A New Approach to Design Rational Harmonic Surface over Rectangular or Triangular Domain ⋆

By the degree elevation-based method of approximating rational curves and surfaces using polynomial curves and surfaces, a new effective approach to construct rational Bézier harmonic surfaces over rectangular or triangular domain is presented. First, rational Bézier 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 Bézier 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.