Abstract
Recently unstructured dense point sets have become a new representation of geometric shapes. In this paper we introduce a novel framework within which several usable error metrics are analyzed and the most basic properties of the progressive point-sampled geometry are characterized. Another distinct feature of the proposed framework is its compatibility with most previously proposed surface inference engines. Given the proposed framework, the performances of four representative well-reputed engines are studied and compared.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T., 2003. Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph., 9(1):3–15. [doi:10.1109/TVCG.2003.1175093]
Amenta, N., Bern, M., 1999. Surface reconstruction by Voronoi filtering. Discret. Comput. Geom., 22(4):481–504. [doi:10.1007/PL00009475]
Amenta, N., Kil, Y.J., 2004. Defining point-set surface. ACM Trans. Graph. (SIGGRAPH’04), 23(3):264–270. [doi:10.1145/1015706.1015713]
Amenta, N., Bern, M., Kamvysselis, M., 1998. A New Voronoi-based Surface Reconstruction Algorithm. Proc. SIGGRAPH’98, p.415–422.
Carr, J.C., Betson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R., 2001. Reconstruction and Representation of 3D Objects with Radial Basis Functions. Proc. SIGGRAPH’01, p.67–76.
Chávez, E., Navarro, G., Baeza-Yates, R., Marroquin, J.L., 2001. Search in metric spaces. ACM Comput. Surv., 33(3):273–321. [doi:10.1145/502807.502808]
Cheng, S.W., Dey, T.K., Ramos, E., Ray, T., 2004. Sampling and Meshing a Surface with Guaranteed Topology and Geometry. Proc. 20th Sympos. Comput. Geom., p.280–289.
Edelsbrunner, H., Mucke, E.P., 1994. Three-dimensional alpha shapes. ACM Trans. Graph., 13(1):43–72. [doi:10.1145/174462.156635]
Lazzaro, D., Montefusco, L.B., 2002. Radial basis functions for the multivariate interpolation of large scattered data. J. Comput. Appl. Math., 140(1–2):521–536. [doi:10.1016/S0377-0427(01)00485-X]
Levin, D., 1998. The approximation power of moving least-squares. Math. Comput., 67(224):1517–1531. [doi:10.1090/S0025-5718-98-00974-0]
Levin, D., 2003. Mesh-independent Surface Interpolation. In: Brunnett, G., Hamann, B., Muller, H., Linsen, L. (Eds.), Geometric Modelling for Scientific Visualization, Springer-Verlag, p.37–49.
Liu, Y.J., 2003. Complex Shape Modelling with Point Sampled Geometry. Ph.D Thesis, Hong Kong Univ. of Sci. & Tech.
Liu, Y.J., Yuen, M.M.F., 2003. Optimized triangle mesh reconstruction from unstructured points. The Visual Computer, 19(1):23–37. [doi:10.1007/s00371-002-0162-2]
Liu, Y.J., Yuen, M.M.F., Tang, K., 2003. Manifold-guaranteed out-of-core simplification of large meshes with controlled topological type. The Visual Computer, 19(7–8):565–580.
Liu, Y.J., Tang, K., Yuen, M.M.F., 2004. Multiresolution free form object modelling with point sampled geometry. J. Comput. Sci. Technol., 19(5):607–617.
Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P., 2003. Multi-level partition of unity implicits. ACM Trans. Graph. (SIGGRAPH’03), 22(3):463–470. [doi:10.1145/882262.882293]
Pauly, M., Gross, M., Kobbelt, L., 2002. Efficient Simplification of Point-sampled Surfaces. Proc. Visualization’02, IEEE, p.163–170.
Pauly, M., Keiser, R., Kobbelt, L.P., Gross, M., 2003. Shape modelling with point-sampled geometry. ACM Trans. Graph. (SIGGRAPH’03), 22(3):641–650.
Renka, R.J., 1988. Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Software, 14(2):139–148. [doi:10.1145/45054.45055]
Sullivan, S., Sandford, L., Ponce, J., 1994. Using geometric distance fits for 3-D object modelling and recognition. IEEE Trans. Patt. Anal. Machine Intell., 16(12):1183–1196. [doi:10.1109/34.387489]
Taubin, G., 1991. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Trans. Patt. Anal. Machine Intell., 13(11):1115–1138. [doi:10.1109/34.103273]
Weiss, V., Andor, L., Renner, G., Varady, T., 2002. Advanced surface fitting techniques. Comput. Aided Geom. D., 19(1):19–42. [doi:10.1016/S0167-8396(01)00086-3]
Wendland, H., 1995. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math., 4(1):389–396. [doi:10.1007/BF02123482]
Zwicker, M., Pauly, M., Knoll, O., Gross, M., 2002. Pointshop 3D: An interactive system for point-based surface editing. ACM Trans. Graph. (SIGGRAPH’02), 21(3):322–329.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Liu, Yj., Tang, K. & Joneja, A. A general framework for progressive point-sampled geometry. J. Zhejiang Univ. - Sci. A 7, 1201–1209 (2006). https://doi.org/10.1631/jzus.2006.A1201
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2006.A1201