Zhejiang Daxue xuebao. Lixue ban, 2017 根据几何代数在地理空间对象建模和多维数据分析应用的特点，研究了共形几何代数交/并(meet/join)算子的含义、构建和应用.利用几何代数多维统一、高维计算适应的优势，设计了基于几何代数meet算子和有向半空间划分理论的时空宗地meet算法.从三维地籍和时空数据建模出发，在共形几何代数和时空代数范畴中，给出了三维、四维时空宗地的定义和表达.同时，以宗地数据的拓扑计算为例，将该算法运用于三维时空宗地拓扑计算场景——历史回溯中，取得了良好的效果.该算法的理念同样适用于四维时空宗地的历史回溯meet求解.
WANGQiaoyan(王巧燕) +4 more
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Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformers [PDF]
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer architecture ...
de Haan, Pim +2 more
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Competitive runtime performance for inverse kinematics algorithms using conformal geometric algebra [PDF]
, 2022 S.5-9Conformal geometric algebra is a powerful tool to find geometrically intuitive solutions. We present an approach for the combination of compact and elegant algorithms with the generation of very efficient code based on two different optimization ...
Hildenbrand, D. +4 more
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Kinematic Analysis of Industrial Robots Based on Conformal Geometric Algebra
Jixie chuandongIn order to solve the problem of high complexity and large amount of computation for kinematics of industrial robots, conformal geometric algebra (CGA) is introduced to the construction of kinematics model of industrial robots.
Yu Yang +4 more
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A Curvature-Based Descriptor for Point Cloud Alignment Using Conformal Geometric Algebra
, 2018 This paper presents a descriptor for course alignment of point clouds using conformal geometric algebra. The method is based on selecting keypoints depending on shape factors to identify distinct features of the object represented by the point cloud, and
A. Kleppe, O. Egeland
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Point Cloud Registration for Assembly using Conformal Geometric Algebra [PDF]
, 2018 This thesis is a collection of five journal papers and one conference paper. The thesis is on pose alignment and point correspondence estimation for 3D point clouds, and inverse kinematics of industrial robots.
Kleppe, Adam Leon
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The Nontriviality of Trivial General Covariance: How Electrons Restrict 'Time' Coordinates, Spinors (Almost) Fit into Tensor Calculus, and 7/16 of a Tetrad Is Surplus Structure [PDF]
, 2011 It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be
Pitts, J. Brian, J. Brian Pitts
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Lie Symmetries of the Wave Equation on the Sphere Using Geometry
DynamicsA semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets:
Michael Tsamparlis +1 more
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Generalized Cross-Curvature Solitons of 3D Lorentzian Lie Groups
AxiomsWe investigate left-invariant generalized cross-curvature solitons on simply connected three-dimensional Lorentzian Lie groups. Working with the assumption that the contravariant tensor Pij (defined from the Ricci tensor and scalar curvature) is ...
Mehdi Jafari
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Conformal geometric algebra and distance geometry [PDF]
, 2018 Orientador: Carlile Campos LavorTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Neste trabalho apresentaremos um método alternativo à resolução de Problemas de Geometria de ...
Camargo, Valter Soares de, 1977-
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