A case study in geometric algebra : Fitting roommodels to 3 D point clouds Author : Moos

Many geometrical problems exist which have been researched thoroughly, but always using classical methods such as linear algebra as a framework for the problem. As linear algebra is an algebra based on coordinates and numbers as basic elements of computation, this leads to longwinded and non-universal code. Geometric algebra is an alternative formalism in which geometric objects are the basic elements of computation. Using this formalism to represent geometrical problems can often yield more readable and more compact code. In this paper we present a case study of such a problem – specifically fitting room models to 3D point clouds – and the advantages geometric algebra has over classical methods in solving this problem.