Interval implicitization of parametric surfaces

Abstract

The interval implicit representations of parametric surfaces have wide applications in Computer Graphics, Geometric Modelling, and others. Based on the properties of interval algebraic surfaces, barycentric coordinates and Bernstein basis functions, this paper presents an algorithm to compute the interval implicit representation of a rational Bézier surface by solving an optimal problem with a quadratic object function and linear constraints. This problem is equivalent to finding the two bounding surfaces of the interval implicit surface. An example is provided to demonstrate the algorithm. © 2010 Springer-Verlag Berlin Heidelberg.