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Spatial graph embeddings and coupler curves - source code and results

Legerský, Jan; Bartzos, Evangelos

This is supplementary material for the paper On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs accepted to ISSAC 2018, see preprint and project website for details. It includes source code and results.

Construction of Geiringer graphs

Sage and Matlab code for construction of Geiringer graphs using Henneberg steps.

Computation of mixed volume and complex solutions

Functions that compute the mixed volume and the (complex) embeddings of a given graph using different algebraic formulations.

Coupler curve visualization and sampling

Implementation of our method for obtaining edge lengths of a Geiringer graph with many real spatial embeddings.
Visualization of coupler curves of the 7-vertex Geiringer graph with the maximal number of real embeddings (G48).

Maple parametric_search

Maple worksheet illustrating a method to improve number of real embeddings of G48 using RootFinding[Parametric] subpackage.

Results

Full list of Geiringer graphs up to 8 vertices.
Edge lengths of graphs obtained by our method that maximizes number of real embeddings. 
Maple script verifying the results.

Files (2.2 MB)
Name Size
Computation_of_mixed_volume_and_complex_solutions.zip
md5:e5af671fb31f8e25d1c1ced2861c6ed9
20.0 kB Download
Construction_of_Geiringer_graphs.zip
md5:a78b31d45e5ef762ec78c670fd0703fa
181.2 kB Download
Coupler_curve_visualization_and_sampling.zip
md5:68db4d1f711db0eb54de9f6abc3a150c
488.7 kB Download
Maple_parametric_search.zip
md5:e0dd7a0109cc78cf4eb1bb4dde5fa8a9
34.9 kB Download
Results.zip
md5:5d0f3b62defd2b948d52d6310857d1b5
1.4 MB Download
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