Restricted Mesh Simplification Using Edge Contractions

  • Mattias Andersson
  • Joachim Gudmundsson
  • Christos Levcopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


We consider the problem of simplifying a triangle mesh using edge contractions, under the restriction that the resulting vertices must be a subset of the input set. That is, contraction of an edge must be made onto one of its adjacent vertices. In order to maintain a high number of contractible edges under this restriction, a small modification of the mesh around the edge to be contracted is allowed. Such a contraction is denoted a 2-step contraction. Given m “important” points or edges it is shown that a simplification hierarchy of size O(n) and depth O(log(n/m)) may be constructed in O(n) time. Further, for many edges not even 2-step contractions may be enough, and thus, the concept is generalized to k-step contractions.


Induction Hypothesis Adjacent Vertex Triangle Mesh Convex Corner Concave Corner 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mattias Andersson
    • 1
  • Joachim Gudmundsson
    • 2
  • Christos Levcopoulos
    • 1
  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.National ICT Australia Ltd., IMAGEN ProgramAlexandriaAustralia

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