brief description of the drawings]

FIG. 1 is an external view of a computer system including an embodiment of a distance calculation apparatus between objects according to the present invention.

FIG. 2 is a block diagram of an embodiment of an inter-object distance calculating apparatus according to the present invention.

FIG. 3 is a block diagram showing a hardware configuration of an embodiment when the inter-object distance calculating device of the present invention is expressed in a computer system.

FIG. 4 is a flowchart showing a processing flow.

FIG. 5 is a flowchart showing details of a nearest neighbor vector calculation algorithm.

FIG. 6 is an explanatory diagram of one embodiment of a first closest vector calculating means according to the present invention.

FIG. 7 is an explanatory diagram of one embodiment of a second closest vector calculating means according to the present invention.

FIG. 8 is a flowchart showing details of a nearest vector calculation algorithm when a target object moves or deforms.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Distance calculation apparatus between objects 11 Shape information storage means 12 Shape information update means 13 Surface patch information generation means 14 Display means 15 First closest vector calculation means 16 Second closest vector calculation means 17 Interference determination means 20 Between objects Distance calculation device 21 Data input device 22 Interface 23 CPU 24 Interface 25 Graphic display 26 RAM 27 Storage device 100 Computer system 101 Main unit 102 Image display unit 103 Keyboard 104 Mouse 105 Storage unit 110 Magneto-optical disk (MO)

Claims (18)

