插值有理Bézier渐近四边形的有理Bézier曲面  

Construction of Rational Bézier Surface Interpolating Asymptotic Quadrilateral

作　　者：王慧[1] 朱春钢[1] 李彩云[2] Wang Hui;Zhu Chungang;Li Caiyun(School of Mathematical Sciences, Dalian University of Technology, Dalian 116024;School of Mathematics and Physics Science, Dalian University of Technology, Panjin 124221)

机构地区：[1]大连理工大学数学科学学院,大连116024 [2]大连理工大学基础教学部,盘锦124221

出　　处：《计算机辅助设计与图形学学报》2017年第8期1497-1504,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(11671068;11271060;11401077);民用飞机专项项目(MJ-F-2012-04);辽宁省高等学校优秀人才支持计划(LJQ2014010);中央高校基本科研业务费专项基金(DUT16LK38;DUT16LK39);中国博士后科学基金资助项目(2015M58132)

摘　　要：为构造封闭的曲线为有理Bézier曲面的边界渐近线,给出封闭四边曲线为渐近四边形的条件,并提出插值该四边形的曲面构造方法.首先在给定角点数据的前提下构造优化的n次有理Bézier渐近四边形;然后利用该四边形和曲面在四边形上的切矢确定曲面沿边界的两排控制顶点和权;最后极小化曲面薄板能量函数确定剩余自由的控制顶点,进而构造出光滑的双5n–7次有理Bézier插值曲面.实例展示边界曲线为有理3,4,5次时曲面的构造结果,以及边界曲线含有直线或者拐点的情况,表明该方法是可行的.Conditions for construction of rational Bézier surface interpolating a closed quadrilateral as its asymptoticboundary are presented.Firstly,from the given corner data,an optimized rational Bézier asymptotic quadrilateralof degree n is constructed.Secondly,two arrays of control points and weights along the boundary curvesare obtained from the quadrilateral and the tangent vectors of the surface.Finally,minimizing the plate spline energydetermines the other free control points and then a smooth rational Bézier surface of bi-(5n–7)degree is constructed.Some representative examples show the construction of surfaces interpolating the cubic,quartic or quinticrational Bézier asymptotic quadrilaterals and verify the effectiveness of the method.

关 键 词：渐近线 有理BÉZIER曲线 曲面构造 插值 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]