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Interpolating and approximating implicit surfaces from polygon soup

Authors:

James F. O'Brien,

Jonathan R. ShewchukAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 23, Issue 3

Pages 896 - 904

https://doi.org/10.1145/1015706.1015816

Published: 01 August 2004 Publication History

Abstract

This paper describes a method for building interpolating or approximating implicit surfaces from polygonal data. The user can choose to generate a surface that exactly interpolates the polygons, or a surface that approximates the input by smoothing away features smaller than some user-specified size. The implicit functions are represented using a moving least-squares formulation with constraints integrated over the polygons. The paper also presents an improved method for enforcing normal constraints and an iterative procedure for ensuring that the implicit surface tightly encloses the input vertices.

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References

[1]

ALEXA, M., BEHR, J., COHEN-OR, D., FLEISHMAN, S., LEVIN, D., AND SILVA, C. T. 2001. Point set surfaces. In IEEE Visualization 2001, 21--28.

Digital Library

[2]

ALEXA, M., BEHR, J., COHEN-OR, D., FLEISHMAN, S., LEVIN, D., AND SILVA, C. T. 2003. Computing and rendering point set surfaces. IEEE Transactions on Visualization and Computer Graphics 9, 1 (Jan.), 3--15.

Digital Library

[3]

BELYTSCHKO, T., KRONGAUZ, Y., ORGAN, D., FLEMING, M., AND KRYSL, P. 1996. Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering 139, 3--47. Special issue on meshless methods.

[4]

BITTAR, E., TSINGOS, N., AND GASCUEL, M.-P. 1995. Automatic reconstruction of unstructured 3D data: Combining a medial axis and implicit surfaces. Proceedings of Eurographics 95, 457--468.

[5]

BLOOMENTHAL, J. 1994. An implicit surface polygonizer. In Graphics Gems IV. 324--349.

Digital Library

[6]

BLOOMENTHAL, J., Ed. 1997. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers, Inc., San Francisco, California.

Digital Library

[7]

BIOSSONNAT, J. D., AND OUDOT, S. 2003. Provably good surface sampling and approximation. In Proceedings of the ACM SIGGRAPH Symposium on Geometry Processing, 9--18.

Digital Library

[8]

CARR, J. C., BEATSON, R. K., CHERRIE, J. B., MITCHELL, T. J., FRIGHT, W. R., MCCALLUM, B. C., AND EVANS, T. R. 2001. Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of ACM SIGGRAPH 2001, 67--76.

Digital Library

[9]

COHEN, J., VARSHNEY, A., MANOCHA, D., TURK, G., WEBER, H., AGARWAL, P., JR., F. P. B., AND WRIGHT, W. 1996. Simplification envelopes. In Proceedings of ACM SIGGRAPH 1996, 119--128.

Digital Library

[10]

COHEN-OR, D., SOLOMOVICI, A., AND LEVIN, D. 1998. Three-dimensional distance field metamorphosis. ACM Transactions on Graphics 17, 2 (Apr.), 116--141.

Digital Library

[11]

DESBRUN, M., MEYER, M., SCHRÖDER, P., AND BARR, A. H. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proceedings of ACM SIGGRAPH 1999, 317--324.

Digital Library

[12]

FLEISHMAN, S., ALEXA, M., COHEN-OR, D., AND SILVA, C. T. 2003. Progressive point set surfaces. ACM Transactions on Graphics 22, 4 (Oct.), 97--1011.

Digital Library

[13]

JONES, T. R., DURAND, F., AND DESBRUN, M. 2003. Non-iterative, feature-preserving mesh smoothing. ACM Transactions on Graphics 22, 3 (July), 943--949.

Digital Library

[14]

KEREN, D., AND GOTSMAN, C. 1998. Tight fitting of convex polyhedral shapes. International Journal of Shape Modeling, 111--126.

[15]

MORSE, B., YOO, T. S., RHEINGANS, P., CHEN, D. T., AND SUBRAMANIAN, K. 2001. Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In Proceedings of Shape Modelling International, 89--98.

