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
Alexa, M., et al.: Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph. 9(1), 3–15 (2003)
Amenta, N., Kil, Y.J.: Defining point-set surface. ACM Trans. Graph (SIGGRAPH 2004) 23(3), 264–270 (2004)
Chavez, E., Navarro, G., Baeza-Yates, R., Marroquin, J.L.: Search in metric spaces. ACM Comput. Surv. 33(3), 273–321 (2001)
de Berg, M., van Kreveld, M., Overmas, M., Schwarzkopf, O.: Computational Geometry: Algorithms and Applications. Springer, Heidelberg (1997)
Hoppe, H.: Progressive meshes. In: Proc. SIGGRAPH 1996, pp. 99–108 (1996)
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)
Levin, D.: Mesh-independent surface interpolation. In: Brunnett, G., et al. (eds.) Geometric Modeling for Scientific Visualization, pp. 37–49. Springer, Heidelberg (2003)
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)
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)
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)
Powell, M.J.D.: The theory of radial basis function approximation in 1990. Advances in Numerical Analysis, 105–210 (1990)
Renka, R.J.: Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Software 14(2), 139–148 (1988)
Wendland, H.: Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree. Adv. Comput. Math. 4, 389–396 (1995)
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)
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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
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