article

Spherical parametrization and remeshing

Authors:

Hugues HoppeAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 22, Issue 3

Pages 340 - 349

https://doi.org/10.1145/882262.882274

Published: 01 July 2003 Publication History

Abstract

The traditional approach for parametrizing a surface involves cutting it into charts and mapping these piecewise onto a planar domain. We introduce a robust technique for directly parametrizing a genus-zero surface onto a spherical domain. A key ingredient for making such a parametrization practical is the minimization of a stretch-based measure, to reduce scale-distortion and thereby prevent undersampling. Our second contribution is a scheme for sampling the spherical domain using uniformly subdivided polyhedral domains, namely the tetrahedron, octahedron, and cube. We show that these particular semi-regular samplings can be conveniently represented as completely regular 2D grids, i.e. geometry images. Moreover, these images have simple boundary extension rules that aid many processing operations. Applications include geometry remeshing, level-of-detail, morphing, compression, and smooth surface subdivision.

Supplementary Material

MP4 File (praun_spherical.mp4)

Download
37.21 MB

References

[1]

ALEXA, M. 2000. Merging polyhedral shapes with scattered features. The Visual Computer, 16(1), pp. 26--37.

Digital Library

[2]

ALEXA, M. 2002. Recent advances in mesh morphing. Computer Graphics Forum, 21(2), pp. 173--196.

[3]

ARVO, J. 1995. Stratified sampling of spherical triangles. ACM SIGGRAPH 95, pp. 437--438.

Digital Library

[4]

BUSS, S., AND FILLMORE, J. 2001. Spherical averages and applications to spherical splines and interpolation. ACM Transactions on Graphics, 20(2), pp. 95--126.

Digital Library

[5]

CIGNONI, P., MONTANI, C., ROCCHINI, C., AND SCOPIGNO, R. 1998. A general method for recovering attribute values on simplified meshes. IEEE Visualization 1998, pp. 59--66.

Digital Library

[6]

COHEN, J., OLANO, M., AND MANOCHA, D. 1998. Appearance-preserving simplification. ACM SIGGRAPH 98, pp. 115--122.

Digital Library

[7]

DAVIS, G. 1996. Wavelet image compression construction kit. http://www.geoffdavis.net/dartmouth/wavelet/wavelet.html.

[8]

ECK, M., DEROSE, T., DUCHAMP, T., HOPPE, H., LOUNSBERY, M., AND STUETZLE, W. 1995. Multiresolution analysis of arbitrary meshes. ACM SIGGRAPH 95, pp. 173--182.

Digital Library

[9]

ECKSTEIN, I., SURAZHSKY, V., AND GOTSMAN, C. 2001. Texture mapping with hard constraints. Eurographics 2001, pp. 95--104.

[10]

FLOATER, M. 1997. Parametrization and smooth approximation of surface triangulations. CAGD 14(3), pp. 231--250.

Digital Library

[11]

FUNKHOUSER, T., MIN, P., KAZHDAN, M., CHEN, J., HALDERMAN, A., DOBKIN, D., AND JACOBS, D. 2003. A search engine for 3D models. ACM Transactions on Graphics, 22(1), January 2003, pp. 83--105.

Digital Library

[12]

FURUTI, C. 1997. http://www.progonos.com/furuti/.

[13]

GREENE, N. 1986. Environment mapping and other applications. IEEE Computer Graphics and Applications, 6(11).

Digital Library

[14]

GRIMM, C. 2002. Simple manifolds for surface modeling and parametrization. Shape Modeling International 2002.

Digital Library

[15]

GU, X., GORTLER, S., AND HOPPE, H. 2002. Geometry images. ACM SIGGRAPH 2002, pp. 355--361.

Digital Library

[16]

GOTSMAN, C., GU, X., AND SHEFFER, A. 2003. Fundamentals of spherical parameterization for 3D meshes. ACM SIGGRAPH 2003.

Digital Library

[17]

GUSKOV, I., VIDIMČE, K., SWELDENS, W., AND SCHRÖDER, P. 2000. Normal meshes. ACM SIGGRAPH 2000, pp. 95--102.

Digital Library

[18]

HAKER, S., ANGENENT, S., TANNENBAUM, S., KIKINIS, R., SAPIRO, G., AND HALLE, M. 2000. Conformal surface parametrization for texture mapping. IEEE TVCG, 6(2), pp. 181--189.

Digital Library

[19]

HOPPE, H. 1996. Progressive meshes. ACM SIGGRAPH 96, pp. 99--108.

