Elsevier

Journal of Algorithms

Volume 6, Issue 3, September 1985, Pages 359-375
Journal of Algorithms

Finding the smallest triangles containing a given convex polygon

https://doi.org/10.1016/0196-6774(85)90005-7Get rights and content

Abstract

For a given convex n-gon P an O(n log2 n) algorithm finds all local minima (with respect to area) among the triangles containing P. No areas are computed, for the algorithm is based on a simple geometric characterization of the local minima.

References (13)

  • D Avis et al.

    On the multimodality of distances in convex polygons

    Comput. Math. Appl

    (1982)
  • J.E Boyce et al.

    Finding extremal polygons

  • B Chazelle et al.

    The power of geometric duality

  • D. P. Dobkin, R. L. Drysdale III, and L. J. Guibas, Finding smallest polygons, Adv. in Comput....
  • D. P. Dobkin and J. I. Munro, Efficient uses of the past, J. Algorithms, in...
  • D.P Dobkin et al.

    On a general method for maximizing and minimizing among certain geometric problems

There are more references available in the full text version of this article.

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