Journal of Zhejiang University-SCIENCE A

, Volume 7, Issue 9, pp 1578–1588 | Cite as

A new representation of orientable 2-manifold polygonal surfaces for geometric modelling

  • Liu Yong-jin 
  • Tang Kai 
  • Joenja Ajay 


Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modern point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used data structures are also presented in terms of time and space efficiency.

Key words

Shape representation Combinatorial data structure Computational topology 

CLC number



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Copyright information

© Zhejiang University 2006

Authors and Affiliations

  • Liu Yong-jin 
    • 1
  • Tang Kai 
    • 2
  • Joenja Ajay 
    • 3
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingChina
  2. 2.Department of Mechanical EngineeringHong Kong University of Science and TechnologyHong KongChina
  3. 3.Department of Industrial Engineering and Logistic ManagementHong Kong University of Science and TechnologyHong KongChina

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