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This paper presents a surface reconstruction algorithm from scattered point sets based on Delaunay. It begins with computing the Delaunay triangulation of the sampling point sets, extract the primary triangles from Delaunay tetrahedrons, and then select surface triangles by manifold extraction. Compared with the traditional approach based on Delaunay, the proposed algorithm requires only one-pass Delaunay computation and needs no Voronoi information, so it is more efficient. Experimental results show that this method is robust and effective on handling surfaces with complex topology, boundaries, and even non-uniform sample points.