The combinatorial geometry of stresses in frameworks

2015/12/08 by Oleg Karpenkov, Karpenkov, O.
Computer Science · Engineering · #05C10 #52C30 #Advanced Materials and Mechanics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.1512.02563

openalex publication_date 2015/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we formulate and prove necessary and sufficient geometric conditions for existence of generic tensegrities in the plane for arbitrary graphs. The conditions are written in terms of "meet-join" relations for the configuration spaces of fixed points and non-fixed lines through fixed points.

Citations

• Some notes on the equivalence of first-order rigidity in various geometries

Related

• Geometric criteria for realizability of tensegrities in higher\n dimensions
• A universality theorem for stressable graphs in the plane
• Geometry of configuration spaces of tensegrities
• Exploring Continuous Tensegrities
• Rational tensegrities through the lens of toric geometry