C^2光滑插值曲面片

C^2 Continue Interpolation Surface Patch

本文给出一种构造C^2光滑参数三角曲面片的方法,所生成的三角曲面片插值空间R^3中的三个已知点,并以这些点处的已知法向量为三角曲面片在相应点处切平面的法向量。在本文给出的方法中,需要的所有Bezier点均可通过简单的代数显式公式求出,并且Bezier点的个数被减少,为在微机上产生复杂插值曲面打下了较好的基础。

A method is introduced for constructing a C^2 smooth partametric triangular surface patchthat interpolates three given points in R3 and has norma1 vectors of its tangent planes whichare the same as those on the given points respectively. All the Beziet points needed can begiven by simple explicit algebraic expression, and the number of Bezier points is reduced.which makes a good base for geneating a more complex interpolating surface on microcompu-ters.