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Mappings for Squaring the Circular Disc


Published on

see accompanying paper in
"Analytical Methods for Squaring the Disc"
by Chamberlain Fong
presented in Seoul ICM 2014

We present and analyze several old and new methods for mapping the disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside a 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 of such mappings to logo design, panoramic photography, and hyperbolic art.

Published in: Science
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