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 m...

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Bibliographic Details
Published in:Computer aided geometric design 2012-10, Vol.29 (7), p.422-434
Main Authors: Yoshihara, Hiroki, Yoshii, Tatsuya, Shibutani, Tadahiro, Maekawa, Takashi
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
B-spline surfaces
Catmull–Clark subdivision surfaces
Computer science
control theory
systems
Exact sciences and technology
Iterative geometric fitting method
Level set method
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Pattern recognition. Digital image processing. Computational geometry
Quadrilateral mesh
Sciences and techniques of general use
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Summary: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. ► We automatically reconstruct an arbitrary topological surface from point clouds. ► Reconstructed surface includes quad mesh, CC-subdivision, and B-spline surfaces. ► The technique is based on the level set method and the iterative geometric fitting. ► The method is not only efficient, but also generates high-quality surfaces.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2012.03.007