Guide to Geometric Algebra in Practice

Tutorial Appendix: Structure Preserving Representation of Euclidean Motions Through Conformal Geometric Algebra

How to Read This Guide to Geometric Algebra in Practice

This book is called a ‘Guide to Geometric Algebra in Practice’. It is composed of chapters by experts in the field and was conceived during the AGACSE-2010 conference in Amsterdam. As you scan the contents, you will find that all chapters indeed use geometric algebra but that the term ‘practice’ means different things to different authors. As we discuss the various Parts below, we guide you thr...

How to Read This Guide to Geometric Algebra in Practice

This book is called a ‘Guide to Geometric Algebra in Practice’. It is composed of chapters by experts in the field and was conceived during the AGACSE-2010 conference in Amsterdam. As you scan the contents, you will find that all chapters indeed use geometric algebra but that the term ‘practice’ means different things to different authors. As we discuss the various Parts below, we guide you thr...

The Shape of Differential Geometry in Geometric Calculus

We review the foundations for coordinate-free differential geometry in Geometric Calculus. In particular, we see how both extrinsic and intrinsic geometry of a manifold can be characterized a single bivector-valued oneform called the Shape Operator. The challenge is to adapt this formalism to Conformal Geometric Algebra for wide application in computer science and engineering.

On Geometric Theorem Proving with Null Geometric Algebra

In algebraic approaches to geometric computing, the general procedure is as follows [11]: first, the geometric configuration, including both the hypotheses and the conclusion, is translated into an algebraic formulation in a prerequisite algebraic language; second, algebraic computations are carried out to the conclusion by utilizing the computational rules of the algebra and the given hypothes...

Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra

The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric da...