Applications of Geometric Algebra in Surveying and Geodesy	

Jorge Ventura, Francisco G. Montoya --	Universidad de Almeria	

This paper introduces a novel method for solving the resection problem in two dimensions based on CGA. An efficient implementation of the recently presented VGA methods is also presented. Advantage is taken because of the characteristics of CGA, which enables the representation of points, lines, planes, and volumes in a unified mathematical framework and offers a more intuitive and geometric understanding of the problem, in contrast to existing purely algebraic methods. Several numerical examples are presented to demonstrate the efficacy of the proposed methods and to compare its validity with established techniques in the field. Our findings suggest that the proposed VGA and CGA-based methods can provide a more efficient and comprehensible solution to the two-dimensional resection problem, paving the way for further applications and advances in geodesy, surveying or navigation research. Furthermore, the method’s emphasis on graphical and geometric representation makes it particularly suitable for educational purposes, allowing the reader to grasp the concepts and principles of resection more effectively.