In this paper, we study four variants of the famous isoperimetric problem. Given a set S of n > 2 points in the plane (in general position), we show how to compute in O(n 2) time, a triangle with maximum (or minimum) area enclosing S among all enclosing triangles with fixed perimeter and one fixed angle. We also show how to compute in O(n 2) time, a triangle with maximum (or minimum) perimeter enclosing S among all enclosing triangles with fixed area and one fixed angle. We also provide an Ω (n log n) lower bound for these problems in the algebraic computation tree model.

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Keywords computational geometry, enclosing problems, Geometric optimization, isoperimetric problems
Persistent URL dx.doi.org/10.1007/s00022-013-0167-1
Journal Journal of Geometry
Citation
Bose, P, & De Carufel, J.-L. (Jean-Lou). (2013). Isoperimetric triangular enclosures with a fixed angle. Journal of Geometry, 104(2), 229–255. doi:10.1007/s00022-013-0167-1