4 Statistical Geometric Reasoning

Abstract

In the last chapter we have developed simple algorithms for geometric reasoning on points, lines and planes in 2D and 3D. They were designed with a perfect world in mind: we have not explicitly represented possible errors in the coordinates of the geometric entities. Only for optimal estimations of objects we have allowed the entities to have small errors, but have not given any error measures for observations and unknowns. The weakness of having no error representation becomes apparent when testing relations between entities, see section 3.3: to check a geometric relation, a distance measure has to be equal to zero, but in practice, the computed distances are only ”almost equal to zero”.