摘要
针对C-Bézier曲线的近似降阶问题,基于遗传算法,给出了一种用n次C-Bézier曲线最小平方逼近n+1次C-Bézier曲线的方法。该方法从最优化思想出发,把C-Bézier曲线的降阶问题转化为求解函数的优化问题,通过选择适应值函数,利用简单的循环执行复制、交叉、变异、选择求出该优化问题的最优值,从而实现了C-Bézier曲线在端点无约束和端点G0约束条件下的近似降阶逼近。实例结果表明,所提方法不仅可以获得较好的降阶效果,而且易于实现、精度高、误差计算简单,可以广泛地应用于计算机辅助设计中对曲线的近似降阶。
Aimingat C-B6zier curve of approximate degree reduction problem, a method for constructing an approximative C-B6zier curve of degree n to a C-B6zier curve of degree n＋ 1 by genetic algorithm is provided. By means of optimization meth- ods, degree reduction of C-B6zier curves is transformed to an optimization problem, by selecting the fitness function, using a simple loop reproduction, copy process, crossover process, mutation process, selection process obtaining the optimal value of the optimization problem to achieve C-Bezier curve endpoints in the endpoint GO unconstrained and constrained approximate reduction. The experimental results illustrate that the proposed method ment, has high precision and is simple for error estimation.
出处
《计算机工程与应用》
CSCD
2013年第5期174-178,共5页
Computer Engineering and Applications
基金
国家自然科学基金(No.10926152)
陕西省自然科学基金(No.2011JM1006)
陕西省教育厅自然科学研究项目(No.11JK1052)
关键词
C-BÉZIER曲线
遗传算法
降阶
最小平方逼近
约束条件
C-Bezier curve
genetic algorithm
degree reduction
not only has a good merging effect, but also is easy to impleleast squares approximation
constraints
