双曲面片的高精度多项式逼近

High Accuracy Approximation of Hyperboloid Surface Patch by Bicubic Bézier Polynomials

用三次 Bézier曲线逼近双曲线段 ,在端点保持 GC1 插值 ,给出单边逼近的误差 ,并进行最优插值点的选择 ,得到最优的误差估计 ;在此基础上 ,用双三次 Bézier多项式逼近单叶和双叶双曲面片 ,给出误差估计 ,逼近达到六阶精度 .相邻的逼近片之间 GC1 连续 .

Bézier curve is required to interpolate the end points of given curve segment with GC 1 continuity. One-sided approximation error is given and the choice of optimal interpolation points is studied, the optimal error estimate is obtained. Based on the above results for curve segments, the approximation of a hyperboloid surface patch using bicubic Bézier polynomials both for one sheet and two sheets is worked out. Its approximation accuracy is of sixth order. Furthermore the adjacent approximation surface patches have the same tangent plane at their common boundaries.