Computational geometry often suffers from problems of complexity and computing efficiency, particularly in multidimensional space. Situated in a geometric context, the paper focuses on random sampling algorithms for geometric optimization, including convex hulls, Delaunay triangles, and Voronoi diagrams. Using a random sample incremental technique, the author optimize the partition of space to represent a set of points in two- and three-dimensional space.Computational geometry often suffers from problems of complexity and computing efficiency, particularly in multidimensional space. Situated in a geometric context, the paper focuses on random sampling algorithms for geometric optimization, including convex hulls, Delaunay triangles, and Voronoi diagrams. Using a random sample incremental technique, the author optimize the partition of space to represent a set of points in two- and three-dimensional space.