A new approach to design rational harmonic surface over rectangular or triangular domain

作者：Zhang Juzheng; Cai Panpan; Wang Guojin^*

来源：Journal of Information and Computational Science, 2011, 8(1): 71-83.

• Boundary curves
• Control point
• Degree-Elevation
• Monterde algorithm
• New approaches
• Nonlinear objects
• Polynomial curve
• Polynomial surface
• Rational curves and surfaces
• Rectangular domain
• Triangular domains

By the degree elevation-based method of approximating rational curves and surfaces using polynomial curves and surfaces, a new effective approach to construct rational Be´zier harmonic surfaces over rectangular or triangular domain is presented. First, rational Be´zier curves, given as the boundaries, are transferred into some approximate polynomial curves, according to which a polynomial harmonic surface T then can be generated by using Monterde's method. On the other hand, the unknown rational Be´zier harmonic surface R with the given rational boundary curves is transferred into an approximate polynomial surface N, whose degree is the same as that of T, so that the control points of N can be expressed as a function of both the weights and control points of R. Comparing T with N, by solving a minimizing problem with nonlinear object function, the rational harmonic surface R can finally be obtained. Several pragmatic illustrations are presented to testify validity of this algorithm.

• 出版日期2011
• 单位浙江大学