# The making of GABLE: a geometric algebra learning environment in Matlab

@inproceedings{Mann2001TheMO, title={The making of GABLE: a geometric algebra learning environment in Matlab}, author={Stephen Mann and Leo Dorst and Timaeus Bouma}, year={2001} }

Geometric algebra extends Clifford algebra with geometrically meaningful operators with the purpose of facilitating geometrical computations. Present textbooks and implementation do not always convey this geometrical flavor or the computational and representational convenience of geometric algebra, so we felt a need for a computer tutorial in which representation, computation and visualization are combined to exhibit the intuition and the techniques of geometric algebra. Current software…

## 36 Citations

Geometric algebra for computer graphics

- Mathematics
- 2008

John Vince tackles complex numbers and quaternions; the nature of wedge product and geometric product; reflections and rotations; and how to implement lines, planes, volumes and intersections in this accessible and very readable introduction to geometric algebra.

Geometric Algebra

- MathematicsComputer Vision, A Reference Guide
- 2004

This half day tutorial will emphasize that Geometric Algebra is a unified language for a lot of mathematical systems used in Computer Graphics, and can be used in an easy and geometrically intuitive way in Computer graphics.

Geometric computing in computer graphics and robotics using conformal geometric algebra

- Computer Science, Mathematics
- 2006

The main contribution of this thesis is the geometrically intuitive and - nevertheless - efficient algorithm for a computer animation application, namely an inverse kinematicsgorithm for a virtual character based on an embedding of quaternions in Conformal Geometric Algebra.

Implementing Geometric Algebra Products with Binary Trees

- Mathematics, Computer Science
- 2014

This paper presents a formalization of geometric algebras within the proof assistant Coq, concentrating on the blade factorization operation in the Grassmann algebra and the different products of Clifford algebra.

Geometric algebra for computer science - an object-oriented approach to geometry

- Computer ScienceThe Morgan Kaufmann series in computer graphics
- 2007

An introduction to Geometric Algebra that will give a strong grasp of its relationship to linear algebra and its significance for 3D programming of geometry in graphics, vision, and robotics is found.

Engineering Graphics in Geometric Algebra

- MathematicsGeometric Algebra Computing
- 2010

The suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications, is illustrated and the potential of geometricgebra for optimizations and highly efficient implementations is included.

A covariant approach to geometry using geometric algebra

- Mathematics, Computer Science
- 2004

Using the mathematical framework of conformal geometric algebra – a 5-dimensional representation of 3-dimensional space – is shown to provide an elegant covariant approach to geometry, thus enabling us to deal simply with the projective and non-Euclidean cases.

Geometric Algebra-The mathematical language for Computational Engineering ?

- Mathematics, Computer Science
- 2008

This work reviews some current engineering applications of geometric algebra and observes the potential of this mathematical language to become a basis for a wide range of computational engineering…

Gaigen 2:: a geometric algebra implementation generator

- Computer ScienceGPCE '06
- 2006

Geometric Algebra (GA) is an algebra that encodes geometry much better than standard techniques, which are mainly based on linear algebra with various extensions. Compared to standard techniques, GA…

Clifford Multivector Toolbox (for MATLAB)

- Computer Science, Mathematics
- 2017

An account of a comprehensive toolbox for matlab to compute with Clifford algebras and matrices of multivectors is presented, which has been developed since 2013 and released publically for the first time in 2015.