Bezier曲线约束降多阶的算法分析与比较.doc

Bézier曲线约束降多阶的算法分析与比较
摘要: 为了产品外形数据的压缩与传递得以顺利进行,急需开发参数曲线降阶这一项关键技术,特别是构造L2范数下Bézier曲线带高阶端点插值条件的降多阶算法,(CAD),对国际CAD期刊近年来发表的此课题中最有代表性的4种算法,从理论机理、误差预测、表达形式、逼近精度、机时消耗这5个方面,作了系统的剖析与对比,并用大量实例对算法效果进行比较,指明了各种算法的优缺点,找到了一种最优的算法,从而为外形设计及图形显示系统的研制提供了富有参考价值的意见.
关键词: 算法比较;Bézier曲线;降多阶;端点约束;L2范数
Analyse parison for some algorithms of multi-degree reduction with constrained Bézier curves
Abstract: In order to actualize pression munication of product model data essfully, it is urgently required to develop a key technique, the reduction of parameter curve, especially to construct an algorithm for multi-degree reduction of Bézier curves with constraints of endpoints continuity of high degree in L2-norm, and to analyze every strongpoint and ing of all kinds of algorithms. This is one of the popular project in the field puter Aided Design (CAD) at present. Based on the request of application of engineering to practice, four typical algorithms, published in the international CAD journals these years, are roundly analyzed pared according to their theoretical mechanism, error forecast, expression form, approximation accuracy puting time. Also numerical tests are made to validate pare the arithmetic effect by using many samples. Then the merits and weaknesses of the above various methods are indicated, and an optimal algorithm is found. Thus the valuable sug