This book presents new results on applications of geometric algebra. The time when researchers and engineers were starting to realize the potential of quaternions for - plications in electrical, mechanic, and control engineering passed a long time ago. Since the publication of Space-Time Algebra by David Hestenes (1966) and Clifford Algebra to Geometric Calculus: A Uni?ed Language for Mathematics and Physics by David Hestenes and Garret Sobczyk (1984), consistent progress in the app- cations of geometric algebra has taken place. Particularly due to the great dev- opments in computer technology and the Internet, researchers have proposed new ideas and algorithms to tackle a variety of problems in the areas of computer science and engineering using the powerful language of geometric algebra. In this process, pioneer groups started the conference series entitled "Applications of Geometric Algebra in Computer Science and Engineering" (AGACSE) in order to promote the research activity in the domain of the application of geometric algebra. The ?rst conference, AGACSE'1999, organized by Eduardo Bayro-Corrochano and Garret Sobczyk, took place in Ixtapa-Zihuatanejo, Mexico, in July 1999. The contri- tions were published in Geometric Algebra with Applications in Science and En- neering, Birkhäuser, 2001. The second conference, ACACSE'2001, was held in the Engineering Department of the Cambridge University on 9-13 July 2001 and was organizedbyLeoDorst,ChrisDoran,andJoanLasenby. Thebestconferencecont- butions appeared as a book entitled Applications of Geometric Algebra in Computer Science and Engineering, Birkhäuser, 2002. The third conference, AGACSE'2008, took place in August 2008 in Grimma, Leipzig, Germany.

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