Arithmetic unit for calculating distance between objects

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, 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.