Mathematical Methods for Curves and Surfaces

Abstract

In this paper, we present a modified method for the computation of approximate rational parameterizations of implicitly given canal surfaces. The designed algorithm, which improves and completes a recent approach from [1], is mainly suitable for implicit blend surfaces of the canal-surface-type. Its main advantage is that it produces rational parameterizations of low bidegree (7, 2). A distinguished feature of our approach is a combination of symbolic and numerical techniques yielding approximate topology-based cubic parameterizations of contour curves which are then applied to compute an approximate parameterization of the given canal surface. © Springer-Verlag 2014.