Three-Dimensional Quadrics in Conformal Geometric Algebras and Their Versor Transformations

Abstract

This work explains how three dimensional quadrics can be defined by the outer products of conformal geometric algebra points in higher dimensions. These multivector expressions code all types of quadrics in arbitrary scale, location and orientation. Furthermore, a newly modified (compared to Breuils et al. in Adv Appl Clifford Algebras 28(35):1–16, 2018. https://doi.org/10.1007/s00006-018-0851-1 ) approach now allows not only the use of the standard intersection operations, but also of versor operators (scaling, rotation, translation). The new algebraic form of the theory will be explained in detail.