Article

Free access

A new general triangulation method for planar contours

Authors:

S. Ganapathy,

T. G. DennehyAuthors Info & Claims

SIGGRAPH '82: Proceedings of the 9th annual conference on Computer graphics and interactive techniques

Pages 69 - 75

https://doi.org/10.1145/800064.801264

Published: 01 July 1982 Publication History

PDF eReader

Abstract

The problem of approximating the surface spanning a given set of 3D points as a polyhedron of triangular faces (“triangulation”) is a significant one, and has many applications in the fields of computer graphics and computer vision. In this paper, several solutions to this problem are reviewed. These solutions can be grouped into two classes, and particular emphasis is given to the class of surfaces spanned by parallel planar contours. For a contour pair P₀,P₁,...P_m−1 and Q₀,Q₁,...Q_n−1, a graph theoretic approach can be used to arrive at a class of solutions, each requiring exactly m+n steps to triangulate the pair. Existing methods (both rigorous and heuristic) for extracting a particular solution from this group are reviewed, and a new heuristic based on inter-contour coherence is proposed. This heuristic is being used in the field of Ultrasonic Non-destructive Evaluation to produce images of flaws in pressure vessels, and its performance is shown to compare favorably with methods of greater computational complexity. It is believed that this heuristic can also be used with success in industrial vision systems where similar contours are obtained using a laser range finder.

References

[1]

Boissonnat, J.D. and Faugeras, O.D., "Triangulation of 3D Objects," PROCEEDINGS OF THE 1981 INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, 658-660.

Google Scholar

[2]

O'Roarke, Joseph, "Triangulation of Minimal Area as 3D Object Models," PROCEEDINGS OF THE 1981 INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, 664-666.

Google Scholar

[3]

Fuchs, H., etal., "Optimal Surface Reconstruction from Planar Contours," COMMUNICATIONS OF THE ACM, XX-10 (October 1977), 693-702.

Digital Library

Google Scholar

[4]

Keppel, E., "Approximating Complex Surfaces by Triangulation of Contour Lines," IBM JOURNAL OF RESEARCH AND DEVELOPMENT, XIX (January 1975), 2-11.

Digital Library

Google Scholar

[5]

Christianson, H. and Sederberg, T.W., "Conversion of Complex Contour Line Definitions into Polygonal Element Mosaics," COMPUTER GRAPHICS, XIII,2 (August, 1978), 187-192.

Digital Library

Google Scholar

[6]

Ganapathy, S., etal., "Ultrasonic Imaging Techniques for Real-time In-service Inspection of Nuclear Power Reactors", Nuclear Regulatory Commission Report NUREG/CR-2154, September, 1981.

Google Scholar

[7]

Nilsson, Nils, PRINCIPLES OF ARTIFICIAL INTELLIGENCE, (Palo Alto: Tioga Publishing Co.) 1980.

Digital Library

Google Scholar

[8]

Horn, Berthold K. P., "Hill Shading and the Reflectance Map," PROCEEDINGS OF THE IEEE, LXIX, 1 (January, 1981) 14-47.

Crossref

Google Scholar

Cited By

View all

Everitt AAlexander JMival OSmyth MDalsgaard P(2017)PolySurfaceProceedings of the 2017 Conference on Designing Interactive Systems10.1145/3064663.3064677(1283-1294)Online publication date: 10-Jun-2017
https://dl.acm.org/doi/10.1145/3064663.3064677
Xu WHou S(2009)Parametric garment modeling from sections2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics10.1109/CADCG.2009.5246843(548-551)Online publication date: Aug-2009
https://doi.org/10.1109/CADCG.2009.5246843
NurzyńSka K(2008)Static methods for object reconstruction overviewAnnales UMCS, Informatica10.2478/v10065-008-0008-28:1(75-86)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.2478/v10065-008-0008-2
Show More Cited By

Index Terms

A new general triangulation method for planar contours

Recommendations

A new general triangulation method for planar contours

The problem of approximating the surface spanning a given set of 3D points as a polyhedron of triangular faces (“triangulation”) is a significant one, and has many applications in the fields of computer graphics and computer vision. In this paper, ...
Approximated algorithms for the minimum dilation triangulation problem

The complexity status of the minimum dilation triangulation (MDT) problem for a general point set is unknown. Therefore, we focus on the development of approximated algorithms to find high quality triangulations of minimum dilation. For an initial ...
Well-Centered Triangulation

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality ...

