摘要
对三角域上的Bernstein-Bezier多项式曲面片,本文给出了九参C^1插值的显式表示,并将其代入常庚哲和Davis的凸性定理中,得出了判别凸性的充分必要条件。对已知的插值条件,可不求插值曲面而知其是否凸。此显式格式和判别条件都易于在计算机上实现。
For the Bernstein-Bezier trianglar patchs, an explicit representation of a nine-parameter interpolated surface is given. Combining this representation and the convexity theorem of Chang and Davis, we obtain the necessary and sufficient conditions explicitly for the convexity-of an interpolated surface. Both the explicit representation and the judging conditions can be easily carried out on a computer.
关键词
三角域
曲面插值
凸性
CAD
computer aided design, convexity, surface interpolation,triangles
