Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants

Abstract

Rational surface patches are popular in computer aided geometric design. But for any given rational parametrization, many questions arise: "Are there base points?", "What is the degree of the surface?", "How to do inversion?", "Is the representation redundant?", "Is a point exceptional?" These and many other problems can be solved in one stroke by using the u-resultant. With a computer algebra system, the implementation of our algorithms is straightforward. A method to speed up the computation is also provided. © 1992.