Solving Euclidean Problems by Isotropic Initialization

An optional description of the image for screen readers. By Caigui Jiang

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, quadmesh mechanisms, composite asymptotic-geodesic gridshells, and asymptotic gridshells with constant node angle.

Publication
arxiv
Click the Cite button above to demo the feature to enable visitors to import publication metadata into their reference management software.
Click the Slides button above to demo Academic’s Markdown slides feature.

Supplementary notes can be added here, including code and math.

Caigui Jiang
Caigui Jiang
Professor

My research interests are in geometric modeling, geometry processing, architectural geometry, computer graphics, and computer vision.