Geometry Algebra & Geometric Algebra

Computer Graphics & Computer Vision
with
Geometric Algebra & Conformal Geometry

Project Leader

Vaclav Skala

GraVisMa conferences
Computer Graphics, Vision and Mathematics Computational and Applied
http://www.GraVisMa.eu

GraVisMa 2018 conference

Venue to be held

May 28-June 1, 2018
Plzen, Czech Republic
Primavera Congress Center
http://www.GraVisMa.eu

Recent Workshops:

GraVisMa 2017, Plzen, Czech Republic
(part of the WSCG 2017 conference http://www.WSCG.eu)
GraVisMa 2016, Plzen, Czech Republic
(part of the WSCG 2016 conference http://www.WSCG.eu)
GraVisMa 2010, Brno Czech Republic
GraVisMa 2009, Plzen, Czech Republic

Plzen City

Goal

This activity is a part of the national research project VIRTUAL targeted specifically to application of theory of non-Euclidean geometry to computation and especially within the framework of Computer Graphics and Vision, Visualization and Scientific Computing, covering also new approaches to linear algebra and numerical computation in general.

Methods based on projective space using geometry algebra and conformal geometry seem to be very promising especially in the context of possible applications in technical fields, chemistry, biosciences etc.

The main contribution of this activity should be:

development of new robust algorithms convenient especially for solution of larger or more complex problems of Computer Graphics and Vision, Visualization and Scientific Computing
a new processor architecture or modification of the current CPU / GPU architecture

Algorithms developed are verified on CPU, using a special library PLib, GPU using CUDA. Specific platform TESLA/NVIDIA will be considered for efficiency designed algorithms evaluation.

Related projects:

VIRTUAL, No 2C06002 [in Czech] - National Center of Excellence project
LC-CPG, No.LC06008 - National Center of Excellence project
3DTV, EU Network of Excellence, FP6-2003-IST-2, No:511568
Intuition, EU Network of Excellence, FP6-2003-IST-2, No:507248-2

2009/2010

2008/2009

2007/2008

Recent related publications

Skala,V.: Barycentric Coordinates Computation in Homogeneous Coordinates, Computers & Graphics, Elsevier, ISSN 0097-8493, Vol. 32, No.1, pp.120-127, 2008
Skala,V.: Intersection Computation in Projective Space using Homogeneous Coordinates, accepted, International Journal of Image and Graphics, ISSN 0219-4678, Vol.7, No.4, pp.615-628, 2008
Skala,V.: Length, Area and Volume Computation in Homogeneous Coordinates, International Journal of Image and Graphics, Vol.6., No.4, pp.625-639, ISSN 0219-4678, 2006
Skala,V., Kaiser,J., Ondracka,V.: Library for Computation in the Projective Space, 6th Int.Conf. Aplimat, Bratislava, ISBN 978-969562-4-1, pp. 125-130, 2007
Skala,V.: GPU Computation in Projective Space Using Homogeneous Coordinates , Game Programming GEMS 6 (Ed.Dickheiser,M.), pp.137-147, ISBN 1-58450-450-1, Charles River Media, 2006
Skala,V.: A new approach to line and line segment clipping in homogeneous coordinates, The Visual Computer, ISSN 0178-2789, Vol.21, No.11, pp.905-914, Springer Verlag, 2005
Skala,V.: A New Line Clipping Algorithm with Hardware Acceleration, Computer Graphics International 2004 conference proceedings, IEEE, ISSN 1530-1052, 2004

Detailed list of publications

http://affrodita.zcu.cz/~skala/publications.htm

Tutorials

Skala,V.: Meshless Interpolations for Computer Graphics, Visualization and Games: An Informal Introduction, Tutorial, Eurographics 2015, doi: 10.2312/egt.20151046, Zurich, 2015
Skala,V.: Projective Geometry, Duality and Precision of Computation in Computer Graphics, Visualization and Games, Tutorial Eurographics 2013, Girona, 2013
Skala,V.: Projective Geometry and Duality for Graphics, Games and Visualization - Course SIGGRAPH Asia 2012, Singapore, ISBN 978-1-4503-1757-3, 2012
Skala,V.: Mathematical Foundations for Computer Graphics and Virtual Reality, Tutorial, FP6 Network of Excellence conference Intuition 2008, Torino, Italy, 2008
Skala,V.: Mathematical Foundations for Computer Graphics and Computer Vision, Tutorial, CGI 2008 conference, Istanbul, Turkey, 2008
Skala,V.: Mathematical Foundations for Computer Graphics and Vision and Computations in Projective Spaces, Tutorial, FP6 Network of Excellence conference 3DTV conference, Torino, Italy, 2007
Skala,V.: Mathematical Foundations of Computer Graphics, Computer Vision and Computation in Projective Space, Tutorial, AMDO 2006 Int.Conf., Spain, 2006

Related events

WSCG - International Conferences in Central Europe on Computer Graphics, Visualization and Computer Vision (http://www.wscg.eu)
Plzen (Pilsen), Czech Republic, since 1992
GraVisMa 2010 Computer Graphics, Computer Vision and Mathematics, Brno, September 2010
GraVisMa 2009 Computer Graphics, Computer Vision and Mathematics, Plzen (Pilsen), Czech Republic, 2009
VIRTUAL project workshop, Plzen, June 3, 2008
- Presentation
  - Skala,V., Ondracka,V.: Computational methods in the projective space
    [in Czech], stream, July 3, 2008
- Photos
WSCG 1992-now - International Conferences in Central Europe on Computer Graphics, Visualization and Computer Vision