Digital Library

[20]

HORMANN, K., GREINER, G., AND CAMPAGNA, S. 1999. Hierarchical parametrization of triangulated surfaces. Vision, Modeling, and Visualization 1999, pp. 219--226.

[21]

KENT, J., CARLSON, W., AND PARENT, R. 1992. Shape transformation for polyhedral objects. ACM SIGGRAPH 92, pp. 47--54.

Digital Library

[22]

KHODAKOVSKY, A., SCHRÖDER, P., AND SWELDENS, W. 2000. Progressive geometry compression. ACM SIGGRAPH 2000, 271--278.

Digital Library

[23]

KOBBELT, L., VORSATZ, J., LABSIK, U., AND SEIDEL, H.-P. 1999. A shrink wrapping approach to remeshing polygonal surfaces. Eurographics 1999, pp. 119--130.

[24]

LEE, A., SWELDENS, W., SCHRÖDER, P., COWSAR, L., AND DOBKIN, D. 1998. MAPS: Multiresolution adaptive parametrization of surfaces. ACM SIGGRAPH 98, pp. 95--104.

Digital Library

[25]

LEE, A., MORETON, H., AND HOPPE, H. 2000. Displaced subdivision surfaces. ACM SIGGRAPH 2000, pp. 85--94.

Digital Library

[26]

LÉVY, B., PETITJEAN, S., RAY, N., AND MAILLOT, J. 2002. Least squares conformal maps for automatic texture atlas generation. ACM SIGGRAPH 2002, pp. 362--371.

Digital Library

[27]

LOSASSO, F., HOPPE, H., SCHAEFER, S., AND WARREN, J. 2003. Smooth geometry images. Submitted for publication.

[28]

MAILLOT, J., YAHIA, H., AND VERROUST, A. 1993. Interactive texture mapping. ACM SIGGRAPH 93, pp. 27--34.

Digital Library

[29]

PRAUN, E., SWELDENS, W., AND SCHRÖDER, P. 2001. Consistent mesh parametrizations. ACM SIGGRAPH 2001, pp. 179--184.

Digital Library

[30]

QUICKEN, M., BRECHBÜHLER, C., HUG, J., BLATTMANN, H., SZÉKELY, G. 2000. Parametrization of closed surfaces for parametric surface description, CVPR 2000, pp. 354--360.

[31]

SANDER, P., SNYDER, J., GORTLER, S., AND HOPPE, H. 2001. Texture mapping progressive meshes. ACM SIGGRAPH 2001, pp. 409--416.

Digital Library

[32]

SANDER, P., GORTLER, S., SNYDER, J., AND HOPPE, H. 2002. Signal-specialized parametrization. Eurographics Workshop on Rendering 2002, pp. 87--100.

Digital Library

[33]

SCHRÖDER, P. AND SWELDENS, W. 1995. Spherical wavelets: Efficiently representing functions on the sphere. ACM SIGGRAPH 95, 161--172.

Digital Library

[34]

SHAPIRO, A. AND TAL, A. 1998. Polygon realization for shape transformation. The Visual Computer, 14 (8--9), pp. 429--444.

[35]

SHEFFER, A., GOTSMAN, C., AND DYN, N. 2003. Robust spherical parameterization of triangular meshes. 4th Israel-Korea Bi-National Conf. on Geometric Modeling and Computer Graphics, pp. 94--99.

[36]

SHEFFER, A., AND HART, J. 2002. Seamster: Inconspicuous low-distortion texture seam layout. IEEE Visualization 2002, pp. 291--298.

Digital Library

[37]

SORKINE, O., COHEN-OR, D., GOLDENTHAL, R., AND LISCHINSKI, D. 2002. Bounded-distortion piecewise mesh parametrization. IEEE Visualization 2002.

Digital Library

[38]

STAUNTON, R. 1999. Hexagonal sampling in image processing. In Advances in imaging and electron physics, Vol. 107, Academic Press.

[39]

TURK, G. 1990. Generating random points in triangles. Graphics Gems, Academic Press, pp. 649--650.

Digital Library

[40]

TODHUNTER, I., AND LEATHEM, J. G. 1949. Spherical Trigonometry, Macmillan and Co, Limited.

[41]

WOOD, Z., DESBRUN, M., SCHRÖDER, P., AND BREEN, D. 2000. Semi-regular mesh extraction from volumes. IEEE Visualization 2000, pp. 275--282.

