保测地曲率的曲面曲线设计

给出一种在给定光滑曲面上进行曲线设计的算法．由于曲面上曲线的曲率向量可分解为测地曲率向量与法曲率向量的和，故可以通过设计平面源曲线，并将这条源曲线保测地曲率对应到给定曲面上，得到一条测地曲率和平面源曲线的曲率相同的目标曲线．取给定曲面上一点为初始点，逐次迭代跟踪得到整条目标曲线．该算法既可以用来进行曲面上的图案设计，也可用于求解光滑曲面上的测地线。

Mapping Algorithm for Surface Curve Design with Preserved Geodesic Curvature

Since the curvature vector of a curve on a surface can be decomposed into normal curvature vector and geodesic curvature vector, a surface curve can be designed first on a plane and then mapped onto the surface. The desired surface curve is first constructed as a plane curve with the given geodesic curvature. After assigning a start point and initial direction on the surface, the whole plane curve is traced onto the surface through point by point mapping. This method can be used for pattern design as well as for geodesic curve computation on smooth surfaces.