2024/12/05 by Zeyuan He, He, Zeyuan, Kentaro Hayakawa +3 · 1 citation
Computer Science · Engineering · #Advanced Materials and Mechanics #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2412.04298
openalex publication_date 2024/12/05 · openalex created_date 2024/12/07 · openalex updated_date 2026/07/28
A quad-mesh rigid origami is a continuously deformable panel-hinge structure where planar, rigid, zero-thickness quadrilateral panels are connected by rotational hinges in the combinatorics of a grid. This article provides a comprehensive exposition of two new families of infinitely refinable quad-mesh rigid origami, generated from linear and equimodular couplings. These constructions expand the current landscape beyond well-known variations such as the Miura-ori, V-hedron (discrete Voss surface or eggbox pattern), anti-V-hedron (flat-foldable pattern), and T-hedron (trapezoidal pattern). We conjecture that as the mesh is refined to infinity, these quad-mesh rigid origami converges to special ruled surfaces in the limit, supported by multiple lines of evidence.