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A two-level approach to implicit surface modeling with compactly supported radial basis functions

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Abstract

We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear combination of compactly supported radial basis functions (CSRBFs). The method preserves the simplicity and efficiency of implicit surface interpolation with CSRBFs and the reconstructed implicit surface owns the attributes, which are previously only associated with globally supported or globally regularized radial basis functions, such as exhibiting less extra zero-level sets, suitable for inside and outside tests. First, in the coarse scale approximation, we choose basis function centers on a grid that covers the enlarged bounding box of the given point set and compute their signed distances to the underlying surface using local quadratic approximations of the nearest surface points. Then a fitting to the residual errors on the surface points and additional off-surface points is performed with fine scale basis functions. The final function is the sum of the two intermediate functions and is a good approximation of the signed distance field to the surface in the bounding box. Examples of surface reconstruction and set operations between shapes are provided.

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Acknowledgments

The authors thank their colleagues at Shandong University and University of West Bohemia for their critical comments and suggestions. This work has been supported by the international exchange scholarship between China and Czech governments, the project VIRTUAL 2C06002 Ministry of Education of the Czech Republic and the Key Project in the National Science & Technology Pillar Program of China under grant No.2008BAH29B02.

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Jinan, China

    Rongjiang Pan

  2. Centre of Computer Graphics and Data Visualization, Department of Computer Science and Engineering, University of West Bohemia, Plzen, Czech Republic

    Vaclav Skala

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  1. Rongjiang Pan
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  2. Vaclav Skala
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Correspondence to Rongjiang Pan.

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Pan, R., Skala, V. A two-level approach to implicit surface modeling with compactly supported radial basis functions. Engineering with Computers 27, 299–307 (2011). https://doi.org/10.1007/s00366-010-0199-1

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