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Compute a Tutte map of a planar surface triangulation

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Compute a Tutte map of a planar surface triangulation


Dylan Muir (view profile)


29 Aug 2011 (Updated )

Map a surface mesh onto a planar unit circle, using Tutte's algorithm

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Usage: [mfTutteMap] = TutteMap(mnTriangulation)
Maintaining the existing triangulation, this function maps a surface mesh onto a planar unit circle. Tutte's algorithm [1] is used. The simple technique for finding point locations is from [2].

'mnTriangulation' is an Nx3 array as returned by delaunayn, defining the triangulation of the surface mesh. 'mfTutteMap' will be an Mx2 array, each row of which defines the planar location of a vertex. The surface triangulation should contain no holes, and must have a boundary! The first boundary cycle will be mapped onto the unit circle, with the interior points mapped inside the circle such that no edge crossings occur.

[1] Tutte, 1963. "How to draw a graph". Proc. Lond. Math. Soc. 13, 743-768.

[2] Kocay & McLeod, 2005. "Novel approaches to placement". Canadian Conference on Electrical and Computer Engineering 2005, 1931-1934.

MATLAB release MATLAB 7.8 (R2009a)
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