A Note on Toroidal Maxwell-Cremona Correspondences

09/24/2020
by   Patrick Lin, et al.
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We explore toroidal analogues of the Maxwell-Cremona correspondence. Erickson and Lin [arXiv:2003.10057] showed the following correspondence for geodesic torus graphs G: a positive equilibrium stress for G, an orthogonal embedding of its dual graph G^*, and vertex weights such that G is the intrinsic weighted Delaunay graph of its vertices. We extend their results to equilibrium stresses that are not necessarily positive, which correspond to orthogonal drawings of G^* that are not necessarily embeddings. We also give a correspondence between equilibrium stresses and parallel drawings of the dual.

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