Arithmetic unit for calculating distance between objects

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.