内心细分法的一个变式

A Variation of Incenter Subdivision Scheme

内心细分法中,临时切向调整的方法比较复杂,且几何意义不明显,为此给出了内心细分法的一个变式.给定初始点列及其切向,内心细分法的每一个细分步骤分为2个阶段:首先根据老点和切向确定新点及其临时切向,然后调整临时切向用于下一步细分.文中给出了调整切向的新方法,使切向计算更简单、几何意义更明显.最后通过大量的数值实例验证了极限曲线的G2连续性及光顺性与细分参数选择之间的关系.

The computation of the new tangents of incenter subdivision scheme is complex and without intuitive geometrical meaning. In this paper, we give a variation of incenter subdivision scheme by modifying the computation of new tangents with simple computation and intuitive geometrical meaning. Given the initial point array and initial tangent vectors, there are two substeps in each subdivision step of our new scheme： firstly the new points and the provisional tangents are determined by the same rules of incenter subdivision scheme, then the new tangent at each point is defined as a linear combination of its provisional tangent as well as the tangent sampled at a circle passing this point and its two adjacent points. The relations between G2 continuity and fairness of the limit curves and the selection of combination coefficient in subdivision process are examined by numerical examples.