Geodesic Bezier Curves: a Tool for Modeling on Triangulations

Abstract

We define a new class of curves, called geodesic Bezier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bezier curves, the new curves are as smooth as possible. We discuss the construction of C0 and C1 piecewise Bezier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks.