基于曲率图小波分解的平面曲线光顺方法  

A Fairing Method for Planar Curves Based on Wavelet Decomposition of Curvature Map

作　　者：张力宁[1] 张定华[1] 刘元朋[1] 赵西峰[2] 

机构地区：[1]西北工业大学现代设计与集成制造技术教育部重点实验室,陕西西安710072 [2]西北工业大学数学与信息科学系,陕西西安710072

出　　处：《计算机应用研究》2005年第11期250-252,共3页Application Research of Computers

基　　金：航空科学基金项目(00H53076);国家教委博士点基金项目(20006992)

摘　　要：针对在逆向工程的实践中常见的轮廓线的光顺问题,给出了一种先对曲率图进行小波分解,提取其低频部分作为新的曲率图,并利用几何Herm ite插值方法,生成G2连续的分段三次有理Bézier曲线,从而重建出光顺的产品轮廓曲线的新方法。该方法具有可直接处理含噪声的点云数据,插值给定曲率,容易实现局部光顺和整体光顺等优点。算例证明该光顺方法比起现有软件中的方法不仅光顺效果更好,而且执行效率更高。In reverse engineering research, problems of how to reconstruct a fairing contour curve that is generally asked to be satisfied with some curvature constraints are often met. A new fairing method for planar curves based on wavelet decomposition and Geometric Hermite Interpolation is given in this paper. We decompose curvature signal with wavelet at first and then use its low frequency coefficients as new smooth curvature signal, which is used to construct a G^2 continuous piecewise rational cubic Bezier curve with （ Geometric Hermite Interpolation, GHI ） GHI method subsequently. Compared with other fairing methods, this method can dispose data with noise directly, realize local fairing and integer fairing easily, and satisfy curvature constraints. The effect and efficiency of this method are also proved with some examples.

关 键 词：光顺 几何Hermite插值 小波 

分 类 号：N391.41[自然科学总论]