2025/06/02 by Khusrav Yorov, Bolun Wang, Yorov, Khusrav +7 · 2 citations
Engineering · Computer Science · #3D Shape Modeling and Analysis #Topology Optimization in Engineering #Computational Geometry and Mesh Generation
paper · pdf · doi:10.1016/j.cagd.2026.102593
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.