Digital Library

Cited By

Cao LPeng C(2024)Hierarchical Spherical Cross‐Parameterization for Deforming CharactersComputer Graphics Forum10.1111/cgf.1519743:6Online publication date: 19-Sep-2024
https://doi.org/10.1111/cgf.15197
Li JCai Z(2024)A Hierarchical Spherical Algorithm Over the Triangular Domain for Lunar Regional Brightness Temperature AnalysisIEEE Transactions on Geoscience and Remote Sensing10.1109/TGRS.2024.343350162(1-11)Online publication date: 2024
https://doi.org/10.1109/TGRS.2024.3433501
Yin MCharon NBrody RLu LTrayanova NMaggioni M(2024)A scalable framework for learning the geometry-dependent solution operators of partial differential equationsNature Computational Science10.1038/s43588-024-00732-24:12(928-940)Online publication date: 9-Dec-2024
https://doi.org/10.1038/s43588-024-00732-2
Show More Cited By

Recommendations

Spherical parametrization and remeshing
SIGGRAPH '03: ACM SIGGRAPH 2003 Papers

The traditional approach for parametrizing a surface involves cutting it into charts and mapping these piecewise onto a planar domain. We introduce a robust technique for directly parametrizing a genus-zero surface onto a spherical domain. A key ...
Using Most Isometric Parametrizations for Remeshing Polygonal Surfaces
GMP '00: Proceedings of the Geometric Modeling and Processing 2000

The importance of triangle meshes with a special kind of connectivity, the so-called subdivision connectivity is still growing. Therefore it is important to develop efficient algorithms for converting a given mesh with arbitrary connectivity into one ...
Geodesic Remeshing Using Front Propagation

In this paper, we propose a complete framework for 3D geometry modeling and processing that uses only fast geodesic computations. The basic building block for these techniques is a novel greedy algorithm to perform a uniform or adaptive remeshing of a ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 22, Issue 3

July 2003

683 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/882262

Issue’s Table of Contents

Copyright © 2003 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 2003

Published in TOG Volume 22, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

218
Total Citations
View Citations
3,327
Total Downloads

Downloads (Last 12 months)82
Downloads (Last 6 weeks)14

Reflects downloads up to 13 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Cao LPeng C(2024)Hierarchical Spherical Cross‐Parameterization for Deforming CharactersComputer Graphics Forum10.1111/cgf.1519743:6Online publication date: 19-Sep-2024
https://doi.org/10.1111/cgf.15197
Li JCai Z(2024)A Hierarchical Spherical Algorithm Over the Triangular Domain for Lunar Regional Brightness Temperature AnalysisIEEE Transactions on Geoscience and Remote Sensing10.1109/TGRS.2024.343350162(1-11)Online publication date: 2024
https://doi.org/10.1109/TGRS.2024.3433501
Yin MCharon NBrody RLu LTrayanova NMaggioni M(2024)A scalable framework for learning the geometry-dependent solution operators of partial differential equationsNature Computational Science10.1038/s43588-024-00732-24:12(928-940)Online publication date: 9-Dec-2024
https://doi.org/10.1038/s43588-024-00732-2
Choi G(2024)Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfacesJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115888447(115888)Online publication date: Sep-2024
https://doi.org/10.1016/j.cam.2024.115888
Xu BHu JHou FLin KWu WQian CHe Y(2024)Parameterization-Driven Neural Surface Reconstruction for Object-Oriented Editing in Neural RenderingComputer Vision – ECCV 202410.1007/978-3-031-72940-9_26(461-479)Online publication date: 29-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-72940-9_26
Cherchi GLivesu M(2023)VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base DomainsComputer Graphics Forum10.1111/cgf.1491542:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14915
Schmidt PPieper DKobbelt L(2023)Surface Maps via Adaptive TriangulationsComputer Graphics Forum10.1111/cgf.1474742:2(103-117)Online publication date: 23-May-2023
https://doi.org/10.1111/cgf.14747
Laga HPadilla MJermyn IKurtek SBennamoun MSrivastava A(2023)4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape DataIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2022.316372045:2(1335-1352)Online publication date: 1-Feb-2023
https://doi.org/10.1109/TPAMI.2022.3163720
Hartman EPierson EBauer MCharon NDaoudi M(2023)BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes2023 IEEE/CVF International Conference on Computer Vision (ICCV)10.1109/ICCV51070.2023.01304(14135-14145)Online publication date: 1-Oct-2023
https://doi.org/10.1109/ICCV51070.2023.01304
Baker EBesnier TSommer S(2023)A Function Space Perspective on Stochastic Shape EvolutionImage Analysis10.1007/978-3-031-31438-4_19(278-292)Online publication date: 18-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-31438-4_19
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents