中文摘要：

为了得到具有更好性质的Lupa?q-Bézier曲线的递归求值算法,通过应用Pascal-type关系和重新参数化,构造具有显式矩阵表示的deCasteljau算法,并得到具有对称性质的Lupa?q-Bézier曲线.首先,利用Pascal-type关系构造具有显式矩阵表示的deCasteljau算法,该算法具有经典Bézier曲线的deCasteljau算法的3个性质;然后,通过重新参数化调整Lupa?q-Bézier曲线上点的分布,得到具有对称性质的Lupa?q-Bernstein基函数和Lupa?q-Bézier曲线,给出重新参数化后Lupa?q-Bézier曲线的一种矩阵累乘的递归生成方法.另外,从应用角度给出了用一条Lupa?q-Bézier曲线逼近2条光滑拼接的Bézier曲线的数值实例,进而验证了文中算法的有效性.

英文摘要：

To obtain Lupa? q-Bézier curves by recursive evaluation algorithms with better properties, new deCasteljau algorithms and Lupa? q-Bézier curves with symmetry are constructed by means of Pascal-typeformula and reparameterization. A new de Casteljau algorithm with explicit matrix representation is constructedby applying Pascal-type formula, and the algorithm shares three properties with de Casteljau algorithmof classical Bézier curves. Lupa? q-Bernstein basis functions and Lupa? q-Bézier curves with symmetry aregained from reparameterization, moreover, Lupa? q-Bézier curves reparameterized can be generated by multiplybidiagonal matrices successively on control polygon. In addition, numerical examples of using oneLupa? q-Bézier curve to approximate two blending Bézier curves are presented as a simple application of deCasteljau algorithm with explicit matrix representation and the effectiveness of the algorithm is verified.