Isometric Deformations of Discrete and Smooth T-surfaces
Differential Geometry
2023-02-20 v1 Discrete Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.2302.08925,
title = {Isometric Deformations of Discrete and Smooth T-surfaces},
author = {Ivan Izmestiev and Arvin Rasoulzadeh and Jonas Tervooren},
journal= {arXiv preprint arXiv:2302.08925},
year = {2023}
}