参数曲线形状修改

提出一种新的、基于余弦伸缩函数、针对参数曲线的形状修改与变形方法。首先定义了特殊的伸缩函数 ,在此基础上构造了形状算子矩阵 ,其次将该矩阵与伸缩中心及主方向结合构造出两种变形矩阵 ,最后用变形矩阵去乘待变形曲线在局部坐标系下的位置向量 ,或用它乘以给定向量场再加待变形曲线在原坐标系下的位置向量从而产生变形效果。伸缩函数含有若干可变参数 ,每个参数可产生不同的形状修改效果 ,比如控制被修改部分与未修改部分间的连续阶 ,容易得到理想的变形效果。理论分析实例表明该方法在几何造型 ,计算机图形学等领域有潜在适用性。

Shape Modification of Parametric Curves

A technique of shape modification and deformation for parametric curves through cosine extension function (CEF) is presented. First, a special extension function is defined, based on which a shape operator matrix is constructed. Then combining such matrix with the center of extension and principal directions, two kinds of deformation matrices are defined. Finally, curve deformation is achieved through multiplying its position vector in a local coordinate system by deformation matrix or adding the multiplication of a vector field and quasi-deformation matrix to its position vector in the original coordinate system. Since CEF contains several variable parameters, each of which generates a different effect of shape modification such as controlling the degree of continuity of the modified part of curve with the unchanged part, ideal deformation effects can be got fairly and easily. Examples of theoretical analysis show that the method is potentially useful for geometric modeling, computer graphics and so on.