The Barycentric Coordinates Solution to the Optimal Road Junction Problem

摘要

The road junction location problems, first posited by Fermat and later generalized by Simpson, is a fundamental component of optimal network design. The barycentric resection formulas of plane surveying provide a solution of elegant simplicity to this problem. Prerequisite junction point angles for the application of the resection formulas are obtained directly from Launhardt's original analytical development of this fundamental problem in route location.