Analytical Methods for Squaring the Disc
History and Overview
2024-12-30 v5 Differential Geometry
Abstract
We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region. Ideally, we want the mapping to be smooth and invertible. In addition, we put emphasis on mappings with desirable properties. These include conformal, equiareal, and radially-constrained mappings. Finally, we present applications to logo design, panoramic photography, and hyperbolic art.
Keywords
Cite
@article{arxiv.1509.06344,
title = {Analytical Methods for Squaring the Disc},
author = {Chamberlain Fong},
journal= {arXiv preprint arXiv:1509.06344},
year = {2024}
}
Comments
Seoul ICM 2014; see also offshoot paper "Elliptification of Rectangular Imagery"