Related references

Journals

Advances in Clifford Algebras (AACA) - ISSN: 0188-7009 (Print) 1661-4909 (Online)
http://link.springer.com/journal/6

Publications

Bayro-Corrochano,E: Geometric Computing: For Wavelet Transforms, Robot Vision, Learning, Control and Action, Springer, 2010
Bayro-Corrochano,E: Geometric Computing for Perception Action Systems, Springer Verlag N.Y., 2001
Bayro-Corrochano,E, Sobczyk,G.: Geometric Algebra with Application in Science and Engineering, Birkhauser, 2001
Browne,J.: Grassmann Algebra - Draft Exploring Application of Extended Vector Algebra with Mathematica, Swinburn University of Technology, Melbourne, Australia, 2001
Chevalley,C.: The Algebraic Theory of Spinors and Clifford Algebras, Springer, 1995
Doran,Ch., Lasenby,A.: Geometric Algebra for Physicists, Cambridge University Press, 2003
Dorst,L., Fontine,D., Mann,S.: Geometric Algebra for Computer Science, Morgan Kaufmann, 2007
Ghali,S.: Introduction to Geometric Computing, Springer, 2008
Gonzales Calvet,R.: Treatise of Plane Geometry through Geometric Algebra, ISBN 978-84-611-9149-9, 2007
Gu,X.D., Yau,S.-T.: Computational Conformal Geometry, International Press, Somerville, USA, 2008
Hildenbrand,D.: Foundations of Geometric Algebra Computing, Springer Verlag, ISBN 978-3-642-31793-4, 2012
Kanatani,K.: Undestanding geometric Algebra, CRC Press, ISBN 978-1-4822-5950-6, 2015 -- NEW --
Li,H., Olver,P.J., Sommer,G.: Computer Algebra and Geometric Algebra with Applications, Springer
MacDonald,A.: Linear and Geometric Algebra, 2010 http://faculty.luther.edu/~macdonal/laga/
Perwass,Ch.: Geometric Algebra with Applications in Engineering, Springer Verlag, 2008
Sommer, G.: Geometric Computing with Clifford Algebras. Theoretical Foundations and Applications in Computer Vision and Robotics, Springer, Berlin, 2001
Suter,J.: Geometric Algebra Primer [PDF] University of Twente, The Netherlands
Vince,J.: Geometric Algebra for Computer Science, Springer, 2008
Vince,J.: Geometric Algebra: An Algebraic System for Computer Games and Animation, Springer, 2009
Advances in Applied Clifford Algebras - Birkhauser-Springer journal [http://www.clifford-algebras.org/]
Wildberger,N.J.: Divine Proportions - Rational Geometry to Universal Geometry, ISBN 0-9757492-0, Wild Egg Pty, Australia, 2005
Digital papers repository of WSCG 1992 - now

Geometric Algebra founders

Herman Gunter Grassmann (1809 - 1877) - conference to honor Grassmann work
William Kingdom Clifford (1845 - 1879)
Sir William Rowan Hamilton (1805 - 1865)
David Hestenes

Research sites worldwide & people

David Hestenes, Geometric Calculus - Research & Developments, [http://modelingnts.la.asu.edu], Arizona State University, USA
Leo Dorst - University of Amsterdam, The Netherlands
Dietmar Hildenbrand Center for Research Excellence Computer Graphics, TU Darmstadt, Germany
Cambridge University GA Research Group, Cambridge, U.K.
Fukui University Research Group, Fukui, Japan & Geometric Calculus worldwide
Eduardo Bayro Corrochano, Cinvestav, Jalisco, Mexico
Geometry at Luther College, Alan Macdonald, Iowa, USA
Clifford Research Group, University of Ghent, Belgium
Geometric Algebras in Physics, University of Windsor, Canada
Bertfried Fauser, University of Konstanz, Germany
Rafal Ablamowicz - Tennessee Technological University, USA
Ramon Gonzales Calvet, Universitat Autonoma de Barcelona, Spain - book: Treatise of Plane Geometry through Geometric Algebra
Bouguet,J.-Y., California Institute of Technology, Pasadena, California, USA
Garret Sobczyk - Universidad de las Americas de Puebla, Mexico
Gerald Sommer, Cognitive Systems - University of Kiel, Germany
Pertti Lounesto, Helsinki Institute of Technology, Finland
John Ryan, Clifford Analysis, University of Arkansas, USA
CAIROS: Clifford Algebras International Research Open Studies

Software

Hilderbrand,D.: Gaalop - C code generator from CLUCalc
Perwass,Ch.: CLUCalc - software for 3D visualization
Perwass,C., Hitzer, E.: Space Group Visualizer - SW for 2D and 3D visualization of point and space groups [Math]
GABLE
Dorst,L., Fontine,D., Mann,S.: Geometric Algebra for Computer Science, Morgan Kaufmann, 2007 [DOWNLOAD]

Contact

Prof. Vaclav Skala
http://www.VaclavSkala.eu
c/o Center of Computer Graphics and Visualization
Department of Computer Science and Engineering
Faculty of Applied Sciences
University of West Bohemia
Univerzitni 8
CZ 30614 Plzen
Czech Republic
SKYPE: use my e-mail address
Tel. (+420) 377 63 2473
Tel.[secretary] (+420) 377 63 2401 , Fax/Tel[secretary]: (+420) 377 63 2402
e-mail: skala..(at)..kiv.zcu.cz http://Graphics.zcu.cz

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Computer Graphics & Computer Vision with Geometric Algebra & Conformal Geometry