geometric_algebra
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| Plücker Coordinates Using Projective Representation]] (2018) - //Vaclav Skala, Michal Smolik// | 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. | 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. | ||
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| + | 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. | ||
| ===== Books ===== | ===== Books ===== | ||
geometric_algebra.txt · Last modified: 2023/12/30 00:23 by pbk