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• 专论：第21届中国计算机辅助设计与图形学暨第11届全国几何设计与计算机联合会议(CAD&CG GDC 2018 桂林) • 上一篇    下一篇

基于稀疏解组合优化的广义重心坐标

  

  1. 桂林电子科技大学数学与计算科学学院，广西 桂林 541004
  • 出版日期:2019-02-28 发布日期:2019-02-27
  • 基金资助:
    国家自然科学基金项目(1170119)；广西高校数据分析与计算重点实验室项目

Generalized Barycentric Coordinates Based on Combinatorial  Optimization of Sparse Solutions

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi 541004, China
  • Online:2019-02-28 Published:2019-02-27

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摘要： 根据广义重心坐标线性运算的性质与特点，运用广义重心坐标的稀疏解权函数的 调和平均组合方法，对空间凸多面体顶点设计了一种求解广义重心坐标的算法，且权函数是带 有保形参数的一元函数，因而具有保形优化的特点。构造了 2 种不同类型的带形参权函数，运 用不同权函数及其参数的广义重心坐标将平面图形映射到空间曲面的实例进行了分析，并应用 重心坐标常用的等值线工具对保形性进行了比较。

关键词: 广义重心坐标, 稀疏解, 组合优化, 权函数

Abstract: According to the nature and characteristic of the linear operation of generalized barycentric coordinates, by means of a combination of weighted harmonic mean funcitons, an algorithm for solving generalized barycentric coordinates is designed to meet the demands of the vertexes of spatial convex polyhedron, in which the weighted function is a unary function with conformal parameters, thus it is characterized with conformal optimization. Two different types of weighted functions are constructed in this paper, and they are both used to calculate the generalized barycentric coordinates. An example of a plane figure is mapped into a space surface by the means, which is to be described and analyzed with different weighted functions and parameters. By means of their contours, the generalized barycentric coordinates for the example are analyzed and compared.

Key words: generalized barycentric coordinates, sparse solution, combinatorial optimization, weighted functions