Minimal rational parametrizations of canal surfaces

Research paper by R. Krasauskas

Indexed on: 07 Mar '07Published on: 07 Mar '07Published in: Computing


It is well known that canal surfaces defined by a rational spine curve and a rational radius function are rational. The aim of the present paper is to construct a rational parameterization of low degree. The author uses the generalized stereographic projection in order to transform the problem to a parameterization problem for ruled surfaces. Two problems are discussed: parameterization with boundary conditions (design of canal surfaces with two curves on it, as is the case for rolling ball blends) and parameterization without boundary conditions.