article

Interactive geometry remeshing

Authors:

Mathieu DesbrunAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 21, Issue 3

Pages 347 - 354

https://doi.org/10.1145/566654.566588

Published: 01 July 2002 Publication History

Abstract

We present a novel technique, both flexible and efficient, for interactive remeshing of irregular geometry. First, the original (arbitrary genus) mesh is substituted by a series of 2D maps in parameter space. Using these maps, our algorithm is then able to take advantage of established signal processing and halftoning tools that offer real-time interaction and intricate control. The user can easily combine these maps to create a control map --- a map which controls the sampling density over the surface patch. This map is then sampled at interactive rates allowing the user to easily design a tailored resampling. Once this sampling is complete, a Delaunay triangulation and fast optimization are performed to perfect the final mesh.As a result, our remeshing technique is extremely versatile and general, being able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semi-regularity, curvature sensitive resampling, and feature preservation. We provide a high level of control over the sampling distribution allowing the user to interactively custom design the mesh based on their requirements thereby increasing their productivity in creating a wide variety of meshes.

References

[1]

www.cgal.org: Computational Geometry Algorithms Library.

[2]

BOROUCHAKI, H. Geometric Surface Mesh. In 2nd International Conference on Integrated and Manufacturing in Mechanical Engineering (may 1998), pp.343-350.

[3]

BOROUCHAKI, H., GEORGE, P. L., HECHT, F., LAUG, P., AND SALTEL, E. Delaunay Mesh Generation Governed by Metric Specifications. Finite Elements in Analysis and Design 25 (1997), pp.61-83.

[4]

BOROUCHAKI, H., HECHT, F., AND FREY, P. J. Mesh Gradation Control. In Proceedings of 6th International Meshing Roundtable, Sandia National Labs (oct 1997), pp. 131-141.

[5]

BOSSEN, F., AND HECKBERT, P. A Pliant Method for Anisotropic Mesh Generation. In 5th Intl. Meshing Roundtable (oct 1996), pp.63-76.

[6]

BOTSCH, M., AND KOBBELT, L. Resampling Feature and Blend Regions in Polygonal Meshes for Surface Anti-Aliasing. In Eurographics proceedings (sep 2001), pp.402-410.

[7]

BOTSCH, M., RÖSSL, C., AND KOBBELT, L. Feature Sensitive Sampling for Interactive Remeshing. In Vision, Modeling and Visualization proceedings (2000), pp. 129-136.

[8]

DE COUGNY, H. L., AND SHEPHARD, M. S. Surface Meshing Using Vertex Insertion. In Proceedings of 5th International Meshing Roundtable, Sandia National Labs (oct 1996), pp.243-256.

[9]

DESBRUN, M., MEYER, M., AND ALLIEZ, P. Intrinsic parameterizations of surface meshes. In Proceedings of Eurographics (2002).

[10]

DYN, N., HORMANN, K., S.-J. KIM, AND LEVIN, D. Optimizing 3D Triangulations using Discrete Curvature Analysis. Mathematical methods for curves and surfaces, Oslo 2000 (2001), pp. 135-146.

[11]

ECK, M., DEROSE, T., DUCHAMP, T., HOPPE, H., LOUNSBERY, M., AND STUETZLE, W. Multiresolution Analysis of Arbitrary Meshes. In Proceedings of SIGGRAPH (1995), pp. 173-182.

[12]

ERIKSON, J., AND HAR-PELED, S. Optimally cutting a surface into a disk. In Proceedings of the 18th Annual ACM Symposium on Computational Geometry (2002). to appear.

[13]

FREY, P. J. About Surface Remeshing. In Proceedings of the 9th Int. Meshing Roundtable (2000), pp. 123-136.

[14]

GARLAND, M., AND HECKBERT, P. Simplifying Surfaces with Color and Texture using Quadric Error Metrics. In IEEE Visualization Conference Proceedings (1998), pp.263-269.

