Dr.-Ing. Dietmar Hildenbrand

Research

My research topic is Geometric Algebra.

One focus is Geometric Algebra Computing. We define it as

• the interactive and visual development and
• the efficient implementation

of geometrically intuitive algorithms based on
Geometric Algebra.

Please find a brief introduction to Geometric Algebra Computing here and an introduction video here.

For more detailed information on Geometric Algebra please find the tutorial script “Aspects of Geometric Algebra in Euclidean, Projective and Conformal Space”.

Please find some information about GAALOP, our tool for the efficient implementation of geometric algebra algorithms, on the GAALOP homepage.

Invited talks

Oct 2022: ”

“Geometric Algebra Computing For Computer Graphics Using GAALOP”, International Conference on Advanced Computational Applications of Geometric Algebra, Denver, USA

June, 17, 2019: ”

“Introduction to Geometric Algebra Computing “, Computer Graphics International Conference, Calgary, Canada

July, 26, 2018: ”

“Fast Geometric Algebra Computing for a wide range of Computing Devices”, AGACSE Conference, Campinas, Brazil

Aug, 2016: Keynote “Foundations of Geometric Algebra Computing “W.K. Clifford’s Geometric Algebra and Geographical Information Science: Development and Applications (GAGIS) ” on Aug 25-26, 2016 at Nanjing Normal University, in the ancient capital city Nanjing in China.

Apr. 23, 2015: “Raytracer mit C++ AMP und Geometrischer Algebra, Konferenz Parallel 2015, Karlsruhe.

Jan. 29, 2015: “Geometrische Algebra – Eine neue Art, geometrisch intuitiv zu rechnen” , Rathausvortrag der Odenwald-Akademie, Rathaus Michelstadt.

May 27, 2014: “The Power of Geometric Algebra Computing for Mathematica”,
European Wolfram Technology Conference 2014, Frankfurt, Germany.

Feb. 27, 2013: “Geometric Algebra Computing Technology for Accelerated Processing Units”,
EmbeddedWorld conference 2013, Nürnberg, Germany.

Sept. 21, 2012: “Foundations of Geometric Algebra Computing”,
ICNAAM conference 2012, Kos.

May 23, 2012: “Neue effiziente Art des Rechnens auf parallelen Rechnerarchitekturen mit geometrischer Algebra” , Parallel 2012
Conference, Karlsruhe, Germany.

March 15, 2012: “Foundations of Geometric Algebra Computing” ,
University of Weimar, Germany.

Jan 19, 2011: “Geometrische Algebra: Eine neue, elegante und effiziente Methode für viele Maschinenbauthemen” , University of Technology Darmstadt, Germany.

Nov. 2010: “Geometrische Algebra und ihre Anwendungen in Computergrafik und Robotik” , University of Applied Sciences, Darmstadt, Germany.

March 2010: “Geometrische Algebra” , Gemeinsame Jahrestagung von Deutsche Mathematiker-Vereinigung und Gesellschaft für Didaktik der Mathematik, Munich, Germany.

Oct 24, 2008: “Einführung in die geometrische Algebra und ihre Anwendung in der Computergrafik” , University of Karlsruhe, Germany.

May 21st, 2008: “Geometrische Algebra
und ihre Anwendung in der Robotik und Computergrafik” , University of Karlsruhe.

March 04th, 2008: “Efficient reconfigurable hardware implementation of geometric algebra algorithms
illustrated by the example of an inverse kinematics application ” , University of Nagoya, Japan.

Nov 07th, 2007: Please find the german presentation of my talk on the application of Geometric Algebra in game engines at the Games Academy in Berlin -> here.

June 11th, 2007: Please find the german abstract of my talk on the application of Geometric Algebra in robotics at the University of Applied Sciences Aschaffenburg -> here.

February 2007: Please find some information on the International workshop for Computational Science with Geometric Algebra”
at the Nagoya University, Japan -> here.

November 2005: Please find my presentation on the geometric algebras
and applications colloquium in Marseille -> here.

Publications

Proceedings of CGI conference Shanghai, China, 2023, “Game Physics Engine Using Optimised Geometric Algebra RISC-V Code Using Fourier Series Data” by Ed Saribatir, Niko Zurstrassen, Dietmar Hildenbrand, Florian Stock, Atilio Morillo Pina, Frederic von Wegner, Zheng Yan, Shiping Wen, Matthew Arnold

MATHEMATICAL METHODS IN THE APPLIED SCIENCES Journal, 2022, “Current Survey of Clifford Geometric Algebra Applications” by Eckhard Hitzer, Carlile Lavor and Dietmar Hildenbrand.

Advances in Applied Clifford Algebras Journal, 2021, “An Online Calculator for Quantum Computing Operations Based on Geometric Algebra” by Rafael Alves, Dietmar Hildenbrand, Jaroslav Hrdina and Carlile Lavor. Here is the view-only link.

