2023/02/17 by Ivan Izmestiev, Izmestiev, Ivan, Arvin Rasoulzadeh +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Materials and Mechanics #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2302.08925
openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quad-surfaces are polyhedral surfaces with quadrilateral faces and the combinatorics of the square grid. A generic quad-surface is rigid. T-hedra is a class of flexible quad-surfaces introduced by Graf and Sauer in 1931. Particular examples of T-hedra are the celebrated Miura fold, discrete surfaces of revolution, and discrete molding surfaces. We provide an explicit parametrization of the isometric deformation of a T-hedron. T-hedra have a smooth analog, T-surfaces. For these we provide a synthetic and an analytic description, both similar to the corresponding descriptions of T-hedra. We also parametrize the isometric deformations of T-surfaces and discuss their deformability range.