The degree reduction of tensor product rational Bézier surfaces

The objective of this paper is to present methods to solve the problem of the degree reduction of rational Bezier surfaces with endpoints continuity. Firstly, under homogenous spaces, we apply degree reduction of the polynomials Bezier surfaces in L₂ and L_¿ norm to the rational Bezier surfaces respectively. In addition, we derive conditions for the reduced-degree weights ¿_i > 0, and point out that the degree reduction methods under the homogenous coordinates is only sufficient condition; secondly, under the affine space, necessary and sufficient condition for the c^¿ -continuity at the endpoints is given. Based on the multi-objective optimization, we utilize Genetic Algorithm achieve the reduction of rational surfaces. Finally several numerical examples are presented to illustrate the effects of methods.