# The power of geometric duality

@article{Chazelle1985ThePO,
title={The power of geometric duality},
author={Bernard Chazelle and Leonidas J. Guibas and Der-Tsai Lee},
journal={BIT Numerical Mathematics},
year={1985},
volume={25},
pages={76-90}
}
• Published 1 June 1985
• Mathematics
• BIT Numerical Mathematics
This paper uses a new formulation of the notion of duality that allows the unified treatment of a number of geometric problems. In particular, we are able to apply our approach to solve two long-standing problems of computational geometry: one is to obtain a quadratic algorithm for computing the minimum-area triangle with vertices chosen amongn points in the plane; the other is to produce an optimal algorithm for the half-plane range query problem. This problem is to preprocessn points in the… Expand
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