局部可调的四次Catmull-Rom样条曲面及其形状优化  

A locally adjustable quadric Catmull-Rom spline surface and its shape optimization

作　　者：李军成 刘成志 LI Juncheng;LIU Chengzhi(College of Mathematics and Finance,Hunan University of Humanities,Science and Technology,Loudi 417000,Hunan Province,China)

机构地区：[1]湖南人文科技学院数学与金融学院,湖南娄底417000

出　　处：《浙江大学学报（理学版）》2024年第6期740-746,共7页Journal of Zhejiang University（Science Edition）

基　　金：湖南省自然科学基金资助项目(2024JJ7254);国家自然科学基金资助项目(12101225).

摘　　要：当控制顶点保持不变时,无法对三次Catmull-Rom样条曲面的形状进行局部调整。为满足实际工程对插值曲面形状设计的要求,给出了一种含局部参数的四次Catmull-Rom样条曲面,并讨论了2种对四次Catmull-Rom样条曲面形状进行优化的方案。结果表明,四次Catmull-Rom样条曲面不仅继承了三次Catmull-Rom样条曲面的插值性与连续性,而且容易利用所含的参数对曲面形状进行局部或整体调整,通过计算所含参数的最优值获得尽可能光顺和尽可能保形的四次Catmull-Rom样条曲面,为插值曲面的构造提供了方法。The shape of the cubic Catmull-Rom spline cannot be adjusted locally when the control points remain unchanged.In order to meet the needs of the shape design of interpolation surfaces in practical engineering problems,a quadric Catmull-Rom spline surface with local parameters is presented,and two schemes for optimizing the shape of the quadric Catmull-Rom spline surface are given.The results show that the quadric Catmull-Rom spline surface not only inherits the interpolation and continuity property of the cubic Catmull-Rom spline surface,but also allow us to use the parameters contained to adjust its shape locally or globally.By determining the optimal values of the parameters,the desired smooth and shape-preserving quadric Catmull-Rom spline surface can be obtained.The proposed quadric Catmull-Rom spline surface and its shape optimization schemes provide methods for the construction of interpolation surfaces.

关 键 词：CATMULL-ROM样条 插值曲面 局部调整 光顺 保形插值 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]