Annette Ebbers-Baumann, Rolf Klein, Christian Knauer, and Günter Rote:

The geometric dilation of three points

Journal of Computational Geometry 10, no. 1 (2019), 532–549. doi:10.20382/jocg.v10i1a18  →BibTeX


Given three points in the plane, we construct the plane geometric network of smallest geometric dilation that connects them. The geometric dilation of a plane network is defined as the maximum dilation (distance along the network divided by Euclidean distance) between any two points on its edges. The optimum network is either a line segment, a Steiner tree, or a curve consisting of two straight edges and a segment of a logarithmic spiral.

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Last update: November 29, 2019.