Advances in Applied Clifford Algebras Journal, 2021, “On Specific Conic Intersections in GAC and Symbolic Calculations in GAALOPWeb” by Roman Byrtus,  Anna Derevianko,   Petr Vašík and Dietmar Hildenbrand.

Proceedings of CGI conference Geneva, Switzerland, 2020, “An online calculator for qubits based on Geometric Algebra” by Dietmar Hildenbrand, Christian Steinmetz, Rafael Alves, Jaroslav Hrdina and Carlile Lavor.

Advances in Applied Clifford Algebras Journal, 2020, “GAALOPWeb for Matlab: an easy to handle solution for industrial geometric algebra implementations” by Dietmar Hildenbrand Christian Steinmetz and Radek Tichy.

Advances in Applied Clifford Algebras Journal, 2020, “Efficient development of competitive Mathematica solutions based on Geometric Algebra with GAALOPWeb” by Rafael Alves, Dietmar Hildenbrand, Christian Steinmetz and Patrick Uftring.

Advances in Applied Clifford Algebras Journal, 2019, “Local controllability of snake robots based on CRA, theory and practice” by Dietmar Hildenbrand, Jaroslav Hrdina,  Ales Navrat, Petr Vasık.

Proceedings of CGI conference Calgary, Canada, 2019, “Gajit: Symbolic Optimisation and JIT Compilation of Geometric Algebra in Python with GAALOP and Numba“ by Hugo Hadfield, Dietmar Hildenbrand, Alex Arsenovic.

Proceedings of CGI conference Calgary, Canada, 2019, “Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra“ by Eckhard Hitzer, Dietmar Hildenbrand.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES Journal, 2017, “Analyzing the inner product of 2 circles with Gaalop” by Dietmar Hildenbrand, Werner Benger, Yu Zhaoyuan.

Advances in Applied Clifford Algebras Journal, 2017, “Practical Geometric Modeling Using Geometric Algebra Motors” by Mauricio C. L. Belon and Dietmar Hildenbrand. The final publication is available here at Springer.

Advances in Applied Clifford Algebras Journal, 2017, “GAPPCO: an easy to configure Geometric Algebra coprocessor based on GAPP programs” by Dietmar Hildenbrand, S. Franchini, A. Gentile, G. Vassallo and S.
Vitabile. The final publication is available here at Springer.

Advances in Applied Clifford Algebras Journal, 2016 “Geometric Algebra Computing for Heterogeneous Systems” by Dietmar Hildenbrand, Justin Albert, Patrick Charrier and Christian Steinmetz. Please find a preprint here.

Visual Computer, 2016 “An inclusive Conformal Geometric Algebra GPU animation interpolation and deformation algorithm” by Margarita Papaefthymiou , Dietmar Hildenbrand and George Papagiannakis. Please find a preprint here

The Electronic Journal of Mathematics and Technology, 2015,  “Geometric Algebra: A Foundation of Elementary Geometry with possible Applications in Computer Algebra based Dynamic Geometry Systems” by Dietmar Hildenbrand and Reinhard Oldenburg. Please find a preprint here.

Frühjahrstagung Didaktik der Physik, 2014 “Fünfdimensionales Licht als Beschreibungsmuster unserer dreidimensionalen Welt” by Martin Erik Horn and Dietmar Hildenbrand. Please find a preprint here.

Advances in Applied Clifford Algebras Journal, January 2014 “Geometric Algebra enhanced Precompiler for C++, OpenCL and Mathematica’s OpenCLLink” by Patrick Charrier, Mariusz Klimek, Christian Steinmetz and Dietmar Hildenbrand. Please find a preprint here.

International Symposium on System on Chip (SoC) 2013, Tampere, Finland, “FPGA-accelerated color edge detection using a Geometric-Algebra-to-Verilog compiler“ by Florian Stock, Dietmar Hildenbrand, Andreas Koch. Please find a preprint here.

Proceedings EmbeddedWorld 2013, Nürnberg, Germany “Geometric Algebra Computing Technology for Accelerated Processing Units” by Patrick Charrier and Dietmar Hildenbrand. Please find a preprint here.

Proceedings ICNAAM 2012, Kos, Greece, “Foundations of Geometric Algebra Computing” by  Dietmar Hildenbrand. Please find a preprint here

Proceedings AGACSE 2012, La Rochelle, France, “Geometric Algebra enhanced Precompiler for C++ and OpenCL” by Patrick Charrier and Dietmar Hildenbrand. Please find a preprint here.

