矩形域上B－B曲面的凸性与强凸自然网的升阶不变性

The Convexity of the B-B Surface Over Rectangle and theInvariance of Degree Elevation for Strongly Convex Net

矩形域上Ｂｅｒｎｓｔｅｉｎ－Ｂｅｚｉｅｒ曲面（简称Ｂ－Ｂ曲面）的凸性问题是ＣＡＧＤ（计算机辅助几何设计）中人们关注的热点之一．曲面的凸性与它的控制网的凸性有密切的关系，但是在矩形域上其Ｂ－网该如何定义一直得不到很好的解决．本文提出了一种新的网──自然网的概念，并且证明了强凸的自然网具有升阶不变性．

The problem of the convexity of the Bernstein-Bezier surface is one of the major comcernsin Computer Aided Geometric Design. The Convexity of the B-B surface is closely related to its controlnet, but how to define the B-net for the B-B surface over a rectangle has not been solved well. In thispaper, a concept of a natural net is presented and it is proved that a natural net with strong convexityis capable of in variance of the degree elevation.