Three special subspaces of ect spline space : polynomial space , the algebraic trigonometric spline space and hyperbolic spline space are investigated in detail . the generalized p lya polynomials , associated with the three subspaces , are calculated . both of boehm algorithm and oslo algorithm for the ect b spline curves of order 4 over the three special subspaces are displayed 三、在多項(xiàng)式樣條空間、代數(shù)三角樣條空間和代數(shù)雙曲樣條空間這三個(gè)具體的ect空間上,給出了相應(yīng)典范ect組和廣義p lya多項(xiàng)式的計(jì)算和顯示表示,展示了幾個(gè)低階ectb樣條曲線各種插入節(jié)點(diǎn)算法的求解全過程
Secondly , we introduce the recurrence definition of the non - uniform algebraic - hyperbolic b - spline basis using divided differences and the de boor - fix recurrence definition on polynomial functions , and based on the new forms , algebraic - hyperbolic b - spline curves are obtained . they share most of the properties as those of the b - spline curves in the polynomial space . we focus on deducing the calculating and knot inserting formulae for this new kind of curves and then prove that they have the variation diminishing properties 二、利用廣義差商,基于多項(xiàng)式b樣條的deboor - fix遞推定義,給出了任意階非均勻代數(shù)雙曲b樣條的遞推定義,由此構(gòu)造曲線,證明它的幾何不變性、仿射不變性、凸包性、 v . d .性等,重點(diǎn)給出了非均勻代數(shù)雙曲b樣條曲線的遞歸求值和節(jié)點(diǎn)插入算法,算法簡單且穩(wěn)定,便于在計(jì)算機(jī)上實(shí)現(xiàn)