三角Bézier曲面的降多阶逼近

Approximate Multi-degree Reduction of Triangular Bézier Surfaces

根据所定义的原n次三角Bézier曲面与降阶后的m(m≤n-1)次三角Bézier曲面间的距离函数取最小值,给出三角Bézier曲面降阶逼近的一种方法.在降阶过程中,考虑了降阶三角Bézier曲面与原三角Bézier曲面在角点达到高阶插值的情形.最后,用数值实例显示所给方法的有效性.

A method of the degree reduction for triangular Bézier surfaces is presented by minimizing the defined distance function between the original triangular Bézier surface of degree n and the degree reduced triangular Bézier surface of degree m（ m≤n - 1）. Continuity at comer points of triangular Bézier surfaces are considered in degree reduction process, Finally sane graphical examples are shown in order to illustrate the validity of the method presented here.