Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Triangulation Data Structures

  • Luca Castelli Aleardi
  • Olivier Devillers
  • Jarek Rossignac
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_589-1

Years and Authors of Summarized Original Work

2008; Castelli Aleardi, Devillers, Schaeffer

2009; Gurung, Rossignac

2012; Castelli Aleardi, Devillers, Rossignac

Problem Definition

The main problem consists in designing space-efficient data structures allowing to represent the connectivity of triangle meshes while supporting fast navigation and local updates.

Mesh Structures: Definition

Triangle meshes are among the most common representations of shapes. A triangle mesh is a collection of triangle faces that define a polyhedral approximation of a surface. A mesh is manifold if every edge is bounding either one or two triangles and if the faces incident to a same vertex define a closed or open fan. Here we focus on manifold meshes. Assuming that the genus and the number of boundary edges are negligible when compared to the number n of vertices, the number m of faces is roughly equal to 2n.

Data Structures: Classification

Mesh data structures can be compared with respect to several...


Triangulations Triangle meshes Compact data structures Succinct representations 
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Recommended Reading

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    Boissonnat JD, Devillers O, Pion S, Teillaud M, Yvinec M (2002) Triangulations in CGAL. Comput Geom 22:5–19. doi:http://dx.doi.org/10.1145/336154.336165Google Scholar
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    Castelli Aleardi L, Devillers O (2011) Explicit array-based compact data structures for triangulations. In: ISAAC, Yokohama, pp 312–322. doi:http://dx.doi.org/10.1007/978-3-642-25591-5_33Google Scholar
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Luca Castelli Aleardi
    • 1
  • Olivier Devillers
    • 2
  • Jarek Rossignac
    • 3
  1. 1.Laboratoire d’Informatique (LIX)École Polytechnique, Bâtiment Alan TuringPalaiseauFrance
  2. 2.INRIANancyFrance
  3. 3.Georgia Institute of TechnologyAtlanta, GAUSA