Full Text:   <1222>

CLC number: TP39

On-line Access: 

Received: 2006-04-17

Revision Accepted: 2006-04-29

Crosschecked: 0000-00-00

Cited: 0

Clicked: 3197

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.7 P.1201~1209


A general framework for progressive point-sampled geometry

Author(s):  LIU Yong-jin, TANG Kai, JONEJA Ajay

Affiliation(s):  Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China; more

Corresponding email(s):   liuyongjin@tsinghua.edu.cn, mektang@ust.hk, joneja@ust.hk

Key Words:  Progressive model, Point-sample geometry, Geometric distance, Error measure, Shape representation

LIU Yong-jin, TANG Kai, JONEJA Ajay. A general framework for progressive point-sampled geometry[J]. Journal of Zhejiang University Science A, 2006, 7(7): 1201~1209.

@article{title="A general framework for progressive point-sampled geometry",
author="LIU Yong-jin, TANG Kai, JONEJA Ajay",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A general framework for progressive point-sampled geometry
%A LIU Yong-jin
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 7
%P 1201~1209
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1201

T1 - A general framework for progressive point-sampled geometry
A1 - LIU Yong-jin
A1 - TANG Kai
A1 - JONEJA Ajay
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 7
SP - 1201
EP - 1209
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1201

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] 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.

[2] Amenta, N., Bern, M., 1999. Surface reconstruction by Voronoi filtering. Discret. Comput. Geom., 22(4):481-504.

[3] Amenta, N., Kil, Y.J., 2004. Defining point-set surface. ACM Trans. Graph. (SIGGRAPH’04), 23(3):264-270.

[4] Amenta, N., Bern, M., Kamvysselis, M., 1998. A New Voronoi-based Surface Reconstruction Algorithm. Proc. SIGGRAPH’98, p.415-422.

[5] 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.

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

[7] 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.

[8] Edelsbrunner, H., Mucke, E.P., 1994. Three-dimensional alpha shapes. ACM Trans. Graph., 13(1):43-72.

[9] 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.

[10] Levin, D., 1998. The approximation power of moving least-squares. Math. Comput., 67(224):1517-1531.

[11] 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.

[12] Liu, Y.J., 2003. Complex Shape Modelling with Point Sampled Geometry. Ph.D Thesis, Hong Kong Univ. of Sci. & Tech.

[13] Liu, Y.J., Yuen, M.M.F., 2003. Optimized triangle mesh reconstruction from unstructured points. The Visual Computer, 19(1):23-37.

[14] 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.

[15] 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.

[16] 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.

[17] Pauly, M., Gross, M., Kobbelt, L., 2002. Efficient Simplification of Point-sampled Surfaces. Proc. Visualization’02, IEEE, p.163-170.

[18] 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.

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

[20] 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.

[21] 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.

[22] Weiss, V., Andor, L., Renner, G., Varady, T., 2002. Advanced surface fitting techniques. Comput. Aided Geom. D., 19(1):19-42.

[23] Wendland, H., 1995. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math., 4(1):389-396.

[24] 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.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE