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--- geometric_algebra [2018/11/11 10:00] – [Personal sites] pbk
+++ geometric_algebra [2018/11/11 10:17] – [Articles] pbk
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 We will do some truly anarchistic computations in basic geometry. We will make these anarchistic computations a part of the establishment. Using the establishment, we will show some quite charming ways of thinking about basic geometry.
-  * [[http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pdf|Computer Graphics using Conformal Geometric Algebra]] (2006) - //Richard James Wareham//
+  * [[http://www2.montgomerycollege.edu/departments/planet/planet/Numerical_Relativity/GA-SIG/Papers/Report.pdf|A Covariant Approach to Geometry using Geometric Algebra]] (2004) - //Anthony Lasenby, Joan Lasenby, Richard 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 this enables us to provide very simple proofs of complicated constructions. We give examples of the use of this system in computer graphics and indicate how it can be extended into an even more powerful tool – we also discuss its advantages and disadvantages as a programming language. Lastly, we indicate how the framework might possibly be used to unify all geometries, thus enabling us to deal simply with the projective and non-Euclidean cases.
+  * [[http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pdf|Computer Graphics using Conformal Geometric Algebra]] (2006) - //Richard Wareham//
 This thesis investigates the emerging field of Conformal Geometric Algebra (CGA) as a new basis for a CG framework. Computer Graphics is, fundamentally, a particular application of geometry. From a practical standpoint many of the low-level problems to do with rasterising triangles and projecting a three-dimensional world onto a computer screen have been solved and hardware especially designed for this task is available.
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 Plücker Coordinates Using Projective Representation]] (2018) - //Vaclav Skala, Michal Smolik//
 This contribution presents a new formulation of Plücker coordinates using geometric algebra and standard linear algebra with projective representation. The Plücker coordinates are usually used for a line representation in space, which is given by two points. However, the line can be also given as an intersection of two planes in space. The principle of duality leads to a simple formulation for both cases.The presented approach uses homogeneous coordinates with the duality principle application. It is convenient for application on GPU as well.
+  * [[https://www.researchgate.net/profile/Debashis_Sen/publication/327262811_Geometric_Algebra_as_the_unified_mathematical_language_of_Physics_An_introduction_for_advanced_undergraduate_students/links/5b8f6e8fa6fdcc1ddd0fea28/Geometric-Algebra-as-the-unified-mathematical-language-of-Physics-An-introduction-for-advanced-undergraduate-students.pdf|Geometric Algebra as the unified mathematical language of Physics: An introduction for advanced undergraduate students]] (2018) - //Debashis Sen, Deeprodyuti Sen//
+In recent years, geometric algebra has emerged as the preferred mathematical framework for physics. It provides both compact and intuitive descriptions in many areas including classical and quantum mechanics, electromagnetic theory and relativity. Geometric algebra has also found prolific applications as a computational tool in computer graphics and robotics. Leading exponents of this extensive mathematical apparatus are fervently insisting its inclusion in the undergraduate physics curriculum and in this paper an introductory exposure, in familiar terms for the advanced undergraduate students, is intended.
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