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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.
Petr Vasik +2 more
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Double Conformal Geometric Algebra
Advances in Applied Clifford Algebras, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eckhard Hitzer +2 more
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Oriented Conformal Geometric Algebra
Advances in Applied Clifford Algebras, 2008In [16] Stolfi developed a complete theory of Oriented Projective Geometry. He showed that assigning meaning to the sign of an otherwise homogeneous representation of geometry could provide a multitude of benefits. This paper extends his work by applying the same approach to Conformal Geometric Algebra.
Joan Lasenby, Lasenby Joan
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Conformal Geometric Algebra for Robotic Vision
Journal of Mathematical Imaging and Vision, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo Bayro-Corrochano +2 more
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Navigation functions in Conformal Geometric Algebra
IX Latin American Robotics Symposium and IEEE Colombian Conference on Automatic Control, 2011 IEEE, 2011Conformal Geometric Algebra (CGA) can greatly improve controllers by simplifying the necessary equations and by its ability to apply geometric operations to more complicated geometric entities. In this paper we extend a singularity free CGA-based angular and linear velocity controller with navigation functions.
Geoff Fink +2 more
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Conformal Geometric Algebra method for detection of geometric primitives
2016 23rd International Conference on Pattern Recognition (ICPR), 2016In this paper, we present a geometric algebra approach for detection of geometric entities in images. Our algorithm is grounded on two methodologies: representation of geometric entities and perceptual properties using Conformal Geometric Algebra, and a voting scheme which is implemented using a clustering algorithm.
Gerardo E. Altamirano-Gómez +1 more
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Detection Geometric Object in the Conformal Geometric Algebra Framework
2011 12th International Conference on Computer-Aided Design and Computer Graphics, 2011An eficient rndomized agorithm for line and circle detection in the Conformal Geometric Algebra framework is designed and implemented. This arithmetic performs well when an image has strong background noise. In conformal geometric algebra, circle and line in conformal space can be represented as multivectors.
Zongmin Li +2 more
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Omnidirectional vision using conformal geometric algebra
IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004, 2004The catadioptric projection can be modeled by an equivalent spherical projection. This idea is more versatile in the conformal geometric algebra, a modern framework for the projective space of hyper-spheres. In this framework we analyze diverse catadioptric mirrors, as a result the algebraic burden is reduced allowing the user to work in a more ...
Carlos López-Franco +1 more
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Radon transform and Conformal Geometric Algebra with lines
2008 19th International Conference on Pattern Recognition, 2008In this paper we apply the classic theory of harmonic analysis and the conformal geometric algebra (CGA) to evaluate the Fourier transform on the unit sphere S2 and on the rotation group SO(3). Since the images taken by omnidirectional sensors can be mapped to the sphere, the problem of attitude estimation of a 3D camera rotation can be treated as a ...
Luis Falcón-Morales +1 more
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2018
This chapter is devoted to a presentation of conformal geometric algebra (CGA) targeted to the sort of applications dealt with in chapters 4 (robotics) and 5 (molecular geometry). This means that the ground space will be the Euclidean space E3 and that the algebra we will be working with is designed so that it can encode all conformal transformations ...
Carlile Lavor +2 more
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This chapter is devoted to a presentation of conformal geometric algebra (CGA) targeted to the sort of applications dealt with in chapters 4 (robotics) and 5 (molecular geometry). This means that the ground space will be the Euclidean space E3 and that the algebra we will be working with is designed so that it can encode all conformal transformations ...
Carlile Lavor +2 more
openaire +1 more source