平面参数曲线变形的仿射映射B样条方法

提出一种新的参数曲线变形方法:采用一种特殊的B样条展开式作为伸缩函数,构造了具有明确几何意义的变换矩阵,用它作用于待变形的曲线,可使曲线发生变形。此方法数学模型简单而变形效果良好。展开式的系数作为变形的控制参数,每个参数具有局部可控性,变形效果较丰富。可分别定量地控制变形的发生区间、变形区间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、CAD等领域。

An Affine Mapping B-spline Method of Deformation for Planar Parametric Curves

A new technique of deformation for parametric curves is presented in this article.First,a special extension factor of B-spline is introduced and a transformation matrix is constructed.Then,original curves are deformed through multiplying it by the transformation matrix.The coefficients of the B-spline expension are the control parameters of the deformation.Interactively adjusting these parameters,we can quantified control the region of deformation,the amount of deformation,the direction of deformation and the continuity and smoothing of junction between deformed and undeformed portions.The implementation shows that the method is simple,intuitive,easy to control and ideal deformation effects to be got.h can be used in many fields such as geometric modeling,computer animation and CAD.