流形网格上Bézier曲线的生成*

针对在流形网格上已有经典的简单割角法不能使用的问题，提出一种流形网格上的简单割角法，此算法使用的边是离散测地线，而经典的简单割角法使用的边是直线段，此算法收敛于网格模型上的Bézier曲线。用几何化生成曲线而不是参数化是研究的主要方法。此Bézier曲线特别适合于网格模型上自由曲线的设计。最后通过实例表明提出的算法正确、稳定、快速且容易实现，具有较好的仿真效果。

Generation of Bézier curve on manifold meshes

Aiming at the problem that classical simple corner-cutting method was not used on manifold meshes, this paper gave a simple corner-cutting method on manifold meshes. Edges that were used in this method were discrete geodesic. Edges that were used in classical simple corner-cutting method were straight segment. It constructed Bézier curves on manifold meshes by using the algorithm. Main method of generating curve was geometrical method, but not method of parameter. Geodesic Bézier curves were suitable for designing free curves on manifold meshes. Under Visual C++6.0, gave some examples of Bézier curve on discrete surface in OpenGL. Examples show that the algorithm is correct, stable, fast and easy in implementation. There is a good effect of simulation for all examples.