关于Bézier三角曲面的保凸条件

Some conditions of convexity for Bernstein-Bézier surfaces over triangles

讨论了Bézier三角曲面保凸的充分条件.为了简化B网弱凸的3个条件,对文献[周昌政.对函数Bézier三角片凸性条件的推广.应用数学与计算数学学报,1991,5(2):87-91]提出的Bézier三角曲面的保凸条件做了进一步改进.在此基础上,将条件转化为一个无穷保凸区域.在该区域内,利用分段线性插值方法得到Bézier三角曲面保凸的线性充分条件.实例表明,该方法在几何造型中是可行、有效的.

The conditions of convexity for Bernstein-Bézier surfaces over triangles were discussed.In order to simplify B-nets weak convex conditions,the convexity preserving conditions of Bézier triangle surfaces in Ref.[Zhou Changzheng.The extension of the conditions of convexity for Bernstein-Bézier surfaces over triangles.Communication on Applied Mathematics and Computation,1991,5(2):87-91]were further improved.On this basis,the conditions were put into an infinite convexity preserving area.In this area,using piecewise linear interpolation method,some Bézier triangle surface convexity preserving linear sufficient conditions were obtained.Examples show that the proposed methods are feasible and effective in geometric modeling.