User Tools

Site Tools


geometric_algebra

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
Next revision Both sides next revision
geometric_algebra [2021/07/02 18:35]
pbk [Videos]
geometric_algebra [2021/10/20 08:03]
pbk [Articles]
Line 321: Line 321:
   * [[https://www.youtube.com/watch?v=cKfC2ZBJulg|Projective Geometric Algebra for Paraxial Geometric Optics]] - // Katelyn Spadavecchia//.   * [[https://www.youtube.com/watch?v=cKfC2ZBJulg|Projective Geometric Algebra for Paraxial Geometric Optics]] - // Katelyn Spadavecchia//.
   * [[https://www.youtube.com/watch?v=11sH9X0OO9Y&list=PLnpuwbuviU2j7OSnZdstP5_g1ejA32bYA|Geometric Algebra Lectures ]] - //Miroslav Josipović//.   * [[https://www.youtube.com/watch?v=11sH9X0OO9Y&list=PLnpuwbuviU2j7OSnZdstP5_g1ejA32bYA|Geometric Algebra Lectures ]] - //Miroslav Josipović//.
 +  * [[https://www.youtube.com/watch?v=HGcBu4TQgRE|Quaternions and Clifford Algebra]] - //Q. J. Ge and Anurag Purwar//, Stony Brook University.
 +  * [[https://www.youtube.com/watch?v=LestlcDk6Iw|Foundations of Geometric Algebra Computing]] - Lecture at ICU Tokyo, //Dietmar Hildenbrand//.
   * [[https://www.youtube.com/watch?v=e5D7Bma9Vhw&list=PLxo3PbygE0PLdFFy_2b02JAaUsleFW8py|Geometric Algebra]] - First Course in STEMCstudio, //David Geo Holmes//.   * [[https://www.youtube.com/watch?v=e5D7Bma9Vhw&list=PLxo3PbygE0PLdFFy_2b02JAaUsleFW8py|Geometric Algebra]] - First Course in STEMCstudio, //David Geo Holmes//.
 +  * [[https://www.youtube.com/playlist?list=PLsSPBzvBkYjyWv5wLVV7QfeS_d8pwCPv_|AGACSE2021]] - Selected talks.
 +  * [[https://www.youtube.com/playlist?list=PLsSPBzvBkYjxrsTOr0KLDilkZaw7UE2Vc|Plane-based Geometric Algebra Tutorial]] - Presentation at SIBGRAPI 2021, //Steven De Keninck and Leo Dorst//.
 ===== Computing frameworks ===== ===== Computing frameworks =====
   * [[http://www.geometricalgebra.net/downloads.html|GAViewer & GA Sandbox]] - //Leo Dorst, Daniel Fontijne, Stephen Mann//.   * [[http://www.geometricalgebra.net/downloads.html|GAViewer & GA Sandbox]] - //Leo Dorst, Daniel Fontijne, Stephen Mann//.
Line 1355: Line 1359:
   * [[https://arxiv.org/pdf/2007.04464.pdf|Deform, Cut and Tear a skinned model using Conformal Geometric Algebra]] (2020) - //Manos Kamarianakis, George Papagiannakis//   * [[https://arxiv.org/pdf/2007.04464.pdf|Deform, Cut and Tear a skinned model using Conformal Geometric Algebra]] (2020) - //Manos Kamarianakis, George Papagiannakis//
 We present a novel, integrated rigged character simulation framework in Conformal Geometric Algebra (CGA) that supports, for the first time, real-time cuts and tears, before and/or after the animation, while maintaining deformation topology. The purpose of using CGA is to lift several restrictions posed by current state-of-the-art character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current state-of-the-art, dual-quaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dual-quaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dual-quaternions as well as the inability to properly dilate a model during animation. Our CGA algorithm also provides easy interpolation and application of all deformations in each intermediate steps, all within the same geometric framework. Furthermore we also present two novel algorithms that enable cutting and tearing of the input rigged, animated model, while the output model can be further re-deformed. We present a novel, integrated rigged character simulation framework in Conformal Geometric Algebra (CGA) that supports, for the first time, real-time cuts and tears, before and/or after the animation, while maintaining deformation topology. The purpose of using CGA is to lift several restrictions posed by current state-of-the-art character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current state-of-the-art, dual-quaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dual-quaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dual-quaternions as well as the inability to properly dilate a model during animation. Our CGA algorithm also provides easy interpolation and application of all deformations in each intermediate steps, all within the same geometric framework. Furthermore we also present two novel algorithms that enable cutting and tearing of the input rigged, animated model, while the output model can be further re-deformed.
 +
 +  * [[https://www.researchgate.net/profile/Carlos-Muro/publication/339249543_Newton-Euler_Modeling_and_Control_of_a_Multi-copter_Using_Motor_Algebra_mathbfG_301G301/links/603d925f299bf1e0784d02bd/Newton-Euler-Modeling-and-Control-of-a-Multi-copter-Using-Motor-Algebra-mathbfG-3-0-1G3-0-1.pdf|Newton-Euler Modelling and Control of a Multicopter using Motor Algebra G^+_3,0,1]] (2020) - //Carlos A. Arellano-Muro, Guillermo Osuna-Gonzalez, et al//
