平面C-B样条的奇拐点分析

平面C-B样条曲线是三次均匀B样条的推广.通过移动C-B样条曲线段的一个控制点而固定其余三个控制点的方法,讨论了在曲线上形成零曲率点的移动控制点的轨迹,得到了C-B样条曲线段的尖点判别曲线、拐点判别区域,同时也给出了在曲线段上生成重结点的移动控制点的轨迹区域.

The Analysis of Singularities and Inflection Points on Planar C-B Spline Curve

The planar C-B spline curve is extension of cubic uniform B-spline curve.Let a control point be vary and the rest three be fixed,we get the cusp discriminant curve and inflection point discriminant region on planar C-B spline curve segment by discussing the locus of the moving control point that yields a zero curvature point.We also specify the region that is desicribed by those positions of the moving control point that yield a loop on the curve segment.