一类多参数的曲线细分格式

A Class of Curve Subdivision Schemes with Several Parameters

构造了一类收敛的多参数差分格式,根据细分格式和差分格式的关系以及连续性条件可得到任意阶连续的多参数曲线细分格式.通过选取合适的参数可以得到一些经典的曲线细分格式,如Chaikin格式、三次样条细分格式和四点插值格式等;同时设计了一种C1连续的不对称三点插值格式,可以生成不对称的极限曲线.给出了同阶差分格式线性组合的性质,从而可设计出更多收敛的多参数曲线细分格式.

A class of convergent difference schemes with several parameters is proposed. According to the relationship between the subdivision scheme and its difference scheme and the sufficient condition for C^1 continuity, we can devise curve subdivision schemes with arbitrary order continuity. By setting appropriate parameters, some classical curve subdivision schemes such as the Chaikin＇s scheme, the cubic B-spline scheme and 4-polnt interpolating scheme can be obtained. A C^1-continuous asymmetric 3-point interpolating scheme is also presented to model asymmetric limit curves. Furthermore, the property of the linear combination of the difference schemes of the same order is analyzed, which can help to devise more convergent curve subdivision schemes with several parameters.