摘要
当α→0时,均匀CB样条曲线逼近相应阶的均匀B样条曲线,改变α的取值时,生成的均匀CB样条曲线逼近控制多边形的极限位置是相应阶的均匀B样条曲线.为了突破这种逼近极限,构造一种新的均匀CB样条曲线.先构造一种三次均匀CB样条基,再运用积分递归定义出任意阶的均匀CB样条基.由这些基构造的均匀CB样条曲线与原CB样条曲线具有类似的性质:凸包性、几何不变性、局部性、对称性等,但随着α取值的不同生成相应阶的均匀B样条两侧曲线,能够更好的逼近控制多边形.最后给出了用新的均匀CB样条曲线精确表示椭圆,圆,抛物线,螺旋线等.定义的新均匀CB样条拓展了均匀CB样条曲线曲面的造型能力.
When α approximate zero, uniform CB spline curves approximate the same order uniform B spline curves. The CB spline curves are constructed with the change of α value. These curves approach the control polygon. Their limited position is the same order uniform B spline curve. Another uniform CB spline curves are presented in order to breaking through the approximation limit. Firstly, constructed a three degree uniform CB spline basis function. Secondly, recursively defined any order uniform CB spline basis functions by integration. The uniform CB spline curves which is constructed on these new CB spline basis functions have similar properties as the original uniform CB spline curves. Such as convex hull, geometric invariance, locality and symmetry. The curves on both sides of the same order uniform B spline ate constructed with the change of α value. They can approximate the control polygon well. Lastly, the ellipse and circle and parabola and spiral can be accurately represented with them. They expand the ability to the uniform CB curve and surface modeling.
出处
《小型微型计算机系统》
CSCD
北大核心
2013年第5期1189-1193,共5页
Journal of Chinese Computer Systems
基金
安徽省教育厅重点项目(2011AJZR0071)资助
安徽省自然科学基金项目(11040606M06)资助
关键词
CB1样条曲线
CB2样条曲线
逼近
控制多边形
uniform CB1 spline curves
uniform CB2 spline curves
approximate
control polygon
作者简介
E-mail： xiong780807@ 163. com熊建，男，1978年生，硕士，讲师，研究方向为数值逼近、CAGD、计算机图形学；
郭清伟，男，1968年生，博士，副教授，主要研究方向为计算机辅助几何设计、数值逼近、计算机图形学等．
