一种基于切向量的非线性ternary插值细分法

A nonlinear ternary interpolatory subdivision scheme based on tangent vector

针对光滑曲线的构造,提出了一种基于切向量的非线性ternary插值细分方法.该细分法通过沿相邻两点的切向量方向产生偏移量来计算新点,其中偏移量可由参数进行控制.文中对该细分格式的性质进行了分析.结果表明该细分格式生成的极限曲线具有G1连续性和保凸性,且在参数合适的取值范围内,极限曲线可以避免自交.

In order to achieve smooth curves ,a nonlinear ternary interpolatory subdivision scheme based on tangent vector is given which got the two new points by computing the offsets in the two adjacent old points and controlled it by the parameters ,then the properties analysis is proposed .The algorithm has the property of convexity-preserving and the limit curve is G1 continuous and in the appropriate range of parameters ,the limit curve can avoid intersection .