Feature preserving multiresolution subdivision and simplification of point clouds: A conformal geometric algebra approach
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DOI: 10.1002/mma.4616
Abstract: Due to the huge volume and complex structure, simplification of point clouds is an important technique in practical applications. However, the traditional algorithms often lose geometric information and have no dynamic expanding structure. In this… read more here.
Keywords: multiresolution subdivision; geometric algebra; point clouds; simplification point ... See more keywords
Application of Geometric Algebra to the Electroweak Sector of the Standard Model of Particle Physics
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DOI: 10.1007/s00006-016-0685-7
Abstract: Geometric algebra (GA) offers an intriguing approach to understanding the fields of the standard model (SM) of elementary particle physics. This paper examines a geometric view of electron and neutrino fields in the electroweak sector… read more here.
Keywords: geometric algebra; standard model; physics; electroweak ... See more keywords
Massive Geometric Algebra: Visions for C++ Implementations of Geometric Algebra to Scale into the Big Data Era
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DOI: 10.1007/s00006-017-0780-4
Abstract: Geometric algebra (GA) is a promising approach to address interoperability bottlenecks that are particularly prominent in the big data era. Similar to how GA unites and simplifies otherwise distinct mathematical branches it may also help… read more here.
Keywords: big data; massive geometric; data era; geometric algebra ... See more keywords
An Extended Implementation Framework for Geometric Algebra Operations on Systems of Coordinate Frames of Arbitrary Signature
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DOI: 10.1007/s00006-018-0827-1
Abstract: There is a steadily increasing interest in applying Geometric Algebra (GA) in diverse fields of science and engineering. Consequently, we need better software implementations to accommodate such increasing demands that widely vary in their possible… read more here.
Keywords: geometric algebra; framework; implementation; coordinate frames ... See more keywords
Kinematic Optimal Design of a 2-DoF Parallel Positioning Mechanism Employing Geometric Algebra
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DOI: 10.1007/s00006-018-0829-z
Abstract: This paper proposes a geometric algebra (GA) based approach to carry out inverse kinematics and design parameters of a 2-degree-of-freedom parallel mechanism with its topology structure 3-RSR&SS for the first time. Here, R and S… read more here.
Keywords: mechanism; geometric algebra; positioning mechanism; parallel positioning ... See more keywords
Consistently Oriented Dart-based 3D Modelling by Means of Geometric Algebra and Combinatorial Maps
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DOI: 10.1007/s00006-018-0927-y
Abstract: The modelling of real world objects is not a straightforward subject. There are many different schemes; constructive solid geometry (CSG), cell decomposition, boundary representation, etcetera. Obviously, somehow, any scheme will be related to any other… read more here.
Keywords: consistently oriented; geometric algebra; based modelling; geometry ... See more keywords
Formalization of Geometric Algebra in HOL Light
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DOI: 10.1007/s10817-018-9498-9
Abstract: Although the theories of geometric algebra (GA) are widely applied in engineering design and analysis, the studies on their formalization have been scarcely conducted. This paper proposes a relatively complete formalization of GA in HOL… read more here.
Keywords: geometric algebra; formalization geometric; algebra hol; formalization ... See more keywords
A geometric algebra algorithm for the closed-form forward displacement analysis of 3-PPS parallel mechanisms
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DOI: 10.1016/j.mechmachtheory.2019.01.035
Abstract: Abstract This paper presents an efficient graphical representation geometric algebra approach for the forward displacement analysis (FDA) of 3-PPS parallel mechanisms (PMs). Our approach based on conformal geometric algebra (CGA) reveals interesting intuitions and insight… read more here.
Keywords: forward displacement; displacement analysis; geometric algebra; algebra ... See more keywords
Towards the next-generation GIS: a geometric algebra approach
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DOI: 10.1080/19475683.2019.1612945
Abstract: ABSTRACT Due to the increasing complexity of GIS data and service modes, there is an urgent need for the next generation of GIS with new representation and computation methods. A number of spatiotemporal models, analytical… read more here.
Keywords: next generation; gis; generation gis; geometric algebra ... See more keywords
Using geometric algebra to represent curvature in shell theory with applications to Starling resistors
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DOI: 10.1098/rsos.171212
Abstract: We present a novel application of rotors in geometric algebra to represent the change of curvature tensor that is used in shell theory as part of the constitutive law. We introduce a new decomposition of… read more here.
Keywords: geometric algebra; analysis; shell theory; curvature ... See more keywords
Joint Sparse Representation Model for Multi-Channel Image Based on Reduced Geometric Algebra
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DOI: 10.1109/access.2018.2819691
Abstract: Sparse representations have been extended to color image processing. However, existing sparse models treat each color image pixel either as a scalar which loses color structures or as a quaternion vector matrix with high computational… read more here.
Keywords: color; image; color image; geometric algebra ... See more keywords