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 C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> and C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> 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.