摘要
构造了三阶三次等距结点的多项式B样条参数曲线,给出了deBoor控制顶点与分段三次Bézier控制顶点的关系式。该曲线具有一些类似于二次B样条曲线的性质:关于参变量为C1连续,每个样条区间上的曲线由三个deBoor控制顶点的线性组合表示,具有仿射变换下的不变性,包含了二次均匀B样条曲线等。还具有形状可调性质:调配函数中含有形状参数,具有明显的几何意义,可用于调控曲线的形状或变形。给出了其具有凸包性、对deBoor控制多边形保形性等性质及其条件,讨论了形状参数对曲线形状的影响。
This paper constructs three order cubic equidistant-knot polynomial B-spline parameter curve,and relationship function of de Boor control point and segment cubic Bézier control point.This curve has the property similar to quadratic B-spline curve： C1-continuous with respect to parametric variable,curves at each spline intervals represented by linear combinations of three de Boor control points,with invariability under affine transformation,including quadratic uniform B-spline curve,etc;And property of shape adjustability：blending function including shape parameter,and with explicit geometric significance,be able applying to control the shape or transform of the curve.And provide the properties and conditions of convex hull property,conformal property of de Boor control polygon,discuss the impact of shape parameter to curve shape.
出处
《计算机工程与应用》
CSCD
北大核心
2010年第15期142-145,共4页
Computer Engineering and Applications
关键词
样条曲线
调配函数
形状参数
仿射不变性
spline curve
blending function
shape parameter
affine invariant
