Spatial graph embeddings and coupler curves - source code and results

This is supplementary material for the paper On the Maximal Number of Real Embeddings of Spatial Minimally Rigid Graphs presented at ISSAC 2018, see the paper 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.