An algorithm for topology reconstruction is promoted that takes as input an unorganized set of points with known density and carries out as output simplicial surfaces. This algorithm uses the local flatness of surface, searches the local reconstruction for every point from the 3D Delaunay triangulation, and from the union of such locale reconstruction, carries out corresponding manifolds by deleting incompatible triangles. With an optimizing surface triangulation as result, this algorithm is suitable for surfaces of arbitrary topology, including nonorientable ones, hence can be applicable to visualization in scientific computing, sculpture surface modeling, and reverse engineering.