Abstract: Aiming at the problem of 3D printing cannot manufacture lattice structure with overhanging rods or nodes,3D shape approximation and infill algorithms with self-supporting lattice structure are proposed.Firstly,rhombic hexahedron is used as the unit cell and the function of the geometry of the unit cell and its self-supporting property is constructed,a self-supporting unit cell with minimal volume is further generated which covers the whole input 3D shape.Then the 3D shape is approximated by the iterative subdivision of the unit cells under the constraint of the shortest edge length and the number of subdivisions.Finally,to guarantee the printability of the generated lattice structure,self-supporting struts are added to support the overhanging nodes.In addition,the 3D self-supporting infill structure is generated by the subdivision of unit cells.Experimental models are selected from 3D ShapeNet,and then the algorithms are implemented and the results on VS2010 and MATLAB R2017a are visualized.The results demonstrate the effectiveness and robustness of the proposed algorithms for 3D shape approximation and infill.