B样条曲线曲面GC^2扩展  

An Extension Algorithm for B-Splines with GC^2-Continuous

作　　者：范辉[1] 张彩明[2] 李晋江[1] 

机构地区：[1]山东工商学院信息与电子工程学院,烟台264005 [2]山东经济学院计算机科学与技术系,济南250014

出　　处：《计算机学报》2005年第6期933-938,共6页Chinese Journal of Computers

基　　金：国家自然科学基金(60173052);山东省自然科学基金(Y2002G08)资助

摘　　要：提出了一个扩展B样条曲线曲面的新方法.扩展B样条曲线曲面的关键是为新增加的点确定节点值.新方法的基本思想是:首先,B样条曲线和扩展部分在连接点处满足GC2连续,用能量极小化方法确定扩展部分的曲线形状,通过对曲线重新参数化使两部分曲线满足C2连续,进而确定新增加点的节点值.新B样条曲线的控制点由一个显式递推公式计算.原B样条曲线和扩展后的部分合在一起形成一条新的B样条曲线.新的B样条曲线满足原B样条曲线和扩展的点.文章还讨论了运用该方法进行B样条曲面扩展,且以实例对新方法与其它方法进行了比较.结果表明新方法的光顺性得到了明显改善,曲率变化更平坦,且有较小的旋转数指标.In CAGD, in order to adjust the curves to pass a new point easily, it is necessary to get a method of extension. A new method is presented for extending B spline to an extension point. The crux of extending B splines is to determine the knot value for the extension point. The basic idea of the new method can be described as follows. First, the GC 2 continuous condition is satisfied at the joint between B spline curve and the part of extension. Curve shape is determined by minimizing energy, and hence the corresponding knot is determined. Original B spline and extended curve are put together to form a new B pline curve. The control point of new B spline can be computed by an explicit recurrence formula. The new B spline curve satisfies original curve and extension points. This method can be extended to B spline surface. Some computing examples for comparing the new method with other methods are also included. The result indicates that the fairing of the new method is obviously improved, having less absolute rotation number, and the changes of curvature is smoother. The extension curve get by new method has low energy and good natural shape.

关 键 词：B样条曲线 参数化 GC^2连续 曲线扩展 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]