三角形上的分片二阶光滑有理插值

三角形上的分片二阶光滑有理插值 Smooth Rational Interpolants of Piecewise Two-Order Over Triangles 余文波 YU Wenbo1 1 first-author 战荫伟 ZHAN Yinwei2 2 江西理工大学软件学院 江西理工大学软件学院 School of Software,Jiangxi University of Science and Technology School of Software,Jiangxi University of Science and Technology 广东工业大学计算机学院 广东工业大学计算机学院 Faculty of Computer,Guangdong University of Technology Faculty of Computer,Guangdong University of Technology 给出三角形上一种C2插值格式,插值函数由偏插值函数加权求和而成.偏插值函数对应于每一个顶点:构造三角形的一种分割,在其上定义一个分片5次多项式,只插值该顶点及其相邻两边上的插值条件.对应于每一个顶点有一个权函数,它由重心坐标定义,是一个有理函数.所得的插值函数是一个分片有理函数,只需被插函数在三角形顶点处的直至2阶导数值,利用多项式的Bernstein-Bézier表示,该插值函数易于表达和计算. In this paper,interpolating function consists of sum of partial interpolations with weight functions in C2 interpolation scheme over triangles.Each partial interpolation with respect to a vertex is a piecewise quintics defined on a split of a triangle,interpolating the vertex and its two sides.The corresponding weight function of each vertex is a rational function in barycentric coordinates.The resulted interpolation,a piecewise rational function,assuming given values and derivatives of orders up to 2 at the vertices of the triangle,is easy to be described and calculated with Bernstein-Bézier polynomials. Berstein-Bézier形式 偏插值 二元样条 有理函数 Bernstein-Bézier form partial interpolation bivariate spines rational functions 10.14188/j.1671-8836.2011.03.013 O241.3 江西省教育厅科技计划资助项目（GJJ11479） 2011-03-01 2021-04-01 3 57