Piecewise rational parametrizations of canal surfaces

Abstract

Canal surfaces, as envelopes of one-parameter families of spheres, correspond to curves in Minkowski space. We show that the continuity properties of a canal surface are inherited from the continuity properties of the associated curve, i.e., two curves joined with G1 or G2 continuity in Minkowski space correspond to two canal surfaces joined with the same level of continuity. We also describe an algorithm for minimal bi-degree rational parametrizations of patches on canal surfaces, and show how this can be used to parametrize piecewise rational corner and edge blends. © Springer-Verlag 2014.