Proceedings AGACSE 2012, La Rochelle, France, “Specialized Machine Instruction Set for Geometric Algebra” by Dietmar Hildenbrand, Patrick Charrier, Christian Steinmetz and Andreas Koch. Please find a preprint here

Proceedings GDCP-Jahrestagung 2012, “Didaktische Wege zum Quanten-Computing” by Paul Drechsel, Dietmar Hildenbrand and Martin Erik Horn. Please find a preprint here

Proceedings Frühjahrstagung Didaktik der Physik, Mainz 2012, “Quanten-Computing und Geometrische Algebra” by Martin Erik Horn, Paul Drechsel and Dietmar Hildenbrand. Please find a preprint here

book chapter “From Grassmann’s vision to geometric algebra computing” by Dietmar Hildenbrand, in Hermann Graßmann, From Past to Future: Graßmann’s Work in Context, Birkhäuser Verlag 2011, H.-J. Petsche, A. C. Lewis, J. Liesen, S. Russ (editors). Please find a preprint here.

ICCA 2011 : International Conference on Clifford Algebras and their Applications in
Weimar, Germany : “Conformal Geometric Objects With Focus On Oriented Points” by Dietmar Hildenbrand and Patrick Charrier”. Please find a preprint here.

book section “Geometric Algebra Computing” by Dietmar Hildenbrand
in Handbook of Mathematical Methods in Imaging, Springer Verlag 2010, Otmar Scherzer (Editor). Please find a preprint here.

Proceedings GDM conference, 2010, Munich, Germany, “Schnittstellenaktivität Geometrische Algebra” by Dietmar Hildenbrand,
Reinhard Oldenburg, and Verena Rembowski. Please find a preprint here.

Proceedings GraVisMa Workshop, 2010, Brno, Czech Republic, “Registration of Multichannel Images using Geometric Algebra” by Andreas Görlitz, Helmut Seibert and Dietmar Hildenbrand.
Please find a preprint here.

Proceedings GraVisMa Workshop, 2010, Brno, Czech Republic, “Gaalop Compiler Driver” by Patrick Charrier and Dietmar Hildenbrand.
Please find a preprint here.

Proceedings GraVisMa Workshop, 2010, Brno, Czech Republic, “Gaalop 2.0 – A Geometric Algebra Algorithm Compiler” by Christian Schwinn, Dietmar Hildenbrand, Florian Stock and Andreas Koch.
Please find a preprint here.

International Conference on Embedded Computer Systems: Architectures, Modeling and Simulation, 2010, Samos, “Accelerating High-Level Engineering Computations by Automatic Compilation of Geometric Algebra to Hardware Accelerators” by Huthmann, J., Müller, P., Stock, F., Hildenbrand, D., Koch, A.
Please find a preprint here.

VISIGRAPP 2010, International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, Angers, France, “Estimation of Curvatures in Point Sets Based on Geometric Algebra” by Seibert, Helmut; Hildenbrand, Dietmar; Becker, Meike; Kuijper, Arjan.
Please find a preprint here.

book chapter “Gaalop – High Performance Parallel Computing based on Conformal Geometric Algebra” by Dietmar Hildenbrand, Joachim Pitt and Andreas Koch, in Geometric Algebra Computing for Engineering and Computer Science, Springer Verlag 2010, E. Bayro-Corrochano and G. Scheuermann (editors).
Please find a preprint here.

book chapter “Engineering Graphics in Geometric Algebra” by Alyn Rockwood and Dietmar Hildenbrand
in Geometric Algebra Computing for Engineering and Computer Science, Springer Verlag 2010, E. Bayro-Corrochano and G. Scheuermann (editors).
Please find a preprint here.

14th Iberoamerican Congress on Pattern Recognition 2009, Guadalajara, Mexico, “Optimization and Performance of a robotics grasping algorithm described in Geometric Algebra” by Florian Wörsdörfer, Florian Stock, Eduardo Bayro-Corrochano and Dietmar Hildenbrand.
Please find a preprint here.

IEEE Symposium on Field-Programmable Custom Computing Machines, 2009, Gent, Belgium, “Acceleration and Energy Efficiency of Geometric Algebra Computations using Reconfigurable Computers and GPUs” by Holger Lange, Florian Stock, Andreas Koch and Dietmar Hildenbrand.
Please find a preprint here.

Proceedings GraVisMa Workshop, 2009, Pilsen, Czech Republic, “Raytracing Point Clouds using Geometric Algebra” by Crispin Deul, Michael Burger, Dietmar Hildenbrand and Andreas Koch.
Please find a preprint here.

Proceedings GraVisMa Workshop, 2009, Pilsen, Czech Republic, “Geometric Algebra Computing on the CUDA Platform” by Christian Schwinn, Andreas Görlitz and Dietmar Hildenbrand.
Please find a preprint here.

Proceedings GraVisMa Workshop, 2009, Pilsen, Czech Republic, “Pose Estimation based on Geometric Algebra” by Cui Yan and Dietmar Hildenbrand.
Please find a preprint here.