Comments

Information & Contributors

Information

Published In

SIGGRAPH '82: Proceedings of the 9th annual conference on Computer graphics and interactive techniques

July 1982

333 pages

ISBN:0897910761

DOI:10.1145/800064

Chairman:
R. Daniel Bergeron

ACM SIGGRAPH Computer Graphics Volume 16, Issue 3
July 1982
308 pages
ISSN:0097-8930
DOI:10.1145/965145
Issue’s Table of Contents

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 1982

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

SIGGRAPH '82

Sponsor:

SIGGRAPH

SIGGRAPH '82: Computer graphics and interactive techniques

July 26 - 30, 1982

Massachusetts, Boston, USA

Acceptance Rates

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

140
Total Citations
View Citations
1,471
Total Downloads

Downloads (Last 12 months)108
Downloads (Last 6 weeks)25

Reflects downloads up to 04 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Everitt AAlexander JMival OSmyth MDalsgaard P(2017)PolySurfaceProceedings of the 2017 Conference on Designing Interactive Systems10.1145/3064663.3064677(1283-1294)Online publication date: 10-Jun-2017
https://dl.acm.org/doi/10.1145/3064663.3064677
Xu WHou S(2009)Parametric garment modeling from sections2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics10.1109/CADCG.2009.5246843(548-551)Online publication date: Aug-2009
https://doi.org/10.1109/CADCG.2009.5246843
NurzyńSka K(2008)Static methods for object reconstruction overviewAnnales UMCS, Informatica10.2478/v10065-008-0008-28:1(75-86)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.2478/v10065-008-0008-2
Nurzynska K(2008)3D Object Reconstruction from Parallel Cross-SectionsProceedings of the International Conference on Computer Vision and Graphics: Revised Papers10.1007/978-3-642-02345-3_12(111-122)Online publication date: 10-Nov-2008
https://dl.acm.org/doi/10.1007/978-3-642-02345-3_12
Paggetti CCiucci TPapa EAllotta BDario P(2005)A system for computer assisted arthroscopyCVRMed-MRCAS'9710.1007/BFb0029291(653-662)Online publication date: 21-Nov-2005
https://doi.org/10.1007/BFb0029291
Jiang XShu HToumoulin CGu JLuo L(2003)Surface reconstruction of complex contour lines by means of chain code matching techniqueProceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No.03CH37439)10.1109/IEMBS.2003.1279753(521-524)Online publication date: 2003
https://doi.org/10.1109/IEMBS.2003.1279753
Yong Zhou Toga A(2000)Voxel-coding for tiling complex volumetric objectsProceedings the Eighth Pacific Conference on Computer Graphics and Applications10.1109/PCCGA.2000.883954(307-451)Online publication date: 2000
https://doi.org/10.1109/PCCGA.2000.883954
Brebin RCarpenter LHanrahan P(1998)Volume renderingSeminal graphics: pioneering efforts that shaped the field10.1145/280811.281028(363-372)Online publication date: 1-Jul-1998
https://dl.acm.org/doi/10.1145/280811.281028
Chu CTakaya K(1993)3-dimensional rendering of MR (magnetic resonance) imagesIEEE WESCANEX 93 Communications, Computers and Power in the Modern Environment - Conference Proceedings10.1109/WESCAN.1993.270569(165-170)Online publication date: 1993
https://doi.org/10.1109/WESCAN.1993.270569
Sederberg TGreenwood E(1992)A physically based approach to 2–D shape blendingACM SIGGRAPH Computer Graphics10.1145/142920.13400126:2(25-34)Online publication date: 1-Jul-1992
https://dl.acm.org/doi/10.1145/142920.134001
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

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

Cited By

Index Terms

Recommendations

A new general triangulation method for planar contours

Approximated algorithms for the minimum dilation triangulation problem

Well-Centered Triangulation