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 G 1 or G 2 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.