Proceedings GraVisMa Workshop, 2009, Pilsen, Czech Republic, “Geometric Algebra Computers” by Dietmar Hildenbrand.
Please find a preprint here.

International Symposium on Frontiers of Computational Science 2008, Nagoya, Japan, “Geometric algebra – The mathematical language for Computational Engineering?” by Dietmar Hildenbrand.
Please find a preprint here.

International Symposium on Frontiers of Computational Science 2008, Nagoya, Japan, “Simulation of Elastic rods using conformal Geometric Algebra” by Elmar Brendel, Thomas Kalbe, Dietmar Hildenbrand, Michael Schäfer.
Please find a preprint here.

Humanoids conference 2008, , Daejeon, Korea, “Inverse Kinematics of a Humanoid Robot based on Conformal Geometric Algebra using optimized code generation” by Joachim Pitt, Dietmar Hildenbrand, Maximilian Stelzer, Andreas Koch.
Please find a preprint here.

Advances in Applied Clifford Algebras, Birkhäuser 2008, Chapter “Inverse kinematics computation in computer graphics and robotics using
conformal geometric algebra” by Dietmar Hildenbrand, Eduardo
Bayro-Corrochano and Julio Zamora
Please find a preprint here. The original publication is available at www.springerlink.com.

AGACSE 2008, Conference on Applied Geometric Algebras in Computer Science and Engineering,
Leipzig, Germany :
“Geometric Algebra Approach to Fluid Dynamics” by Carsten Cibura and Dietmar Hildenbrand.
Please find a preprint here

GRAPP 2008, Madeira :
“EFFICIENT INVERSE KINEMATICS ALGORITHM BASED ON CONFORMAL GEOMETRIC ALGEBRA Using Reconfigurable Hardware” by Dietmar Hildenbrand, Holger Lange, Florian Stock and Andreas Koch.
Please find a preprint here

GRAPP 2008, Madeira :”ANALYSIS OF POINT CLOUDS Using Conformal Geometric
Algebra” by Dietmar Hildenbrand and Eckhard Hitzer.
Please find a preprint here

Dissertation at Technische Universitaet Darmstadt, 2006, “Geometric Computing in Computer Graphics and Robotics using Conformal Geometric Algebra” by Dietmar Hildenbrand. The dissertation is available here.

Eurographics 2006, Vienna : “Competitive runtime performance for inverse kinematics algorithms using conformal geometric algebra “ by Dietmar Hildenbrand, Daniel Fontijne, Yusheng Wang, Marc Alexa and Leo Dorst Please find a preprint here

Computers & Graphics 2005 :
volume 29, no. 5, october, 2005 :
Tutorial “Geometric Computing in Computer Graphics using Conformal Geometric
Algebra” by Dietmar Hildenbrand
Please download a preprint as well as several corresponding CLUCalc scripts for the inverse kinematics of a simple
robot and refer to the journal´s homepage .

ICCA7 2005 :

7th International Conference on Clifford Algebras and their Applications in
Toulouse, France :
“Inverse kinematics computation in computer graphics and robotics using
conformal geometric algebra” by Dietmar Hildenbrand, Eduardo
Bayro-Corrochano and Julio Zamora
Please find several presented CLUCalc scripts for a grasping algorithm.

ICRA 2005 :
International Conference on Robotics and Automation in Barcelona, Spain :
“Advanced geometric approach for graphics and visual guided robot object
manipulation” by Dietmar Hildenbrand, Eduardo Bayro-Corrochano and
Julio Zamora. Please find a preprint here

Eurographics 2004, Grenoble :
Tutorial “Geometric Algebra and its Application to Computer Graphics” by
Dietmar Hildenbrand, Daniel Fontijne, Christian Perwass and Leo Dorst.
Please download our updated tutorial notes as well as several corresponding CLUCalc scripts .

Courses

Please find the homepage of my course “Geometric Algebra Computing” in the winter term (WS 14/15) -> here.

Please find the information of my course “Geometric Algebra Computing” in the winter term (WS 13/14) in the Moodle system of TU Darmstadt.

Please find the homepage of my course “Geometric Algebra Computing” in the winter term (WS 12/13) -> here.

Please find the homepage of my course “Geometric Algebra Computing” in the winter term (WS 10/11) -> here.

Please find the homepage of my course “Geometric Algebra Computing” in the winter term (WS 09/10) -> here.

Please find the homepage of “GDV III – Geometric Computing” in the winter term (WS 08/09) -> here.

Please find the homepage of Graphische Datenverarbeitung II (GDV II) SS 08

Downloads

Inverse kinematics algorithm of a simple robot:

Please find several CLUCalc scripts for an inverse kinematics algorithm of a simple robot. The main file is called InverseKinematics.clu.

Robot grasping algorithm :

Please find several CLUCalc scripts for a grasping algorithm. The main file is called CircleGrasping.clu.