Computing Euler Number Of Global Discrete Grids Based On Diamond

摘要

Global Discrete Grids Based on Diamond has become a research topic recently which is one of important Global Discrete Grids. In digital topology the Euler number is one of the important parameters to deal with the digital image. And the computation of Euler number of Spherical Grids is also the problem that should be solved firstly when describing and referring the spherical surface grids topological relation. In this paper, diamond-shaped block is taken as a basic unit of global discrete grids to compute the Spherical surface Grids Euler number. The rows and columns subdivision algorithm of spherical surface grids is given firstly when subdividing global discrete grids based on diamond, then the rows and columns are used to compute the binary code of diamond-shaped block and convert the binary code to the position code of linear quadtree, finally the position code of linear quadtree is used as keyword for diamond-shaped block adjacent search in global scale. And this paper will mainly discuss how to compute the Euler number of spherical surface grids after making the use of the geometry similarity between square grids and diamond-shaped grids. And then the method will be given to compute four-connectivity and eight-connectivity of Euler number of Global Discrete Grids based on diamond. Most importantly, the algorithm has been realized by Direct3D and C++, and the result turns out to be correct and feasible. In the future, we will use this Spherical Grids Euler number to compute the topological relation between complex spherical object.