How to flatten a soccer ball
Algebraic Geometry
2018-01-15 v2 Optimization and Control
Abstract
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general instances, the boundary of the image is given by two highly singular curves. We determine these curves and show how they demarcate the "flattened soccer ball". We explore cylindrical algebraic decompositions, by working through concrete examples. Maps onto convex polygons and connections to convex optimization are also discussed.
Cite
@article{arxiv.1606.02253,
title = {How to flatten a soccer ball},
author = {Kaie Kubjas and Pablo A. Parrilo and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1606.02253},
year = {2018}
}
Comments
21 pages, 8 figures; to appear in Homological and Computational Methods in Commutative Algebra