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Morphological analysis of terrains based on discrete curvature and distortion

Authors:

Mohammed Mostefa Mesmoudi,

Leila De Floriani,

Paola MagilloAuthors Info & Claims

GIS '08: Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems

Article No.: 53, Pages 1 - 4

https://doi.org/10.1145/1463434.1463498

Published: 05 November 2008 Publication History

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Abstract

In order to characterize the morphology of a triangulated terrain, we define several discrete estimators that mimic mean and Gaussian curvatures in the discrete case. We start from concentrated curvature, a discrete notion of Gaussian curvature for polyhedral surfaces, defined by Troyanov [7]. Since concentrated curvature does not depend on the local geometric shape of the terrain, we introduce Ccurvature that allows us to obtain discrete counterparts of both Gaussian and mean curvature. Finally, we define distortion, which behaves as an approximation of mean curvature. We apply all such measures to the analysis of the morphology of triangulated terrains.

References

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[2]

T. Gatzke and C. Grimm. Estimating curvature on triangular meshes. Int. J. Shape Modeling, 12:1--29, 2006.

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[3]

M. M. Mesmoudi, L. De Floriani, and P. Magillo. Discrete curvatures for TIN morphology. Technical report, DISI, University of Genova, Italy, 2008.

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[4]

M. M. Mesmoudi, L. De Floriani, and U. Port. Discrete distortion in triangulated 3-manifolds. In Proceedings Eurographics Symposium on Geometry Processing (SGP08), 2008.

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E. Saux, R. Thibaud, K.-J. Li, and M.-H. Kim. A new approach for a topographic feature-based characterization of digital elevation data. In Proceedings ACM Int. Workshop on Advances in Geographic Information Systems (ACM-GIS), pages 73--81, 2004.

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M. Spivak. A Comprehensive Introduction to Differential Geometry. Houston Texas, 1979.

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M. Troyanov. Les surfaces euclidiennes à singularités coniques. L'enseignement Mathématique, 32:79--94, 1986.

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Cited By

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Fellegara RIuricich FSong YFloriani L(2022)Terrain trees: a framework for representing, analyzing and visualizing triangulated terrainsGeoInformatica10.1007/s10707-022-00472-327:3(525-564)Online publication date: 27-Aug-2022
https://doi.org/10.1007/s10707-022-00472-3
Sun WWang HZhao X(2017)A simplification method for grid-based DEM using topological hierarchiesSurvey Review10.1080/00396265.2017.131035550:362(454-467)Online publication date: 10-Apr-2017
https://doi.org/10.1080/00396265.2017.1310355
De Floriani LIuricich FMagillo PMesmoudi MWeiss K(2012)Discrete Distortion for 3D Data AnalysisVisualization in Medicine and Life Sciences II10.1007/978-3-642-21608-4_1(3-25)Online publication date: 2012
https://doi.org/10.1007/978-3-642-21608-4_1
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Index Terms

Morphological analysis of terrains based on discrete curvature and distortion
1. Applied computing
  1. Physical sciences and engineering
    1. Earth and atmospheric sciences
2. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
        Shape representations
  2. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Published In

GIS '08: Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems

November 2008

559 pages

ISBN:9781605583235

DOI:10.1145/1463434

Program Chairs:
Walid G. Aref
Purdue University
,
Mohamed F. Mokbel
University of Minnesota
,
Markus Schneider
University of Florida

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Published: 05 November 2008

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GIS '08: 16th International Symposium on Advances in Geographic Information Systems

November 5 - 7, 2008

California, Irvine

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Overall Acceptance Rate 257 of 1,238 submissions, 21%

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Fellegara RIuricich FSong YFloriani L(2022)Terrain trees: a framework for representing, analyzing and visualizing triangulated terrainsGeoInformatica10.1007/s10707-022-00472-327:3(525-564)Online publication date: 27-Aug-2022
https://doi.org/10.1007/s10707-022-00472-3
Sun WWang HZhao X(2017)A simplification method for grid-based DEM using topological hierarchiesSurvey Review10.1080/00396265.2017.131035550:362(454-467)Online publication date: 10-Apr-2017
https://doi.org/10.1080/00396265.2017.1310355
De Floriani LIuricich FMagillo PMesmoudi MWeiss K(2012)Discrete Distortion for 3D Data AnalysisVisualization in Medicine and Life Sciences II10.1007/978-3-642-21608-4_1(3-25)Online publication date: 2012
https://doi.org/10.1007/978-3-642-21608-4_1
Weiss KDe Floriani LFellegara RVelloso M(2011)The PR-star octreeProceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems10.1145/2093973.2093987(92-101)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1145/2093973.2093987
Mesmoudi MDe Floriani LMagillo PWolfson OAgrawal DLu C(2009)Morphology analysis of 3D scalar fields based on morse theory and discrete distortionProceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems10.1145/1653771.1653799(187-196)Online publication date: 4-Nov-2009
https://dl.acm.org/doi/10.1145/1653771.1653799

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Concentrated curvature for mean curvature estimation in triangulated surfaces

Lines of curvature and umbilical points for implicit surfaces

Curvature formulas for implicit curves and surfaces

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