 +In this work the dynamic model and the nonlinear control for a multi-copter have been developed using the geometric algebra framework specifically using the motor algebra G^+_3,0,1. The kinematics for the aircraft model and the dynamics based on Newton-Euler formalism are presented. Block-control technique is applied to the multi-copter model which involves super twisting control and an estimator of the internal dynamics for maneuvers away from the origin. The stability of the presented control scheme is proved. The experimental analysis shows that our non-linear controller law is able to reject external disturbances and to deal with parametric variations.
 +
 +  * [[http://i-us.ru/index.php/ius/article/download/13579/14098|Human action recognition method based on conformal geometric algebra and recurrent neural network]] (2020) - //Nguyen Nang Hung Van, Pham Minh Tuan et al//
 +The use of Conformal Geometric Algebra in order to extract features and simultaneously reduce the dimensionality of a dataset for human activity recognition using Recurrent Neural Network.
 +
 +  * [[https://arxiv.org/pdf/2107.00343.pdf|Explicit Baker-Campbell-Hausdorff-Dynkin formula for Spacetime via Geometric Algebra]] (2021) - //Joseph Wilson, Matt Visser//
 +We present a compact Baker-Campbell-Hausdorff-Dynkin formula for the composition of Lorentz transformations e^σi in the spin representation (a.k.a. Lorentz rotors) in terms of their generators σi. This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension ≤4, naturally generalising Rodrigues' formula for rotations in R3. In particular, it applies to Lorentz rotors within the framework of Hestenes' spacetime algebra, and provides an efficient method for composing Lorentz generators.
 +
 +  * [[https://arxiv.org/pdf/2107.03771.pdf|Graded Symmetry Groups: Plane and Simple]] (2021) - //Martin Roelfs, Steven De Keninck//
 +The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the classic matrix Lie algebra approach, while retaining information about the number of reflections in a given transformation. This imposes a graded structure on Lie groups, which is not evident in their matrix representation. By embracing this graded structure, the invariant decomposition theorem was proven: any composition of k linearly independent reflections can be decomposed into ⌈k/2⌉ commuting factors, each of which is the product of at most two reflections. This generalizes a conjecture by M. Riesz, and has e.g. the Mozzi-Chasles' theorem as its 3D Euclidean special case.
 +
 +  * [[https://www.pacm.princeton.edu/sites/default/files/pacm_arjunmani_0.pdf|Representing Words in a Geometric Algebra]] (2021) - //Arjun Mani//
 +In this paper we introduce and motivate geometric algebra as a better representation for word embeddings. Next we describe how to implement the geometric product and interestingly show that neural networks can learn this product. We then introduce a model that represents words as objects in this algebra and benchmark it on large corpuses; our results show some promise on traditional word embedding tasks. Thus, we lay the groundwork for further investigation of geometric algebra in word embeddings.
 +
 +  * [[https://ietresearch.onlinelibrary.wiley.com/doi/pdfdirect/10.1049/cmu2.12188|An approach to adaptive filtering with variable step size based on geometric algebra]] (2021) - //Haiquan Wang, Yinmei He et al//
 +Recently, adaptive filtering algorithms have attracted much more attention in the field of signal processing. By studying the shortcoming of the traditional real-valued fixed step size adaptive filtering algorithm, this paper proposed the novel approach to adaptive filtering with variable step size based on Sigmoid function and geometric algebra (GA).
 +
 +  * [[https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9488174|A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020]] (2021) - //Eduardo Bayro-Corrochano//
 +Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering from 1995 to 2020.
 +
 +  * [[https://dspace.library.uu.nl/bitstream/handle/1874/403340/thesis.pdf|Clifford algebras and their application in the Dirac equation]] (2021) - //Paul van Hoegaerden//
 +The aim of this thesis will be to study the Clifford algebras that appear in the derivation of the Dirac equation and investigate alternative formulations of the Dirac equation using (complex) quaternions. To this end, we will first look at the symmetries of the Dirac equation and some of the additional insights that follow from the Dirac equation. We will also give a derivation of the Dirac equation starting from the Schrödinger equation, in which we will come across the gamma matrices.
 ===== Books ===== ===== Books =====
  
geometric_algebra.txt · Last modified: 2021/11/03 14:55 by pbk