6 papers
Obstructions to Reality: Torsors & Visual Paradox
Robert Ghrist, Zoe Cooperband
Visual paradoxes like the Penrose staircase present a fundamental tension: locally coherent geometric relationships that cannot be realized globally. Inspired by Penrose's observat…
Unified Origami Kinematics via Cosheaf Homology
Zoe Cooperband, Robert Ghrist
We establish a novel local-global framework for analyzing rigid origami mechanics through cosheaf homology, proving the equivalence of truss and hinge constraint systems via an ind…
Homology of Moment Frames
Zoe Cooperband, Allan McRobie, Cameron Millar +1
Using homological techniques we show that a pin-anchored frame that involves only moments and shears provides a conceptual bridge between the statics of moment frames and the kinem…
Equivariant Cosheaves and Finite Group Representations in Graphic Statics
Zoe Cooperband, Miguel Lopez, Bernd Schulze
This work extends the theory of reciprocal diagrams in graphic statics to frameworks that are invariant under finite group actions by utilizing the homology and representation theo…
A Cosheaf Theory of Reciprocal Figures: Planar and Higher Genus Graphic Statics
Zoe Cooperband, Robert Ghrist, Jakob Hansen
This paper introduces cellular sheaf theory to graphical methods and reciprocal constructions in structural engineering. The elementary mechanics and statics of trusses are derived…
Towards Homological Methods in Graphic Statics
Zoe Cooperband, Robert Ghrist
Recent developments in applied algebraic topology can simplify and extend results in graphic statics - the analysis of equilibrium forces, dual diagrams, and more. The techniques i…