Local, Polynomial G 1 PN Quads

Abstract

In this paper, we introduce the concept of local, polynomial G 1 PN quads. These are degree bi-5 polynomial surface patches in Bernstein-Bezier form. As the classic PN patch, ours interpolates the vertices of a quadrilateral control polygon and is orthogonal to a normal specified at each vertex. In contrast to the original concept, the proposed quad is orthogonal to four (continuous) normal fields — one defined at each boundary. Each of these normal fields and the corresponding patch boundary are uniquely determined by the data at two adjacent vertices of the control polygon. Thus, the patch construction is local in the sense that it is based solely on the information provided at the four control vertices. In this way, it is easy to stitch together multiple quads to construct a manifold G 1 continuous surface of arbitrary topological type. In contrast to other approaches, vertices at which 3 or more than 4 patches meet do not require special treatment.