# 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} }

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…

## 179 Citations

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