Conformal geometric algebra

Abstract

This chapter is devoted to a presentation of conformal geometric algebra (CGA) targeted to the sort of applications dealt with in chapters 4 (robotics) and 5 (molecular geometry). This means that the ground space will be the Euclidean space E3 and that the algebra we will be working with is designed so that it can encode all conformal transformations of E3 in spinorial form. Except for noting that conformal means angle-preserving, we can defer the necessary precisions to the most convenient moments in our exposition. Here are some references: Foundational paper: [64]; a nice expository memoir: [55]; computationally oriented: [49]; vision and graphics oriented, [54]; oriented conformal geometry: [12]; treatises: [20, 30, 63, 79].