Minimum-Area Enclosing Triangle with a Fixed Angle
Computational Geometry
2013-05-31 v2
Abstract
Given a set S of n points in the plane and a fixed angle 0 < omega < pi, we show how to find in O(n log n) time all triangles of minimum area with one angle omega that enclose S. We prove that in general, the solution cannot be written without cubic roots. We also prove an Omega(n log n) lower bound for this problem in the algebraic computation tree model. If the input is a convex n-gon, our algorithm takes Theta(n) time.
Keywords
Cite
@article{arxiv.1009.3006,
title = {Minimum-Area Enclosing Triangle with a Fixed Angle},
author = {Prosenjit Bose and Jean-Lou De Carufel},
journal= {arXiv preprint arXiv:1009.3006},
year = {2013}
}