Living Reference Work Entry

Encyclopedia of Algorithms

pp 1-7

Date: Latest Version

Triangulation Data Structures

  • Luca Castelli AleardiAffiliated withLaboratoire d’Informatique (LIX), École Polytechnique, Bâtiment Alan Turing Email author 
  • , Olivier DevillersAffiliated withINRIA
  • , Jarek RossignacAffiliated withGeorgia Institute of Technology

Keywords

Triangulations Triangle meshes Compact data structures Succinct representations

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 criteria. A basi ...

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