摘要
1.引论计算几何中的曲面设计,由于在汽车、船舶、飞机的外型设计,以及在人造器官和机器人等领域中的广泛应用,已越来越引起人们的注意,尤其几何光滑(或称视觉光滑,记为GC^1)曲面的研究更是受到人们的重视.所谓几何光滑是指两个曲面片沿连接处位置连续和切平面连续.这个问题Barnhill[2]做为一个公开问题提出来.本文构造出插值位置向量的五次GC^1光滑曲面.
A kind of GC' surface constructing scheme on arbitrary triangular mesh is presented. The surface formed by this scheme can pass the given position vectors and take the given planes as its tangent planes at the vertices of the triangular mesh. Triangular mesh referred here is a set of space triangles and their faces such that the intersection of any two edges in this set is a vertex or an empty set.
