The way of triangulating spatial points based on manifold study is advanced in this paper. According to the theory of manifold

spatial points is the measurement result of a certain 2D manifold in 3D space

so the process of triangulation is to search 2D manifold substantively.Therefore

the paper divides triangulating spatial points into three steps.The first step is to decrease the dimension of points on basis of the correlative relation among points within a certain distance and the condition of minimizing the reconstruction error.The second step is to carry out Delaunay partition for points on plane.At last

the topology connection relation is mapped to 3D spatial points.The result is that the difference between the triangle net and object’s surface achieves minimum practicality.This way can be easily acknowIedged

reduces complication and diminish the diversity in triangulation.Many experiments show the method provided in paper can achieve good result for objects which are not homeomorphism to sphere by choosing appropriate method of manifold study and neighborhoods.