【摘要】 基于B样条的光滑性,利用Laurent多项式与细分生成多项式之间的关系,构造出可生成一类m重融合型细分格式的Laurent多项式.构造的Laurent多项式不仅包含了较多经典格式,还可衍生出C~3连续且保持细节特征的新格式;特别地,分析了双参数四点三重融合型格式的支集和连续性,并给出和证明了格式C~3连续的充分必要条件.最后通过大量数值实例展示了参数对极限曲线的影响;对比图例表明,文中格式生成的极限曲线能较好地保持细节特征.更多还原

【Abstract】 Based on the smoothness of B-splines, a Laurent polynomial which can generate a class of m-ary combined subdivision schemes is constructed by the relationship between Laurent polynomials and generated polynomials. The new Laurent polynomial can not only contain some classical subdivision schemes but also generalize C3-continuous new-type schemes with detailed features. Specifically, the support and continuities of the combined four-point ternary scheme has been analyzed; the necessary and sufficient condition for its C3 continuity are also given and proved. Plenty of numerical examples are given to illustrate the influence of parameters on the limit curves. The comparisons show that the limit curves generated by the scheme can keep the detail features well.更多还原