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A method of boundary estimation from 3D scattered point data without normals by implicit function and Delaunay tetrahedralization

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Abstract

A method of boundary estimation from 3D scattered point data has been proposed. For estimating a boundary, the implicit function-based method and the Delaunay tetrahedralization are mainly used in the proposed method. An advantage of the proposed method is that point coordinates are only required as input data. Namely, normals on each of given points are not required as input data. Instead, the point normals are estimated three times. After each procedure for estimating point normals, the accuracy of the estimated normals may be better. Therefore, the geometric structure of a surface generated with the estimated normals is gradually closer to the original surface. Numerical experiments demonstrate that the proposed method enables to estimate an expected boundary without normals as input data. In addition, the performance of the proposed method is numerically investigated. The estimated boundary can be obtained as an implicit surface or as a set of triangles.

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References

  • Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37:229–256

    Article  MathSciNet  MATH  Google Scholar 

  • Bloomenthal J (1988) Polygonization of implicit surfaces. Comput Aided Geom Design 5(4):341–355

    Article  MathSciNet  MATH  Google Scholar 

  • Brebbia CA, Dominguez J (1992) Boundary elements: an introductory course, 2nd edn. WIT Press, McGraw-Hill

    MATH  Google Scholar 

  • Chati MK, Mukherjee S (2000) The boundary node method for three-dimensional problems in potential theory. Int J Numer Methods Eng 47:1523–1547

    Article  MathSciNet  MATH  Google Scholar 

  • George A, Liu JWH (1981) Computer solution of large sparse positive definite systems. Prentice-Hall Inc., Englewood Cliffs

    MATH  Google Scholar 

  • Gumhold S, Wang X, Macleod R (2001) Feature extraction from point clouds. In: Proceedings of the 10th international meshing roundtable. Newport Beach, California, pp 293–305

  • Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. In: Proceedings of ACM SIGGRAPH 92. Chicago, pp 71–78

  • Itoh T (2009) A method of boundary estimation from 3D scattered point data without normals by implicit function and Delaunay tetrahedralization. In: Proceedings of Asia simulation conference 2009 (CD-ROM), Paper ID: 064, Kusatsu

  • Itoh T, Saitoh A, Kamitani A, Nakamura H (2010) Three dimensional extended boundary node method to potential problem. Plasma Fusion Res 5:S2111

    Article  Google Scholar 

  • Liu GR (2009) Meshfree methods: moving beyond the finite element method, 2nd edn. CRC Press LLC, Boca Raton

    Book  Google Scholar 

  • Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel HP (2003) Multi-level partition of unity implicits. ACM Trans Graph 22(3):463–470

    Article  Google Scholar 

  • Otsu N (1980) An automatic threshold selection method based on discriminant and least squares criteria (in Japanese). IEICEJ J63-D(4):349–356

  • Taniguchi T, Moriwaki K (2006) Automatic mesh generation for 3D FEM—robust Delaunay triangulation (in Japanese). Morikita, Tokyo

    Google Scholar 

  • Tobor I, Reuter P, Schlick C (2004) Efficient reconstruction of large scattered geometric datasets using the partition of unity and radial basis functions. WSCG 12(3):467–474

    Google Scholar 

  • Turk G, O’Brien JF (2002) Modelling with implicit surfaces that interpolate. ACM Trans Graph 21(4):855–873

    Article  Google Scholar 

  • Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Adv Comput Math 4(4):389–396

    Article  MathSciNet  MATH  Google Scholar 

  • Yamashita Y, Moriwaki K, Taniguchi T (2001) Surface generation of arbitrary 3-dimensional domain by using nodes on its surface (in Japanese). Transactions of JSCES 2001(20010032). http://www.jstage.jst.go.jp/article/jsces/2001/0/2001_20010032/_article/-char/ja/

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Acknowledgments

We would like to thank the Computer Graphics Laboratory of Ritsumeikan University for the Rits Bunny model. We would also like to thank the Stanford 3D Scanning Repository for the Stanford Bunny model and for the David model. This work was supported by KAKENHI (No. 20700098 and No. 22360042).

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  1. Faculty of Science and Technology, Seikei University, Musashino, Tokyo, 180-8633, Japan

    Taku Itoh

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  1. Taku Itoh
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Correspondence to Taku Itoh.

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Itoh, T. A method of boundary estimation from 3D scattered point data without normals by implicit function and Delaunay tetrahedralization. J Vis 14, 381–391 (2011). https://doi.org/10.1007/s12650-011-0088-8

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  • DOI: https://doi.org/10.1007/s12650-011-0088-8

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