Computer Graphics & Computer Vision with Geometric Algebra & Conformal Geometry

Project Leader Vaclav Skala

GraVisMa - Computer Graphics, Vision and Mathematics International Workshops    GraVisMa 2011 workshop Venue: September, 2011 Ostrava, Czech Republic Recent Workshops: 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://herakles.zcu.cz/~skala/Sh-publ.htm

Tutorials

• 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

External fellows

• Kolcun, Alexej, Institute of Geosciences, Czech Academy of Sciences, Ostrava, Czech Republic
• Sojka, Eduard, Ostrava, VSB-Technical University Ostrava, Ostrava, Czech Republic

Related events

• WSCG 2011 - 19^th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, Plzen (Pilsen), Czech Republic, January 2011
• GraVisMa 2010 Computer Graphics, Computer Vision and Mathematics, Brno, September 2010
• WSCG 2010 - 18^th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, Plzen (Pilsen), Czech Republic, 2010
• GraVisMa 2009 Computer Graphics, Computer Vision and Mathematics, Plzen (Pilsen), Czech Republic, 2009
  
• WSCG 2009 - 17^thInternational Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, 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 1992-2009 International Conferences in Central Europe on Computer Graphics, Visualization and Computer Vision

Related references

• Geometric Algebra - Wikipedia
• Conformal Geometry - Wikipedia
• Projective Geometry - Wikipedia
• Geometric Algebra - Geometrical Interpretation

• 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
• Gu,X.D., Yau,S.-T.: Computational Conformal Geometry, International Press, Somerville, USA, 2008
• Li,H., Olver,P.J., Sommer,G.: Computer Algebra and Geometric Algebra with Applications, Springer
• 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
• Macdonald,A: A Survey of Geometric Algebra and Geometric Calculus, http://faculty.luther.edu/~macdonal, 2009
• Advances in Applied Clifford Algebras - Birkhauser-Springer journal [http://www.clifford-algebras.org/]
• 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
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://herakles.zcu.cz/~skala    http://Graphics.zcu.cz

We have had visitors