Solving Euclidean Problems by Isotropic Initialization
Computational Geometry
2025-06-03 v1 Differential Geometry
Metric Geometry
Abstract
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous problems in isotropic geometry. Isotropic geometry can be viewed as a structure-preserving simplification of Euclidean geometry. The solutions found in the isotropic case give insight and can initialize optimization algorithms to solve the original Euclidean problems. We illustrate this general approach with three examples: quad-mesh mechanisms, composite asymptotic-geodesic gridshells, and asymptotic gridshells with constant node angle.
Cite
@article{arxiv.2506.01726,
title = {Solving Euclidean Problems by Isotropic Initialization},
author = {Khusrav Yorov and Bolun Wang and Mikhail Skopenkov and Helmut Pottmann and Caigui Jiang},
journal= {arXiv preprint arXiv:2506.01726},
year = {2025}
}