基函数构造参数样条曲线.DOC

中图法分类号:TP391.7 文献标识码:A 带形状控制的自由曲线曲面参数样条 彭丰富,田良 (桂林电子科技大学数学系，广西桂林，541004) 摘 要： 目的:样条曲线曲面的构造是工程制图中的一个重要部分。针对双曲抛物面上参数样条曲线的构造，在已有的研究基础上提出了一种样条方法使曲线曲面可以任意地逼近一个多边形或者一个网格。方法：在标准四面体内构造一个双曲抛物面，在该曲面上以基函数参数化的方法定义一种带形状参数的参数样条曲线曲面样条基函数通过将双曲抛物面的有理参数化进行限定，生成单参数有理样条基函数。G2-连续空间曲线，同样对于空间网格可以构造G2-连续的拟合曲面，它所对应的基函数可以是有理形式。结论：实验结果表明，本文在笔者已有的研究基础上提出的参数样条曲线可以通过重心坐标系变换适应为任意的四边形,除了空间四面体内的样条曲线，四面体退化成四边形同样可实现。 关键词 ：基函数；有理样条函数；逼近样条函数；G2-连续 Parametrical spline for free-form curve and surface Peng Fengfu，Tian Liang Guilin University of Electronic Technology, Guilin, Guangxi 541004Abstract: Objective: The spline curve surface is an important part of CAGD. In order to get the parameter spline curve on the hyperbolic paraboloid. The four rational basis functions presented in this paper have a changeable control handle and a unary function respectively. Method: A hyperbolic paraboloid is constructed in the standard tetrahedron, on the surface the base function defines a parameterized method with the parameters of the shape parameter spline curve surface. The basis function of spline through the rational parameters of the hyperbolic paraboloid is limited. Generate a single parameter rational basis function of spline. Additionally, the nature of shape preserving and endpoints are considered.Result: The nature of shapepreserving and endpoints are detailed considered, and derive that the curvature of twoendpoints are zero, for a range of points, consequently, a G2-continuity curve can be attached by this spline curves without any additional requirements. Conclusion: Experiment shows that we use this spline to arise surface for spatial mesh, which also can implement G2-continuity withmany freedom. Key words: Basis function; rational spline; approximate spline; G2-continuity 0 引言 在计算机辅助几何设计(CAGD)和计算机图形学领域中有两种定义样条曲线曲面的方法，分别是参数和代数形式[1-4].后者有更多的自由度及简单的表示和更好的几何操作特性等，但是计算相对复杂. 因此，基于生成样条曲线曲面的便利性,前者在几何设计中成为了不可替代的方法.与此同时，一个控制多边形或一个网格还经常使用有理样条曲线来生成光滑曲线曲面，用于模型重构，具有良好的逼近效果、易于实现、具有人机交互的形状因子[5]等.有