A Simple Criterion for Nodal 3-connectivity in Planar Graphs

  • Authors:

  • Colm Ó Dúnlaing

  • Affiliations:

  • Mathematics, Trinity College, Dublin 2, Ireland

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

This paper gives a simple characterisation of nodally 3-connected planar graphs, which have the property that barycentric mappings, and more generally convex combination mappings, are embeddings. This has applications in numerical analysis (grid generation), and in computer graphics (image morphing, surface triangulations, texture mapping): see [Michael S. Floater (2002). Convex combination maps. In Algorithms for Approximation IV, 18-23, J. Levesley, I.J. Anderson, and J.C. Mason (eds), University of Huddersfield; Geoffrey White (2004). Mesh parametrization for texture mapping. Undergraduate computer science project, Oxford University].