[15]

GARLAND, M., WILLMOTT, A., AND HECKBERT, P. Hierarchical Face Clustering on Polygonal Surfaces. In ACM Symposium on Interactive 3D Graphics (2001).

[16]

GEORGE, P. L., AND BOROUCHAKI, H., Eds. Delaunay Triangulation and Meshing Application to Finite Elements. HERMES, Paris, 1998.

[17]

GRAY, A., Ed. Modern Differential Geometry of Curves and Surfaces. Second edition. CRC Press, 1998.

[18]

GRIMM, C. M., AND HUGHES, J. F. Modeling Surfaces of Arbitrary Topology using Manifolds. In Proceedings of SIGGRAPH (1995), pp.359-368.

[19]

GU, X., GORTLER, S., AND HOPPE, H. Geometry Images. In Proceedings of SIGGRAPH (2002).

[20]

GUSKOV, I., SWELDENS, W., AND SCHRÖDER, P. Multiresolution Signal Processing for Meshes. In Proceedings of SIGGRAPH (1999), pp. 325-334.

[21]

GUSKOV, I., VIDIMCE, K., SWELDENS, W., ANDSCHRÖDER, P. Normal Meshes. In Proceedings of SIGGRAPH (2000), pp.95-102.

[22]

HORMANN, K., LABSIK, U., AND GREINER, G. Remeshing Triangulated Surfaces with Optimal Parameterizations. Computer-Aided Design 33 (2001), pp.779-788.

[23]

LAZARUS, F., POCCHIOLA, M., VEGTER, G., AND VERROUST, A. Computing a Canonical Polygonal Schema of an Orientable Triangulated Surface. In Proceedings of 17th Annu. ACM Sympos. Comput. Geom. (2001), pp.80-89.

[24]

LEE, A. W. F., SWELDENS, W., SCHRÖDER, P., COWSAR, L., AND DOBKIN, D. MAPS: Multiresolution Adaptive Parameterization of Surfaces. In Proceedings of SIGGRAPH (1998), pp.95-104.

[25]

LÉVY, B. Constrained Texture Mapping for Polygonal Meshes. In Proceedings of SIGGRAPH (2001), pp.417-424.

[26]

LÉVY, B., PETITJEAN, S., RAY, N., AND MAILLOT, J. Least Squares Conformal Maps for Automatic Texture Atlas Generation. In Proceedings of SIGGRAPH (2002).

[27]

LINDSTROM, P., AND TURK, G. Fast and Memory Efficient Polygonal Simplification. In IEEE Visualization Proceedings (1998), pp. 279-286.

[28]

MEYER, M., DESBRUN, M., SCHRÖDER, P., AND BARR, A. H. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds, 2002. http://multires.caltech.edu/pubs/diffGeoOps.pdf.

[29]

OSTROMOUKHOV, V. A Simple and Efficient Error-Diffusion Algorithm. In Proceedings of SIGGRAPH (2001), pp.567-572.

[30]

P. VÉRON, J.-C. L. Static Polyhedron Simplification using Error Measurements. Computer-Aided Design 29(4) (1997), pp.287-298.

[31]

PAULY, M., AND GROSS, M. Spectral Processing of Point-Sampled Geometry. In Proceedings of SIGGRAPH (2001), pp.379-386.

[32]

PINKALL, U., AND POLTHIER, K. Computing Discrete Minimal Surfaces and Conjugates. Experimental Mathematics 2(1) (1993), pp. 15-36.

[33]

RASSINEUX, A., VILLON, P., SAVIGNAT, J.-M., AND STAB, O. Surface Remeshing by Local Hermite Diffuse Interpolation. International Journal for numerical methods in Engineering 49 (2000), pp.31-49.

[34]

SHEFFER, A. Spanning Tree Seams for Reducing Parameterization Distortion of Triangulated Surfaces. In Proceedings of Shape Modeling International (2002). to appear.

