重心坐标系下三次C样条奇拐点分析

The singularity and inflection points distribution of planar cubic C-spline in barycentric coordinate space

介绍三次C样条和重心坐标,同时给出重心坐标系下三次C样条的参数表示形式,利用仿射不变量来研究三次C样条奇拐点存在判别条件,并且对仿射不变量p的各种情况进行讨论,同时简化奇拐点判别条件。

This paper first introduces the concepts of cubic C-spline and barycentric coordinate space,and then gives the cubic C-spline parametric form in barycentric coordinate space. The affine invariant is introduced to find the sufficient and necessary discriminant of singularity and inflection points in the barycentric space. Every situations of affine invariant p is also discussed so that it can be easier to distinguish the singularity and inflection points.