参数曲面的拟自适应三角化

Semi Adaptive Triangulation of Parametric Surface

提出了一种参数曲面的拟自适应三角化离散算法。该算法通过对曲面的参数域进行预剖分，以及引入曲面上一点处的“最大绝对法曲率”的概念，采用“分而治之”的方法分片对参数曲面的参数域进行三角形网格剖分。该方法基本上可以像“自适应”方法一样，根据曲面的法曲率变化来控制三角化剖分的密度，生成的三角片数量较少，并且可以避免在三维空间产生狭长的三角形、退化三角形与“裂缝”，运行速度明显比自适应方法快。

A semi adaptive triangulation of parametrically defined surface is presented. By pre dividing parametric region of the surface and introducing the concept “maximum absolute normal curvature” at a point on the surface, the method adopts “divide and conquer” approach triangulating the parametric region of the surface piecewise. Basically like “adaptive approach”, the method can control triangulation density with respect to the change of normal curvature of the surface generating a small number of triangular facets, and thiny triangles, degenerate triangles and “cracks” in 3D space will not occur, but the speed of the algorithm is higher than that of adaptive one.