基于伸缩函数的平面参数曲线自由变形技术(英文)  

The Technique of Free-from Deformation Based on Extension Function for Planar Parametric Curve

作　　者：王小平[1] 叶正麟[1] 李红达[1] 胡晓敏[2] 孟雅琴[1] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]杭州电子工业学院文理学院,杭州310037

出　　处：《工程数学学报》2002年第1期115-119,67,共6页Chinese Journal of Engineering Mathematics

基　　金：NaturalScienceFoundationofShaanXiProvince(2 0 0 0SL0 8)

摘　　要：提出了一种新的平面参数曲线自由变形方法 ,建立了相应的数学模型 :构造出特殊的伸缩函数 ,在此基础上得到变形算子矩阵 ,用它作用待变形曲线方程 ,或乘以某一向量场再加到曲线方程上去 ,从而使曲线发生形变。通过交互改变控制参数 ,可达到预期变形效果。实验表明 ,该方法数学背景简单 ,易于控制 ,重复使用可获得丰富的变形效果。适用于几何造型、计算机动画、CAD/CAM等领域。A new technique of free form deformation about parametric curves through so called extension function (EF) is presented. First, a special extension function is given out and an operator matrix is constructed. Then original curve is deformed through acting on it's equation by the operator matrix or adding the equation by the multiplication of some vector field and the operator matrix. Interactively modifying control parameters, ideal deformation effects can be got. The implementation shows that the method is simple, intuitive and easy to control. It can be used in many fields such as geometric modeling and computer animation.

关 键 词：几何造型 CAD CAM 伸缩函数 平面参数曲线自由变形技术 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O18[自动化与计算机技术—计算机科学与技术]