On the Clifford Algebraic Description of Transformations in a 3D Euclidean Space

Current survey of Clifford geometric algebra applications

“…How transformations in R 3 can be described in terms of the GA Cl (3,3) of quadratic space R 3,3 is discussed in Vaz and Mann. 81 It is shown that this algebra describes in a unified way the operations of reflection, rotation (circular and hyperbolic), translation, shear, and nonuniform scale. Moreover, using Hodge duality, cotranslation is defined, showing that perspective projection can be written in this GA as composition of translation and cotranslation.…”

“…How transformations in $$$ {\mathbb{R}}^3 $$$ can be described in terms of the GA $$$ Cl\left(3,3\right) $$$ of quadratic space $$$ {\mathbb{R}}^{3,3} $$$ is discussed in Vaz and Mann 81 . It is shown that this algebra describes in a unified way the operations of reflection, rotation (circular and hyperbolic), translation, shear, and nonuniform scale.…”