Figure 1 . Modeling on the surface of a cow. From left: the control polygons of some curves and a C 1 spline, the corresponding curves, a region is filled and other is trimmed, final result. Abstract We define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. We discuss the construction of C 0 and C 1 piecewise Bézier splines. We also describe

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... to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks.