多项式混合曲线曲面方法构造

Construction of Polynomial Blending Curves and Surfaces

针对混合曲线表示及其求导和求积困难的问题,通过计算构造出一种多项式混合曲线曲面形式.当待混合曲线是多项式时,混合曲线也为多项式形式.该多项式混合公式可以推广得到任意参数连续C(n)和几何连续G(n)的混合曲线曲面.另外,在得到的混合曲线曲面族中构造出了新的更优能量光顺方程,通过设置参数可得到合适的混合曲线曲面.实验结果表明,文中提出的混合曲线曲面造型方法稳定、有效.

As the traditional blending curve has difficulty for computing its derivative and integral, this paper presents a new presentation for polynomial blending curve and surface. If the curve or surface to be blended is polynomial, the blending curve or surface is also the polynomial. This blending formula can be extended for the blending curve and surface with any parametric continuity C^（n） and geometric continuity G^（n）. After obtaining a family of blending curves and surfaces, we construct a new energy smoothing equation for determining the parameters to get the desirable blending curve and surface. Experimental results show that the new blending method is stable and effective.