Elliptification of Rectangular Imagery

TL;DR

This paper explores algorithms for transforming rectangular images into elliptical shapes using invertible mathematical mappings, extending square-to-disc mappings to handle rectangles and ellipses.

Contribution

It introduces a method to extend invertible square-to-disc mappings to rectangular and elliptical regions, enabling precise shape transformations.

Findings

Developed invertible mappings for shape conversion

Extended square-to-disc mappings to rectangles and ellipses

Provided mathematical framework for shape transformation

Abstract

We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We mainly focus on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with invertible mappings between the square and the circular disc then extend it to handle rectangles and ellipses. This extension can be done by simply removing the eccentricity and reintroducing it back after using a chosen square-to-disc mapping.