[35]

SHEWCHUK, J. R. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In Proceedings of the First workshop on Applied Computational Geometry, Philadelphia, Pennsylvania (1996), pp. 123-133.

[36]

SIMPSON, R. B. Anisotropic Mesh Transformations and Optimal Error Control. Appl. Num. Math. 14(1-3) (1994), pp. 183-198.

[37]

TRISTANO, J. R., OWEN, S. J., AND CANANN, S. A. Advancing Front Surface Mesh Generation in Parametric Space Using a Riemannian Surface Definition. In Proceedings of 7th International Meshing Roundtable, Sandia National Labs (oct 1998), pp.429-445.

[38]

TURK, G. Re-Tiling Polygonal Surfaces. In Proceedings of SIGGRAPH (1992), pp.55-64.

[39]

ULICHNEY, R. A. Dithering with Blue Noise. In Proceedings of the IEEE (1988), vol. 76(1), pp.56-79.

[40]

VAN DAMME, R., AND ABOUL, L. Tight Triangulations. Mathematical Methods for Curves and Surfaces (1995).

[41]

VORSATZ, J., RÖSSL, C., KOBBELT, L., AND SEIDEL, H.-P. Feature Sensitive Remeshing. In Eurographics proceedings (sep 2001), pp. 393-401.

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Index Terms

Interactive geometry remeshing
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 21, Issue 3

July 2002

548 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/566654

Issue’s Table of Contents

Copyright © 2002 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 2002

Published in TOG Volume 21, Issue 3

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Cited By

Wibowo MNugrhono SWibowo A(2024)Visual aesthetics of narrative animation of 3D computer graphics: From both realist and expressive points of viewHumanities, Arts and Social Sciences Studies10.69598/hasss.24.1.260646Online publication date: 30-Apr-2024
https://doi.org/10.69598/hasss.24.1.260646
Yang G(2023)Geometry Processing with Neural FieldsSIGGRAPH Asia 2023 Doctoral Consortium10.1145/3623053.3623365(1-5)Online publication date: 28-Nov-2023
https://dl.acm.org/doi/10.1145/3623053.3623365
Liu HGillespie MChislett BSharp NJacobson ACrane K(2023)Surface Simplification using Intrinsic Error MetricsACM Transactions on Graphics10.1145/359240342:4(1-17)Online publication date: 26-Jul-2023
https://dl.acm.org/doi/10.1145/3592403
Coudert‐Osmont YDesobry DHeistermann MBommes DRay NSokolov D(2023)Quad Mesh Quantization Without a T‐MeshComputer Graphics Forum10.1111/cgf.1492843:1Online publication date: 17-Sep-2023
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Ho JFarhat C(2023)Aerodynamic optimization with large shape and topology changes using a differentiable embedded boundary methodJournal of Computational Physics10.1016/j.jcp.2023.112191488:COnline publication date: 1-Sep-2023
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Zeng QOhsaki MZhang JZhu SLi ZGuo X(2023)Structured triangular mesh generation method for free-form gridshells based on conformal mapping and virtual interaction forcesEngineering Structures10.1016/j.engstruct.2023.116879295(116879)Online publication date: Nov-2023
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Hertz APerel OGiryes RSorkine‐Hornung OCohen‐Or D(2022)Mesh Draping: Parametrization‐Free Neural Mesh TransferComputer Graphics Forum10.1111/cgf.1472142:1(72-85)Online publication date: 30-Nov-2022
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Khan DPlopski AFujimoto YKanbara MJabeen GZhang YZhang XKato H(2022)Surface Remeshing: A Systematic Literature Review of Methods and Research DirectionsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.301664528:3(1680-1713)Online publication date: 1-Mar-2022
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Panchal DJayaswal D(2022)Feature sensitive geometrically faithful highly regular direct triangular isotropic surface remeshingSādhanā10.1007/s12046-022-01866-747:2Online publication date: 3-May-2022
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