A tracing method for parametric Bezier triangular surface/plane intersection over triangular domain

Abstract

Surface/plane intersection problem is a special case of surface/surface intersection, and is an active area of research across many disciplines in computer-aided geometric design. This paper presents, in general the setting of derivational continuities, (i.e. C0, C1, and C2), a surface/plane intersection algorithm for parametric Bezier triangular surface over triangular domain. The present algorithm is a combinatorial algorithm that is based on a tracing method, in which the intersection curves are traced out in the direction of tangent vectors at intersectionpoints. The intersection curves are represented by their piecewise polynomial approximations, given by orderedpair of surface domain points. The aim is to obtain the smallest number of ordered points that correctly represent the topology of the true intersection curves. Since the points on the intersection curves are obtained in an ordered manner, no sorting is essential. The refinement of the intersection curve may include fitting an interpolatory cubic spline, or adding and deleting points. The method has been used to compute different planar sections (i.e. intersection curves with X, Y, and Z planes) for surfaces having different derivational continuities (i.e. C0, C1 and C2).