Design for Rational Bézier Harmonic and Biharmonic Surfaces

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.