Geometric Algebra Computing (eBook)

Part I: Geometric Algebra

New Tools for Computational Geometry and Rejuvenation of Screw Theory
David Hestenes
Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra
Leo Dorst
Engineering Graphics in Geometric Algebra
Alyn Rockwood and Dietmar Hildenbrand

Parametrization of 3D Conformal Transformations in Conformal Geometric Algebra
Hongbo Li

Part II: Clifford Fourier Transform

Two-Dimensional Clifford Windowed Fourier Transform
Mawardi Bahri, Eckhard M. S. Hitzer and Sriwulan Adji

The Cylindrical Fourier Transform
Fred Brackx, Nele De Schepper, and Frank Sommen

Analyzing Real Vector Fields with Clifford Convolution and Clifford Fourier Transform
Wieland Reich and Gerik Scheuermann

Clifford Fourier Transform for Color Image Processing
Thomas Batard, Michel Berthier and Christophe Saint-Jean

Hilbert Transforms in Clifford Analysis
Fred Brackx, Bram De Knock and Hennie De Schepper

Part III: Image Processing, Wavelets and Neurocomputing

Geometric Neural Computing for 2D Contour and 3D Surface Reconstruction
Jorge Rivera-Rovelo, Eduardo Bayro-Corrochano and Ruediger Dillmann

Geometric Associative Memories and their Applications to Pattern Classification
Benjamin Cruz, Ricardo Barron, Humberto Sossa

Classification and Clustering of Spatial Patterns with Geometric Algebra
Minh Tuan Pham, Kanta Tachibana, Eckhard M. S. Hitzer, Tomohiro Yoshikawa, and Takeshi Furuhashi

QWT: Retrospective and New Applications
Yi Xu, Xiaokang Yang, Li Song, Leonardo Traversoni and Wei Lu

Part IV: Computer Vision

Image Sensor Model using Geometric Algebra: from Calibration to Motion Estimation
Thibaud Debaecker, Ryad Benosman and Sio H. Ieng
Model-Based Visual Self-Localization Using Gaussian Spheres
D. Gonzalez-Aguirre, T. Asfour, E. Bayro-Corrochano and R. Dillmann

Part V: Conformal Mapping and Fluid Analysis

Geometric Characterization of M-conformal Mappings
K. Gürlebeck and J. Morais
Fluid Flow Problems with Quaternionic Analysis: An Alternative Conception
K. Gürlebeck and W. Sprössig
Part VI: Cristalography, Holography and Complexity
Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra
Eckhard Hitzer, Christian Perwass and Daisuke Ichikawa
Geometric Algebra Model of Distributed Representations
Agnieszka Patyk
Computational Complexity Reductions using Clifford Algebras
René Schott and G. Stacey Staples
Part VII: Efficient Computing with Clifford (Geometric) Algebra
Efficient Algorithms for Factorization and Join of Blades
Daniel Fontijne, Leo Dorst
Gaalop - High Performance Parallel Computing based on Conformal Geometric Algebra
Dietmar Hildenbrand, Joachim Pitt, Andreas Koch
Some Applications of Gröbner Bases in Robotics and Engineering
Rafal Ablamowicz