A function f: R → R is unimodal if it increases to a maximum value and then decreases. It is strictly unimodal if the increase and decrease are strict. Unimodality is important for the design of efficient search algorithms because it permits prune-and-search strategies. It also simplifies proofs. An algorithm for R3 is presented which has an application to shape matching. Given convex polygon P and Q and a direction in which to translate P, it is easy to find the translation having maximum overlap with Q in linear time.

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Conference Proceedings of the 1996 12th Annual Symposium on Computational Geometry
Citation
Avis, David (David), Bose, P, Shermer, Thomas C. (Thomas C.), Snoeyink, Jack (Jack), Toussaint, Godfried (Godfried), & Zhu, Binhai (Binhai). (1996). On the sectional area of convex polytopes. In Proceedings of the Annual Symposium on Computational Geometry.