Arithmetic unit for calculating distance between objects
First Claim
1. An arithmetic unit in a computer for computing a closest distance between a first and a second three-dimensional convex object, at least one of the objects being a convex curved surface object, in accordance with shape information including arrangement position information about the objects, the arithmetic unit comprising:
- first closest vector arithmetic means for identifying a preliminary closest vector coupling the closest points of the two objects, displayed on a computer screen by repeatedly calculating for each object an inner product of a candidate for the preliminary closest vector directed from a first of the two objects to a second of the two objects and a plurality of position vectors, each position vector being one of;
a position vector of a vertex where the first object is a convex polyhedron defined by vertexes, anda position vector of a control point of a convex curved surface patch where the first object is a convex curved surface object comprising sets of convex curved surface patches defined by control points, wherein a position vector for each object having a maximum inner product is extracted and a new candidate for the preliminary closest vector is formed by a vector connecting the two position vectors; and
second closest vector arithmetic means for correcting the preliminary closest vector identified by said first closest vector arithmetic means to identify a new closest vector perpendicularly intersecting a tangent plane in contact with the object having a convex curved surface at the closest point of the object having a convex curved surface by starting from the preliminary closest vector and sequentially updating a given coordinate on the surface of the object having a convex curved surface until an inner product of a vector on the tangent plane and the closest vector on the given coordinates has the smallest possible value.
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Abstract
A unit in a computer for computing a closest distance between two three-dimensional convex objects. At least one of the objects is a convex curved surface object. A first closest vector arithmetic unit is provided for identifying a preliminary closest vector coupling the closest points of the two objects by repeatedly calculating for each object an inner product of a candidate for the preliminary closest vector directed from a first of the two objects to a second of the two objects and a plurality of position vectors. Each position vector being one of a position vector of a vertex where the first object is a convex polyhedron, and a position vector of a control point of a convex curved surface patch where the first object is a convex curved surface object comprising sets of convex curved surface patches. A position vector for each object having a maximum inner product is extracted and a new candidate for the preliminary closest vector is formed by a vector connecting the two position vectors. A second closest vector arithmetic unit corrects the preliminary closest vector to identify a new closest vector perpendicularly intersecting a tangent plane in contact with the object having a convex curved surface at the closest point by starting from the preliminary closest vector and sequentially updating a given coordinate on the surface of the object until an inner product of a vector on the tangent plane and the closest vector on the given coordinates has the smallest possible value.
17 Citations
10 Claims
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1. An arithmetic unit in a computer for computing a closest distance between a first and a second three-dimensional convex object, at least one of the objects being a convex curved surface object, in accordance with shape information including arrangement position information about the objects, the arithmetic unit comprising:
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first closest vector arithmetic means for identifying a preliminary closest vector coupling the closest points of the two objects, displayed on a computer screen by repeatedly calculating for each object an inner product of a candidate for the preliminary closest vector directed from a first of the two objects to a second of the two objects and a plurality of position vectors, each position vector being one of; a position vector of a vertex where the first object is a convex polyhedron defined by vertexes, and a position vector of a control point of a convex curved surface patch where the first object is a convex curved surface object comprising sets of convex curved surface patches defined by control points, wherein a position vector for each object having a maximum inner product is extracted and a new candidate for the preliminary closest vector is formed by a vector connecting the two position vectors; and second closest vector arithmetic means for correcting the preliminary closest vector identified by said first closest vector arithmetic means to identify a new closest vector perpendicularly intersecting a tangent plane in contact with the object having a convex curved surface at the closest point of the object having a convex curved surface by starting from the preliminary closest vector and sequentially updating a given coordinate on the surface of the object having a convex curved surface until an inner product of a vector on the tangent plane and the closest vector on the given coordinates has the smallest possible value. - View Dependent Claims (2, 3, 4, 5)
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6. An arithmetic unit in a computer for computing a closest distance between a first and a second two dimensional convex object, at least one of the objects being a convex curved line object, in accordance with shape information including arrangement position information about the objects, comprising:
first closest vector arithmetic means for identifying a preliminary closest vector coupling the closest points of the two objects, displayed on a computer screen by repeatedly calculating for each object an inner product of a candidate for the preliminary closest vector directed from a first of the two objects to a second of the two objects and a plurality of position vectors, each position vector being one of; a position vector of a vertex where the first object is a convex polyhedron defined by vertexes, and a position vector of a control point of a convex curved line patch where the first object is a convex curved line object comprising sets of convex curved surface patches defined by control points, wherein a position vector for each object having a maximum inner product is extracted and a new candidate for the preliminary closest vector is formed by a vector connecting the two position vectors; and second closest vector arithmetic means for correcting the preliminary closest vector identified by said first closest vector arithmetic means to identify a new closest vector perpendicularly intersecting a tangent plane in contact with the convex curved line object at the closest point of the convex curved line object by starting from the preliminary closest vector and sequentially updating a given coordinate on the surface of the object having a convex curved surface until an inner product of a vector on the tangent plane and the closest vector on the given coordinates has the smallest possible value. - View Dependent Claims (7, 8, 9, 10)
Specification