带形状参数Bézier型曲线曲面及其应用

Parameter Bézier-type Curve/Surface And Its Application

在三角函数空间中构造了一组带有形状参数的基函数,具有类似于Bernstein基函数的性质,称其为Bern-stein型基函数,利用此基函数定义Bézier型曲线及张量积Bézier型曲面。分析了形状参数对曲线曲面形状的调节作用,调节形状参数可以使Bézie型曲线从双边逼近Bézier曲线,且可以精确表示抛物线、椭圆弧(圆弧)等,同时,Bézier型曲面仅需较少的曲面片即可精确重建椭球面(球面)及圆柱型曲面,可以达到C1连续足以满足工程中的需求。

A kind of trigonometric blending functions is constructed based on trigonometric spaces, which is called as Bernstein - type blending functions. The corresponding Bézier - type curve and Bézier - type tensor product surface are defined. The effect of parameter to adjust the curves and surfaces shape is analyzed. Bézier - type curve can approach Bézier curve form both sides and accurately represent parabolic curve, elliptic（circular） arcs through adjusting the shape parameter. Moreover, the corresponding tensor product surface can reconstruct ellipsoid, spherical surface exactly with less patches, and the patches can achieved Cl continuous enough to satisfy the engineering requirements.