一类矩形域上生成保单调面的细分法

A class of montonicity-preserving subdivision scheme.

离散细分法是构造曲线曲面的一类重要方法,而在实际中某些细分法要求是保形的,即初始控制点是单调的,那么细分最终生成的曲线或曲面也要求是单调的.本文用构造法构造了一类在等距离意义下矩形域上生成线性保单调曲面的细分法,该细分法具有插值性、局部性、线性不变性,齐次性和仿射不变性,并用数学归纳法证明了该类细分法的保单调性、收敛性和光滑性.

Montonicity- preserving subdivision scheme is constructed and its convergence and smoothness are proved by mathematical induction. The subdivision scheme is interpolatory, local, invariable and affine invariant. Such subdivision scheme is needed to obtain final curves and surface which maintain the property of montonicity from these original montonicity data because some original montonicity data can be only gotten in some industrial application.