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General triangular midpoint subdivision

Authors
Journal
Computer Aided Geometric Design
0167-8396
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.cagd.2014.06.002
Keywords
  • Subdivision Surfaces
  • Loop Subdivision Algorithm
  • Midpoint Subdivision Algorithm
  • Difference Schemes
  • Extraordinary Points
  • Characteristic Map
Disciplines
  • Computer Science

Abstract

Abstract In this paper, we introduce triangular subdivision operators which are composed of a refinement operator and several averaging operators, where the refinement operator splits each triangle uniformly into four congruent triangles and in each averaging operation, every vertex will be replaced by a convex combination of itself and its neighboring vertices. These operators form an infinite class of triangular subdivision schemes including Loop's algorithm with a restricted parameter range and the midpoint schemes for triangular meshes. We analyze the smoothness of the resulting subdivision surfaces at their regular and extraordinary points by generalizing an established technique for analyzing midpoint subdivision on quadrilateral meshes. General triangular midpoint subdivision surfaces are smooth at all regular points and they are also smooth at extraordinary points under certain conditions. We show some general triangular subdivision surfaces and compare them with Loop subdivision surfaces.

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