Multi-Level Partition of Unity Algebraic Point Set Surfaces

Abstract

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

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Correspondence to Chun-Xia Xiao.

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This work was partly supported by the National Natural Science Foundation of China under Grant Nos. 60803081, 61070081, the National High Technology Research and Development 863 Program of China under Grant No. 2008AA121603, the Fundamental Research Funds for the Central Universities under Grant No. 6081005, and the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No. 200804861038.

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Xiao, CX. Multi-Level Partition of Unity Algebraic Point Set Surfaces. J. Comput. Sci. Technol. 26, 229–238 (2011). https://doi.org/10.1007/s11390-011-9429-2

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Keywords

  • moving least squares
  • surface reconstruction
  • implicit modeling
  • partition of unity approximation