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Compute a Tutte map of a planar surface triangulation

version 1.4.0.0 (4.43 KB) by Dylan Muir
Map a surface mesh onto a planar unit circle, using Tutte's algorithm

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Updated 16 Aug 2017

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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.
References:
[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.

Cite As

Dylan Muir (2020). Compute a Tutte map of a planar surface triangulation (https://www.mathworks.com/matlabcentral/fileexchange/32726-compute-a-tutte-map-of-a-planar-surface-triangulation), MATLAB Central File Exchange. Retrieved .

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MATLAB Release Compatibility
Created with R2009a
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