  In this paper we consider historical genesis of trifocal curve as an optimal
curve for solving the Fermat's problem (minimizing the sum of distance of one
point to three given points in the plane). Trifocal curves are basic plane
geometric forms which appear in location problems. We also analyze algebraic
equation of these curves and some of their applications in architecture,
urbanism and spatial planning. The area and perimeter of trifocal curves are
calculated using a Java application. The Java applet is developed for
determining numerical value for the Fermat-Torricelli-Weber point and optimal
curve with three foci, when starting points are given on an urban map. We also
present an application of trifocal curves through the analysis of one specific
solution in South Stream gas pipeline project.
