平面参数曲线周期性形状修改与变形  

A New Method for Periodic Shape Deformation of Parametric Curves Based on EF (Extension Factor)

作　　者：王小平[1,2] 叶正麟[3] 周儒荣[1] 孟雅琴[3] 

机构地区：[1]南京航空航天大学CAD/CAM工程研究中心 [2]西北工业大学应用数学系陕西西安710072 [3]西北工业大学应用数学系

出　　处：《西北工业大学学报》2003年第2期184-186,共3页Journal of Northwestern Polytechnical University

基　　金：陕西省自然科学基金 (2 0 0 0 SL0 8)

摘　　要：提出了一种新的参数曲线变形方法 :构造了周期性伸缩因子函数和变换矩阵 ,用它作用于待变形的曲线 ,可使曲线发生周期性形变。该方法数学背景简单 ,控制参数少且易于控制 ,变形效果较丰富 ;各个控制参数有各自明显的几何属性 ,可分别定量、较精确地用于控制变形的发生区间、伸缩比例、变形周期、界点处的连续性与光滑性、变形方向和变形幅度等。实验表明 ,该方法通过交互改变控制参数 ,可获得预期的丰富的形状修改和变形效果。适用于几何造型、计算机动画。Refs.3 through 6 improved on FFD method as proposed by Sederberg and Parry in 1986 and extended by Coquillart in 1990 . After commenting briefly on Refs.3 through 6 at the beginning of this article, we are of the opinion that Refs.3 through 6 are not quite satisfactory in that deformation effect(including accurate control of deformation region, quantitative control of amount of deformation, and the continuity and smoothing of the junction between deformed and undeformed portions) is not ideal; also Refs.3 through 6 are limited to NURBS (non uniform rational B-spline) curves and are inapplicable to planar parametric curves; finally Refs.3 through 6 are inapplicable to periodic shape modification or deformation. We present now a new technique of shape modification or deformation for parametric curves. First we introduce a periodic EF (extension factor) function which includes four parameters; then we construct a geometric transformation matrix based on EF operator matrix. When the user operates the geometric transformation matrix on the curve to be deformed, it will be periodically deformed in the way expected by the user. The advantage of this method is that adjusting control parameters is rather easy and precise even for a user without advanced mathematical knowledge. Especially each control parameter presents evident geometric meaning; so the four parameters allow the user to make respectively the following four adjustments concerning: (1) the region of deformation, (2) the amount of deformation, (3) the period of deformation, (4) the continuity and smoothing of junction between deformed and undeformed portions. We emphasize that, different from Refs. 3 through 6, we do not need differentiation, integration and conversion of tangent vector, thus simplifying greatly the computation needed. We expect that our method can be used in geometric modeling, computer animation and CAD.

关 键 词：参数曲线 伸缩因子 自由变形 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]