Analysing Willerding’s formula for solving the planar three point resection problem

Abstract

Abstract The main mathematical problem in the planar three point resection problem of surveying is to find a necessary and sufficient condition that a point on a plane is uniquely determined if the directions from that point to three given points are known only up to an unknown offset. It will be shown in this paper that such a condition is the applicability of Willerding’s formula for computing the point in question, and that this condition is equivalent to the well-known necessary condition that the four considered points are not located on a circle or a line. Because of this result, the easy evaluation and the short derivation of Willerding’s formula, it can be expected, that this formula will be widely used in surveying, and also for autonomous robot localization.