Piecewise Rational Parametrizations of Canal Surfaces
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.
Academic chapter/article/Conference paper
- Heidi Elisabeth Iuell Dahl
- SINTEF Digital / Mathematics and Cybernetics
Mathematical Methods for Curves and Surfaces. 8th International Conference, MMCS 2012, Oslo, Norway, June 28 – July 3, 2012, Revised Selected Papers
88 - 111