Spherical Bézier curve based on corner cutting

摘要

The classical de Casteljau algorithm for constructing Bézier curves can be generalized to sphere of arbitrary dimension by replacing line segments with shortest great circle arcs. The resulting spherical Bézier curve is C^∞ and interpolates the endpoints of its control polygons. In this paper, a new method is proposed to construct spherical Bézier curves, which extends corner cutting method, introduced by Lane-Riesenfeld to sphere. The final curve created by this method converges to spherical Bézier curves named corner cutting spherical Bézier curves. The necessary and sufficient condition of G1 continuity for two spherical Bézier curves is presented. Finally, as a by-product geodesic can be created on free-form surfaces with presented approach.