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