# Difference between revisions of "Main Page"

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== Projective Geometric Algebra == | == Projective Geometric Algebra == | ||

− | This wiki is a repository of information about Projective Geometric Algebra, and specifically the four-dimensional Clifford algebra $$\mathcal G_{3,0,1}$$. This | + | This wiki is a repository of information about Projective Geometric Algebra, and specifically the four-dimensional Clifford algebra $$\mathcal G_{3,0,1}$$. This is a mathematical model that naturally incorporates representations for Euclidean points, lines, and planes as well as operations for performing rotations, reflections, and translations in a single algebraic structure. It completely subsumes conventional models that include homogeneous coordinates, Plücker coordinates, quaternions, and screw theory (which makes use of dual quaternions). This makes projective geometric algebra a natural fit for areas of computer science that routinely use these mathematical concepts, especially computer graphics and robotics. |

Please note that this wiki is still under construction and new information is actively being added. | Please note that this wiki is still under construction and new information is actively being added. |

## Revision as of 06:54, 27 April 2021

## Projective Geometric Algebra

This wiki is a repository of information about Projective Geometric Algebra, and specifically the four-dimensional Clifford algebra $$\mathcal G_{3,0,1}$$. This is a mathematical model that naturally incorporates representations for Euclidean points, lines, and planes as well as operations for performing rotations, reflections, and translations in a single algebraic structure. It completely subsumes conventional models that include homogeneous coordinates, Plücker coordinates, quaternions, and screw theory (which makes use of dual quaternions). This makes projective geometric algebra a natural fit for areas of computer science that routinely use these mathematical concepts, especially computer graphics and robotics.

Please note that this wiki is still under construction and new information is actively being added.

- Point
- Line
- Plane
- Motor
- Flector
- Geometric property
- Complements
- Reverses
- Grade and antigrade
- Bulk and weight
- Exterior products
- Geometric products
- Interior products
- Geometric norm
- Unitization
- Projections
- Commutators
- Join and meet
- Euclidean distance
- Translation
- Rotation
- Reflection
- Inversion
- Transflection