Minimizing the maximal ratio of weights of rational Bezier curves and surfaces

作者：Cai Hong Jie; Wang Guo Jin^*

来源：Computer Aided Geometric Design, 2010, 27(9): 746-755.

DOI：10.1016/j.cagd.2010.08.001

• Rational Bezier curve
• Rational Bezier surface
• Bound
• Derivative
• Invariant

Applying the Mobius transformation to rational Bezier curves and surfaces, the weights can be modified whereas the control points remain unchanged. With appropriate transformation parameters, the maximal ratio of the weights of rational Bezier curves and surfaces can be minimized, which have applications in improving the bounds of derivatives, optimizing degree reduction of rational Bezier curves. In the surface case, there has not yet been a solution for the problem of finding transformation parameters such that the maximal ratio of the weights reaches its minimum. In this paper, a new method for the problem in the curve case is presented, and the uniqueness of the solution can be easily proved; then the method is generalized to the surface case with geometric perception. Some numerical examples are given for showing our results in improving the bounds of derivatives of rational Bezier curves and surfaces.

• 出版日期2010-12
• 单位浙江大学