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

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.