Topologically robust B-spline surface reconstruction from point clouds using level set methods and iterative geometric fitting algorithms Original Research Article

In this paper, we present a procedure for automatically reconstructing an arbitrary topological surface from an unorganized point data set; this surface will have three representations, namely quadrilateral meshes, Catmull–Clark subdivision surfaces, and B-spline surfaces. Our novel reconstruction method adapts a level set method to capture the topology of the point clouds in a robust manner and then employs an iterative geometric fitting algorithm to generate high-quality Catmull–Clark subdivision surfaces. A quadrilateral mesh is generated by projecting the control net of the resulting Catmull–Clark surface onto its limit surface. Finally, the control net of the Catmull–Clark surface is converted to that of a B-spline surface. The reconstructed models of topologically complex models show the effectiveness of the proposed algorithm.