• Corpus ID: 124816889

A covariant approach to geometry using geometric algebra

  title={A covariant approach to geometry using geometric algebra},
  author={A Lasenny and Joan Lasenby and Rj Wareham},
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… 
Calculating the Rotor Between Conformal Objects
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Conformal Geometric Algebra
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Some Applications of Clifford Algebra in Geometry
  • Ying-Qiu Gu
  • Mathematics
    Structure Topology and Symplectic Geometry
  • 2020
In this chapter, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation, and profound insight of this
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Real physical systems with reflective and rotational symmetries such as viruses, fullerenes and quasicrystals have recently been modeled successfully in terms of three-dimensional (affine) Coxeter
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A new method for pose and position interpolation based on CGA is discussed which firstly allows for existing interpolation methods to be cleanly extended to pose andposition interpolation, but also allows for this to be extended to higher-dimension spaces and all conformal transforms (including dilations).
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As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the
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By moving from a projective to a conformal representation (5d representation of 3d space), one is able to extend the range of geometrical operations that can be carried out in an efficient and elegant way.
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Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with
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The standard algebraic model for Euclidean space E n is an n-dimensional real vector space ℝ n or, equivalently, a set of real coordinates. One trouble with this model is that, algebraically, the
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Geometric algebra extends Clifford algebra with geometrically meaningful operators with the purpose of facilitating geometrical computations. Present textbooks and implementation do not always convey
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My purpose in this chapter is to introduce you to a powerful new algebraic model for Euclidean space with all sorts of applications to computer-aided geometry, robotics, computer vision and the like.
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We introduce the third of the classical geometries, hyperbolic geometry.