有理Bézier调和与双调和曲面的设计

Design for Rational Bézier Harmonic and Biharmonic Surfaces

针对有理Bézier调和曲面的复杂的有理性,提出一种构造有理Bézier调和曲面的近似算法.借助于有理曲线曲面的Hybrid多项式逼近方法与Bézier调和曲面的Monterde算法,将有理Bézier调和曲面的造型问题转换为线性约束条件下关于有限维变量的一个非线性目标函数的最小化问题.进一步,将该算法推广到有理Bézier双调和曲面的造型问题中去,并用有理双2次、双3次调和曲面与有理双3次双调和曲面的实例对文中算法进行了验证.结果表明,该算法对有理Bézier调和曲面与双调和曲面的构造问题有一定的实际应用价值.

Considering the complexity of the rational Bézier harmonic surfaces, in this paper an approximated algorithm for constructing rational Bézier harmonic surfaces is proposed. By using polynomial curves and surfaces to approximate rational curves and surfaces and constructing Bézier harmonic surfaces with the Monterde method, the rational Bézier harmonic surface modeling problem can be transformed into an optimization problem of how to minimize a nonlinear function with a limited number of variables under a linear constrained condition. The proposed algorithm is also extended into constructing the rational Bézier biharmonic surfaces. The method is validated by examples of biharmonic surfaces of degree three and harmonic surfaces of degree two and three .The experimental results show that the algorithm proposed performs well in the application of constructing rational Bézier harmonic surfaces and biharmonic surfaces.