Restricted Mesh Simplification Using Edge Contractions

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.

• Type: Conference
• Year: 2006
• Where: COCOON
• Authors: Mattias Andersson, Joachim Gudmundsson, Christos Levcopoulos
• Keywords: 2-step Contractions, COCOON 2006, Combinatorics, Edge, Edge Contractions