Simple Solution to the Three Point Resection Problem

Abstract

The paper presents a simple method of finding the solution to the planar three point resection problem. The main concept leading to the solution is based on an idea of two intersecting circles (which is not new in the literature). The points of intersection of two circles (of which one solves the problem) are obtained by solving a quadratic equation. As a result of the fact that one root of the quadratic equation is known, Vieta’s formula is applied to find the other. When one of the measured angles is equal to 0 or 180°, the problem reduces to the intersection of a straight line and a circle. This also leads to a quadratic equation which is solved by Vieta’s formula. The derivation of the method is very simple (purely analytic) and free from any intermediate parameters, for example, angles, distances, or azimuths.