Abstract: When performing the multi-resolution DEM expression based on Quad-tree structure, topological crack generates at the meeting of areas of different resolution levels. Holes appear in the mesh between neighboring faces of different refinement depths. Although there are many methods of eliminating the crack, but mostly belong to the "post processing", and there are many restrictions. A new theory of multi-resolution combination maps is introduced, and a seamless expression of global multi-resolution DEM is discussed based on multi-resolution half-edges. The main contents are as follows. Firstly, the unified expression and principle of crack elimination of Global discrete grids are studied based on multi-resolution combination maps, and some methods are put forward based on spherical diamond grids, including encoding and coordinate transformation. Then, seamless expression algorithm is designed and achieved. Finally, by using C++ language and DirectX tools, an experimental system is developed, and the results show that seamless expression of the global multi-resolution DEMs can be carried out with a method of making a tiny adjustment of node subdivision. Compared with the traditional methods, the method in the paper can solve the crack problem from the underlying data structure.