• Corpus ID: 124816889

A covariant approach to geometry using geometric algebra

@inproceedings{Lasenny2004ACA,
  title={A covariant approach to geometry using geometric algebra},
  author={A Lasenny and Joan Lasenby and Rj Wareham},
  year={2004}
}
This report aims to show that using the mathematical framework of conformal geometric algebra – a 5-dimensional representation of 3-dimensional space – we are able to provide an elegant covariant approach to geometry. In this language, objects such as spheres, circles, lines and planes are simply elements of the algebra and can be transformed and intersected with ease. In addition, rotations, translation, dilations and inversions all become rotations in our 5-dimensional space; we will show how… 
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31 Citations
Highly Influential Citations
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Background Citations
14
Methods Citations
8
Results Citations
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31 Citations

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Direct Linear Interpolation of Geometric Objects in Conformal Geometric Algebra
Typically we do not add objects in conformal geometric algebra (CGA), rather we apply operations that preserve grade, usually via rotors, such as rotation, translation, dilation, or via reflection…
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Primitives and transformations in discrete geometry, such as lines, circles, hyperspheres, hyperplanes, have been defined with classical linear algebra in dimension 2 and 3, leading to different…
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