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An Efficient Implementation of RBF-Based Progressive Point-Sampled Geometry

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Geometric Modeling and Processing - GMP 2006 (GMP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4077))

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Abstract

In this paper we address practical implementation issues of generating a progressive representation of point-sampled geometry. Fast and stable algorithms are proposed to efficiently implement a progressive version of the modified RBF Shepard’s method. Comparisons with several well-known methods are presented, showing that the proposed algorithms can achieve good balance between geometric error reduction and time efficiency.

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References

  1. Alexa, M., et al.: Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph. 9(1), 3–15 (2003)

    Article  Google Scholar 

  2. Amenta, N., Kil, Y.J.: Defining point-set surface. ACM Trans. Graph (SIGGRAPH 2004) 23(3), 264–270 (2004)

    Article  Google Scholar 

  3. Chavez, E., Navarro, G., Baeza-Yates, R., Marroquin, J.L.: Search in metric spaces. ACM Comput. Surv. 33(3), 273–321 (2001)

    Article  Google Scholar 

  4. de Berg, M., van Kreveld, M., Overmas, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  5. Hoppe, H.: Progressive meshes. In: Proc. SIGGRAPH 1996, pp. 99–108 (1996)

    Google Scholar 

  6. Lazzaro, D., Montefusco, L.B.: Radial basis functions for the multivariate interpolation of large scattered data. J. Comput. Appl. Math. 140(1-2), 521–536 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Levin, D.: Mesh-independent surface interpolation. In: Brunnett, G., et al. (eds.) Geometric Modeling for Scientific Visualization, pp. 37–49. Springer, Heidelberg (2003)

    Google Scholar 

  8. Liu, Y.J., Tang, K., Yuen, M.M.F.: Efficient and stable numerical algorithms on equilibrium equations for geometric modeling. In: Proc. GMP 2004, pp. 291–300 (2004)

    Google Scholar 

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

    Article  Google Scholar 

  10. Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M.: Shape modeling with point-sampled geometry. ACM Trans. Graph (SIGGRAPH 2003) 22(3), 641–650 (2003)

    Article  Google Scholar 

  11. Powell, M.J.D.: The theory of radial basis function approximation in 1990. Advances in Numerical Analysis, 105–210 (1990)

    Google Scholar 

  12. Renka, R.J.: Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Software 14(2), 139–148 (1988)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. Zwicker, M., Pauly, M., Knoll, O., Gross, M.: Pointshop 3D: an interactive system for point-based surface editing. ACM Trans. Graph. 21(3), 322–329 (2002)

    Article  Google Scholar 

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Liu, YJ., Tang, K., Ajay, J. (2006). An Efficient Implementation of RBF-Based Progressive Point-Sampled Geometry. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_51

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  • DOI: https://doi.org/10.1007/11802914_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36711-6

  • Online ISBN: 978-3-540-36865-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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