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Advances in Applied Clifford Algebras, 2018
The authors define the Geometric Algebra for Conics (GAC) as a special Clifford algebra, together with a special embedding of two-dimensional Euclidean space. This is followed by the inner product representations of all the geometric entities available in GAC; these correspond to all possible conic sections and their intersections.
Jaroslav Hrdina +2 more
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The authors define the Geometric Algebra for Conics (GAC) as a special Clifford algebra, together with a special embedding of two-dimensional Euclidean space. This is followed by the inner product representations of all the geometric entities available in GAC; these correspond to all possible conic sections and their intersections.
Jaroslav Hrdina +2 more
exaly +2 more sources
Geometric Reasoning With Geometric Algebra
, 2001 This chapter starts with an introduction to Clifford algebra for Euclidean geometry and shows how geometric theorems can be proved automatically in the Clifford algebra formalism. A short review of available approaches is given and examples are provided.
Wang, Dongming, Dongming Wang
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Implementation of Geometric Algebra in Computer Algebra Systems
Programming and Computer Software, 2023For describing specialized mathematical structures, it is preferable to use a special formalism rather than a general one. However, tradition often prevails in this case. For example, to describe rotations in the three-dimensional space or to describe motion in the Galilean or Minkowski spaces, vector (or tensor) formalism, rather than more specialized
Migran N. Gevorkyan +4 more
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, 2023 Práce se zaměřuje na geometrickou algebru. Začneme neformálním úvodem do pojmů geometrické algebry, jako jsou: orientované délky, odrazy, rotace. Ukazujeme také podstatu geometrické algebry, geometrického součinu.
Terry E. Moschandreou, Khoa Nguyen
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An algebra of geometric shapes
IEEE Computer Graphics and Applications, 1993A simple algebra of shapes with 2D planar regions is developed. The fact that a 2D region can be completely described by a one-dimensional, closed-boundary curve if it is homogeneous is used in the presented approach, which first converts the spatial description of the closed curve into an equivalent Fourier series description and then uses the Fourier-
Pijush K. Ghosh, Pradeep K. Jain
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A Geometric Algebra Implementation using Binary Tree
Advances in Applied Clifford Algebras, 2017 International audienceThis paper presents an efficient implementation of geometric algebra, based on a recursive representation of the algebra elements using binary trees.
Stéphane Breuils +2 more
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Geometric Algebra in Linear Algebra and Geometry
Acta Applicandae Mathematica, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pozo, José María, Sobczyk, Garret
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GEOMETRIC EQUIVALENCE OF ALGEBRAS
International Journal of Algebra and Computation, 2001In this paper, we study the geometric equivalence of algebras in several varieties of algebras. We solve some of the problems formulated in [2], in particular, that of geometric equivalence for real-closed fields and finitely generated commutative groups.
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