有理Bézier曲线的降阶

Degree Reduction of Rational Bézier Curves

从最优化思想出发,把有理Bzier曲线的降阶问题转化为求解优化问题,这样使得权因子和控制顶点能被分开考虑,从而保证了权因子的非负性.同时,结合智能计算中的仿生学方法和程序设计方法,给出有理Bzier曲线降阶的一种新方法.该方法首先计算简单,应用适应值函数和简单的循环执行复制、交叉、变异、选择求出最优值或次优值,其次实现了有理Bzier曲线的保端点插值的多次降阶,降阶后的有理Bzier曲线直接以显式给出.

By means of optimization methods, degree reduction of rational Bzier curves is changed to an optimization problem so that both weights and vertices are considered respectively. Using programming method and Genetic Algorithms, a new method on the reduction of rational Bzier curves is presented. The method has the following virtues: Firstly, it is simply to get the result by fitness function, copy process, crossover process, mutation process, and selection process. Secondly, the rational Bzier Curves can be reduced many times and interpolated. Finally, the reduced Bzier curves can be represented explicitly.