拟Hermite曲线/曲面及其应用

Quasi-Hermite Curve/surface and Its Application

在代数三角函数空间中构造了一种代数三角基函数,具有类似于Herm ite基函数的性质,称其为拟Herm ite基函数。利用此基函数定义拟Herm ite曲线,结合Bézier曲线的思想,给出了拟Herm ite曲线的另一种定义及张量积拟Herm ite曲面的定义。实验表明,拟Herm ite曲线可以精确表示直线段、正弦线、余弦线、椭圆弧(圆弧)及摆线,Herm ite曲面可以精确表示椭球面(球面)、圆锥面及圆环面等二次曲面。

A kind of algebraic and trigonometric blending functions is constructed based on algebraic and trigonometric spaces,which is called as quasi-Hermite blending functions.Then,the corresponding quasi-Hermite curve is defined.Another definitions of quasi-Hermite curve and quasi-Hermite tensor product surface are given as well as the cases of Bézier curve and surface.Experiment indicates that the quasi-Hermite curve can accurately represent straight line segment,sine curve,cosine curve,elliptic（circular） arcs and cycloid,the corresponding tensor product surface can represent ellipsoid,spherical surface,circular conical surface and torus exactly.