多裁剪曲面的三角划分算法

An Algorithm for Triangulating Multitrimmed Surfaces

提出一种新的多裁剪曲面三角划分的方法。把裁剪曲面展开,得到曲面的平面展开图。在平面展开图内进行三角划分,把三角形上点的拓扑关系映射到裁剪曲面,生成三角网格。由于平面展开图上两点的欧氏距离接近这两点在裁剪曲面上的测地距离,所以生成的三角网格保持了平面展开图中三角形的形态,解决了在参数域内进行三角划分所产生的狭长三角形的问题。此外,还提出了一种对带孔的平面散乱点进行三角划分的办法,有效的防止了划分网格出现裂缝和覆盖等现象。

An algorithm for triangulating multi trimmed surfaces is introduced in this paper. Flatten the trimmed surfaces to get the surface development. Triangulating in the flattening surfaces instead of in the parameter surfaces will reduce the number of the narrow triangulations. Because the distance between two points in the flattening surfaces is near to the geometric distance between the two points in the trimmed surfaces, it will keep the shape of the triangulations. Besides, an method of triangulating the scattered points with holes is introduced, which will avoid splitting and overlaying.