[Claims] 1. The distance between closest points of contact of two three-dimensional convex objects, one of which is allowed to be a convex polyhedron and the other or both of which are composed of convex curved surface objects composed of a set of convex curved surface patches, is defined as 2 An inter-object distance calculating apparatus that calculates a distance between two convex objects based on shape information including arrangement position information of the two convex objects. The closest vector in the direction from one convex object to the other convex object, and the position vector of the vertex when the one convex object is a convex polyhedron, which constitutes the one convex object, or the one convex object Of the inner product with the position vector of the control point for forming the convex surface patch that constitutes the convex surface object when is a convex surface object, of the one convex object, the closest point to the other convex object Close vertices Or a first nearest neighbor vector calculating means for obtaining a nearest vector whose inner product about the control point is larger than the inner product of the vertex or the control point of the one convex object which is farther from the closest point of the one convex object; A second closest vector calculating means for correcting the closest vector obtained by the first closest vector calculating means into a new closest vector orthogonal to a plane tangent to the convex curved object at the closest point of the convex curved object; An inter-object distance calculation device, comprising: 2. The method according to claim 2, wherein the second closest vector calculating means calculates the second closest vector based on the new closest vector.
2. The apparatus according to claim 1, further comprising an interference determination unit configured to determine whether two convex objects are interfering with each other. 3. A control point for forming a convex surface patch constituting the convex surface object, comprising a set of vertices of the convex polygon when one of the two convex objects is a convex polyhedron. A shape information storage means for storing shape information consisting of a set of, and, based on information instructing movement or deformation of the convex object, calculating coordinates of the vertex or control point of the convex object after movement or deformation. A shape information updating unit for obtaining new shape information, and a surface patch information generating unit for generating a convex surface patch constituting the convex surface object based on the shape information of the convex surface object. Item 2. The apparatus for calculating the distance between objects according to Item 1. 4. The second closest vector calculating means,
When the convex object is moved or deformed, the first
In place of calculating the nearest vector after movement or deformation by the nearest vector calculation means of (a), a new nearest vector obtained before the current movement or deformation by the second nearest vector calculation means is further updated. 4. The inter-object distance calculating apparatus according to claim 3, wherein the distance is corrected to a closest vector. 5. A display device for displaying a convex object drawn based on shape information stored in said shape information storage means and new shape information obtained by said shape information updating means. The distance calculation apparatus according to claim 3, wherein 6. The distance between the closest points of two two-dimensional convex objects, one of which is allowed to be a convex polygon and the other or both of which are composed of convex curve objects consisting of a set of convex curve patches, An inter-object distance calculation device that calculates two convex objects based on shape information including arrangement position information, the closest convex vector connecting the closest points of the two convex objects. The closest vector in the direction from one convex object to the other convex object, and the position vector of the vertex when the one convex object is a convex polygon, or the position vector of the vertex constituting the one convex object, or When the convex object is a convex curve object, the inner product of the convex vector and the position vector of the control point for forming the convex curve patch constituting the convex curve object, the one of the convex objects with respect to the other convex object The vertices close to the point of contact Or a first nearest neighbor vector calculating means for obtaining a nearest vector whose inner product about the control point is larger than the inner product of the vertex or the control point of the one convex object which is farther from the closest point of the one convex object; A second closest vector calculating means for correcting the closest vector obtained by the first closest vector calculating means to a new closest vector orthogonal to a straight line tangent to the convex curve object at the closest point of the convex curve object; An inter-object distance calculation device, comprising: 7. The method according to claim 2, wherein the second closest vector calculating means calculates the second closest vector based on the new closest vector.
7. The inter-object distance calculating apparatus according to claim 6, further comprising: an interference determining unit configured to determine whether the two convex objects interfere with each other. 8. A control for forming a convex curve patch constituting the convex curve object, comprising a set of vertices of the convex polygon when one of the two convex objects is a convex polygon. Shape information storage means for storing shape information consisting of a set of points; and calculating coordinates of the vertices or control points of the convex object after movement or deformation based on information instructing movement or deformation of the convex object. A shape information updating means for obtaining new shape information, and a curve patch information generating means for generating a convex curve patch constituting the convex curve object based on the shape information of the convex curve object. An apparatus for calculating the distance between objects according to claim 6. 9. The method according to claim 8, wherein the second closest vector calculating means includes:
When the convex object is moved or deformed, the first
In place of calculating the nearest vector after movement or deformation by the nearest vector calculation means of (a), a new nearest vector obtained before the current movement or deformation by the second nearest vector calculation means is further updated. 9. The apparatus according to claim 8, wherein the distance is corrected to a nearest vector. 10. A display device for displaying a convex object drawn based on shape information stored in said shape information storage means and new shape information obtained by said shape information updating means. The apparatus for calculating the distance between objects according to claim 8. 11. The distance between closest contacts of two three-dimensional convex objects, one of which is allowed to be a convex polyhedron, and the other or both of which are composed of convex curved surface objects consisting of a set of patches of convex curved surfaces, is defined as 2 An inter-object distance calculation program that is calculated based on shape information including arrangement position information of two convex objects, and is a closest vector connecting the closest points of the two convex objects. The nearest vector in the direction from one of the convex objects to the other convex object, and the position vector of the vertex when the one convex object is a convex polyhedron, which constitutes the one convex object, or the one of the one In the case where the convex object is a convex curved object, the inner product of the convex vector and the position vector of the control point for forming the convex curved surface patch constituting the convex curved surface object is one of the latest products of the one convex object with respect to the other convex object. Close to contact A first nearest neighbor vector calculating means for obtaining a nearest vector whose inner product about a vertex or a control point has a larger value than an inner product about a vertex or a control point far from the nearest point of the one convex object; A second closest vector calculating means for correcting the closest vector obtained by the first closest vector calculating means into a new closest vector orthogonal to a plane tangent to the convex curved object at the closest point of the convex curved object; And a storage medium for storing an inter-object distance calculation program, comprising: 12. The inter-object distance calculation program determines whether or not the two convex objects are interfering with each other based on the new closest vector obtained by the second closest vector calculation means. The storage medium according to claim 11, further comprising interference determination means for determining. 13. The convex curved surface constituting the convex curved object, wherein the inter-object distance calculation program includes a set of vertices of the convex polygon when one of the two convex objects is a convex polyhedron. By calculating shape information consisting of a set of control points for forming a patch, and calculating coordinates of the vertices or control points of the convex object after the movement or deformation of the convex object based on the information instructing the movement or deformation of the convex object. Shape information updating means for updating to new shape information; and surface patch information generating means for generating a convex surface patch constituting the convex surface object based on the shape information of the convex surface object. The storage medium according to claim 11, wherein: 14. The method according to claim 14, wherein the second closest vector calculating means calculates the moved or deformed closest vector in the first closest vector calculating means when the convex object is moved or deformed. Alternatively, the second
14. The inter-object distance calculation program according to claim 13, wherein the closest vector calculation means corrects the new closest vector obtained before the current movement or deformation to a new closest vector. Storage medium. 15. The distance between closest points of contact of two two-dimensional convex objects, one of which is allowed to be a convex polygon and the other or both of which are composed of convex curve objects consisting of a set of convex curve patches, An inter-object distance calculation program that is calculated based on shape information including arrangement position information of two convex objects, wherein the two convex objects are closest vectors connecting the closest points of the two convex objects. The closest vector in the direction from one of the convex objects to the other convex object and the position vector of the vertex when the one convex object is a convex polygon, which constitutes the one convex object, or In the case where one convex object is a convex curve object, the inner product of the one convex object and the position vector of a control point for forming a convex curve patch constituting the convex curve object, the other convex object Nearest point of contact for A first nearest neighbor vector calculating means for obtaining a nearest vector whose inner product about a vertex or a control point has a larger value than an inner product about a vertex or a control point far from the nearest point of the one convex object; A second closest vector calculating means for correcting the closest vector obtained by the first closest vector calculating means to a new closest vector orthogonal to a straight line tangent to the convex curve object at the closest point of the convex curve object; And a storage medium for storing an inter-object distance calculation program, comprising: 16. The inter-object distance calculation program determines whether or not the two convex objects interfere with each other based on the new closest vector obtained by the second closest vector calculation means. 16. The storage medium according to claim 15, further comprising interference determination means for determining. 17. The convex curve constituting the convex curve object, wherein the inter-object distance calculation program includes a set of vertices of the convex polygon when one of the two convex objects is a convex polygon. Calculating shape information comprising a set of control points for forming a curved patch, and coordinates after movement or deformation of vertices or control points of the convex object based on information instructing movement or deformation of the convex object. And a curve patch information generating means for generating a convex curve patch constituting the convex curve object based on the shape information of the convex curve object. The storage medium according to claim 15, wherein the program is for calculating a distance between objects. 18. The method according to claim 18, wherein, when the convex object is moved or deformed, the second closest vector calculating means calculates the moved or deformed closest vector in the first closest vector calculating means. Alternatively, the second
18. The program according to claim 17, wherein the closest vector calculating means corrects the new closest vector obtained before the current movement or deformation to a new closest vector. Storage medium.