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geometric_algebra [2021/07/02 18:46] pbk [Videos] 
geometric_algebra [2021/10/20 07:20] pbk [Articles] 
* [[https://www.youtube.com/watch?v=cKfC2ZBJulgProjective Geometric Algebra for Paraxial Geometric Optics]]  // Katelyn Spadavecchia//.  * [[https://www.youtube.com/watch?v=cKfC2ZBJulgProjective Geometric Algebra for Paraxial Geometric Optics]]  // Katelyn Spadavecchia//. 
* [[https://www.youtube.com/watch?v=11sH9X0OO9Y&list=PLnpuwbuviU2j7OSnZdstP5_g1ejA32bYAGeometric Algebra Lectures ]]  //Miroslav Josipović//.  * [[https://www.youtube.com/watch?v=11sH9X0OO9Y&list=PLnpuwbuviU2j7OSnZdstP5_g1ejA32bYAGeometric Algebra Lectures ]]  //Miroslav Josipović//. 
 * [[https://www.youtube.com/watch?v=HGcBu4TQgREQuaternions and Clifford Algebra]]  //Q. J. Ge and Anurag Purwar//, Stony Brook University. 
* [[https://www.youtube.com/watch?v=LestlcDk6IwFoundations of Geometric Algebra Computing]]  Lecture at ICU Tokyo, //Dietmar Hildenbrand//.  * [[https://www.youtube.com/watch?v=LestlcDk6IwFoundations of Geometric Algebra Computing]]  Lecture at ICU Tokyo, //Dietmar Hildenbrand//. 
* [[https://www.youtube.com/watch?v=e5D7Bma9Vhw&list=PLxo3PbygE0PLdFFy_2b02JAaUsleFW8pyGeometric Algebra]]  First Course in STEMCstudio, //David Geo Holmes//.  * [[https://www.youtube.com/watch?v=e5D7Bma9Vhw&list=PLxo3PbygE0PLdFFy_2b02JAaUsleFW8pyGeometric 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=PLsSPBzvBkYjxrsTOr0KLDilkZaw7UE2VcPlanebased Geometric Algebra Tutorial]]  Presentation at SIBGRAPI 2021, //Steven De Keninck and Leo Dorst//. 
===== Computing frameworks =====  ===== Computing frameworks ===== 
* [[http://www.geometricalgebra.net/downloads.htmlGAViewer & GA Sandbox]]  //Leo Dorst, Daniel Fontijne, Stephen Mann//.  * [[http://www.geometricalgebra.net/downloads.htmlGAViewer & GA Sandbox]]  //Leo Dorst, Daniel Fontijne, Stephen Mann//. 
* [[https://arxiv.org/pdf/2007.04464.pdfDeform, Cut and Tear a skinned model using Conformal Geometric Algebra]] (2020)  //Manos Kamarianakis, George Papagiannakis//  * [[https://arxiv.org/pdf/2007.04464.pdfDeform, 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, realtime 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 stateoftheart character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current stateoftheart, dualquaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dualquaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dualquaternions 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 redeformed.  We present a novel, integrated rigged character simulation framework in Conformal Geometric Algebra (CGA) that supports, for the first time, realtime 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 stateoftheart character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current stateoftheart, dualquaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dualquaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dualquaternions 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 redeformed. 
 
 * [[https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9488174A Survey on Quaternion Algebra and Geometric Algebra Applications in Engineering and Computer Science 1995–2020]] (2021)  //Eduardo BayroCorrochano// 
 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. 
===== Books =====  ===== Books ===== 
 