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Study on Spatial Geometric Similarity Based on Conformal Geometric Algebra [PDF]
International Journal of Environmental Research and Public Health, 2022 The study of spatial geometric similarity plays a significant role in spatial data retrieval. Many researchers have examined spatial geometric similarity, which is useful for spatial analysis and data retrieval. However, the majority of them focused on objects of the same type.
Xiaomin Jiang, Yangfei Huang, Feng Zhang
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Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra [PDF]
Advances in Applied Clifford Algebras, 2021 We show that if PGA is understood as a subalgebra of CGA in mathematically correct sense, then the flat objects share the same representation in PGA and CGA. Particularly, we treat duality in PGA. This leads to unification of PGA and CGA objects which is important especially for software implementation and symbolic calculations.
Jaroslav Hrdina +3 more
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LAPLACE EQUATIONS, CONFORMAL SUPERINTEGRABILITY AND BÔCHER CONTRACTIONS [PDF]
Acta Polytechnica, 2016 Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often ``hidden''.The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define ...
Ernest G. Kalnins +2 more
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Inverse Kinematics for Industrial Robots using Conformal Geometric Algebra [PDF]
Modeling, Identification and Control, 2016 This paper shows how the recently developed formulation of conformal geometric algebra can be used for analytic inverse kinematics of two six-link industrial manipulators with revolute joints.
Adam L. Kleppe, Olav Egeland
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IEEE Access, 2022 This article presents a revisited proposal for the formulation of objects and geometric relations and constraints in the conformal space. For modeling, graphics engineering, kinematics, and dynamics, the solution of problems using only points and lines ...
Eduardo Jose Bayro-Corrochano +4 more
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Reinterpreting the Smith Chart Using Conformal Geometric Algebra
IEEE Access, 2023 In this study, transmission line calculations using the Smith chart were reinterpreted within the context of Conformal Geometric Algebra (CGA). Reflection coefficients and immittances (representing either impedances or admittances depending on the ...
Michael J. Neve
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IEEE Access, 2023 The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model
Eduardo Bayro-Corrochano +2 more
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Motion generation of a planar 3R serial chain based on conformal geometric algebra with applications to planar linkages [PDF]
Mechanical Sciences, 2022 A planar three-revolute (3R) serial chain is an important part of many mechanisms. The classical approach in motion generation of a planar 3R serial chain is to construct closed-loop equations based on complex numbers, which yields a large-scale ...
L. Wang +7 more
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Direct Linear Interpolation of Geometric Objects in Conformal Geometric Algebra [PDF]
Advances in Applied Clifford Algebras, 2019 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 and inversion. However, here we show that direct linear interpolation of conformal geometric objects can be both intuitive and of practical use. We present a
Hadfield, H., Lasenby, J.
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Lifshitz Holography with Isotropic Scale Invariance [PDF]
, 2014 Is it possible for an anisotropic Lifshitz critical point to actually exhibit isotropic conformal invariance? We answer this question in the affirmative by constructing a concrete holographic realization.
Gary, Michael +3 more
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