# Conformal Geometric Algebra

@inproceedings{Lavor2018ConformalGA, title={Conformal Geometric Algebra}, author={Carlile Lavor and Sebasti{\'a}n Xamb{\'o}-Descamps and Isiah Zaplana}, year={2018} }

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…

## References

SHOWING 1-10 OF 10 REFERENCES

Oriented Conformal Geometric Algebra

- Mathematics
- 2008

Abstract.In [16] Stolfi developed a complete theory of Oriented Projective Geometry. He showed that assigning meaning to the sign of an otherwise homogeneous representation of geometry could provide…

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.

Foundations of Geometric Algebra Computing

- Computer ScienceGeometry and Computing
- 2013

The goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry.

Geometric Algebra with Applications in Engineering

- MathematicsGeometry and Computing
- 2009

Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.

Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics

- Mathematics
- 2015

Understanding Geometric Algebra: Hamilton, Grassmann, and Clifford for Computer Vision and Graphics introduces geometric algebra with an emphasis on the background mathematics of Hamilton, Grassmann,…

Articulating Space: Geometric Algebra for Parametric Design - Symmetry, Kinematics, and Curvature

- Mathematics
- 2015

Author(s): Colapinto, Pablo | Advisor(s): Peljhan, Marko | Abstract: To advance the use of geometric algebra in practice, we develop computational methods for parameterizing spatial structures with…

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.

A mathematical introduction to conformal field theory

- Mathematics
- 1997

Mathematical Preliminaries.- Conformal Transformations and Conformal Killing Fields.- The Conformal Group.- Central Extensions of Groups.- Central Extensions of Lie Algebras and Bargmann's Theorem.-…

A universal model for conformal geometries of Euclidean, spherical and double-hyperbolic spaces

- Mathematics
- 2001

The study of relations among Euclidean, spherical and hyperbolic geometries dates back to the beginning of last century. The attempt to prove Euclid’s fifth postulate led C. F. Gauss to discover…