Interrogation of Offsets of Polynomial Surface Patches

Abstract

This paper presents an algorithm for computing the intersection of the offset (or parallel) surface of a polynomial surface patch ( rogenitor) of arbitrary degree, with a straight line. The rogenitor patch is expressed in the tensor product Bernstein form. The intersection problem is reformulated in terms of computing the intersection of two algebraic curves within the parameter s ace of the patch. The tensor product Bernstein form is emplo ed for the representation of these algebraic curves. The solution method is based on subdivision relying on the convex hull roperty of the Bernstein representation of algebraic curves and minimization techniques. The resulting algorithm can form the basis for accurate visualization of offset surfaces through ray tracing methods.