Digital Library

[16]

MURAKI, S. 1991. Volumetric shape description of range data using "blobby model". In Proceedings of ACM SIGGRAPH 1991, 227--235.

Digital Library

[17]

MUSETH, K., BREEN, D. E., WHITAKER, R. T., AND BARR, A. H. 2002. Level set surface editing operators. ACM Transactions on Graphics 21, 3 (July), 330--338.

Digital Library

[18]

NOORUDDIN, F. S., AND TURK, G. 2000. Interior/exterior classification of polygonal models. In IEEE Visualization 2000, 415--422.

Digital Library

[19]

NOORUDDIN, F. S., AND TURK, G. 2003. Simplification and repair of polygonal models using volumetric techniques. IEEE Transactions on Visualization and Computer Graphics 9, 2 (Apr.), 191--205.

Digital Library

[20]

OHTAKE, Y., BELYAEV, A., ALEXA, M., TURK, G., AND SEIDEL, H.-P. 2003. Multi-level partition of unity implicits. ACM Transactions on Graphics 22, 3 (July), 463--470.

Digital Library

[21]

OHTAKE, Y., BELYAEV, A., AND SEIDEL, H.-P. 2003. A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions. In Proceedings of Shape Modelling International, 292--300.

Digital Library

[22]

SAVCHENKO, V. V., PASKO, A. A., OKUNEV, O. G., AND KUNII, T. L. 1995. Function representation of solids reconstructed from scattered surface points and contours. Computer Graphics Forum 14, 4 (Oct.), 181--188.

[23]

TAUBIN, G. 1995. A signal processing approach to fair surface design. In Proceedings of ACM SIGGRAPH 1995, 351--358.

Digital Library

[24]

TURK, G., AND O'BRIEN, J. F. 1999. Shape transformation using variational implicit functions. In Proceedings of ACM SIGGRAPH 1999, 335--342.

Digital Library

[25]

TURK, G., AND O'BRIEN, J. F. 2002. Modelling with implicit surfaces that interpolate. ACM Transactions on Graphics 21, 4 (Oct.), 855--873.

Digital Library

[26]

YNGVE, G., AND TURK, G. 2002. Robust creation of implicit surfaces from polygonal meshes. IEEE Transactions on Visualization and Computer Graphics 8, 4 (Oct.), 346--359.

Digital Library

[27]

ZHAO, H.-K., OSHER, S., AND FEDKIW, R. 2001. Fast surface reconstruction using the level set method, In IEEE Workshop on Variational and Level Set Methods, 194--202.

Digital Library

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Jiang XXie YNa CYu WMeng Y(2024)Algorithm for Point Cloud Dust Filtering of LiDAR for Autonomous Vehicles in Mining AreaSustainability10.3390/su1607282716:7(2827)Online publication date: 28-Mar-2024
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Index Terms

Interpolating and approximating implicit surfaces from polygon soup
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Approximation algorithms

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 23, Issue 3

August 2004

684 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1015706

Editor:
John C. Hart

Issue’s Table of Contents

Copyright © 2004 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]

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Publication History

Published: 01 August 2004

Published in TOG Volume 23, Issue 3

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Jiang XXie YNa CYu WMeng Y(2024)Algorithm for Point Cloud Dust Filtering of LiDAR for Autonomous Vehicles in Mining AreaSustainability10.3390/su1607282716:7(2827)Online publication date: 28-Mar-2024
https://doi.org/10.3390/su16072827
Ströter DThiery JHormann KChen JChang QBesler SMueller‐Roemer JBoubekeur TStork AFellner D(2024)A Survey on Cage‐based Deformation of 3D ModelsComputer Graphics Forum10.1111/cgf.1506043:2Online publication date: 30-Apr-2024
https://doi.org/10.1111/cgf.15060
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https://doi.org/10.1080/17538947.2024.2376269
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