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Scientific Visualization

In the lecture, the basics of scientific visualization and their applications in mathematics, in computer graphics, and in STEM  will be introduced. Some carefully chosen from the following topics will be presented:

  • basic data structures
  • representation of geometries as meshes
  • theory of discrete surfaces
  • subdivision schemes for curves and surfaces
  • wavelets
  • modeling
  • visualization of vectorfields
  • visualization software and important examples

(19222401)

TypeLecture
InstructorProf. Dr. Konrad Polthier, Henriette Lipschütz
LanguageEnglish
RoomArnimallee 6 Lecture:
StartApr 20, 2020 | 10:00 AM
endJul 16, 2020 | 12:00 PM
Time

Lecture: Tue 10:00-12:00, Thu 10:00-12:00

Tutorials: Fri 8:00-10:00

Short project presentation: tba

Final presentations: tba

Submission deadline: tba

Because of holidays, there will be no tutorial on May, 1st, and on May, 8th, and no lecture on May, 21st.

Requirements

B.Sc. in mathematics or computer science

Literature

Additional reading and supplement for lectures and tutorials:

  • M. de Berg, M. Kreveld et al.: "Computational Geometry", Springer Verlag, 2008.
    Classical algorithms for computational geometry, space partitioning, kd-tree structures, triangulations
  • H.C. Hege and K. Polthier: "Visualization and Mathematics III", Springer Verlag 2003.
    Collection of seminal research articles on conformal mappings, discrete differential operators on triangle meshes, discrete vector fields, 
  • D. Salomon: "The Computer Graphics Manual", Springer, 2011
    Heavy allrounder (almost 1500 pages), contains sections about subdivision, colors, texture mappings, raster graphics, Beziér splines, rendering, fractals, wavelets, compression, with very digestible math
  • E. Stollnitz, T. DeRose, D. Salesin: "Wavelets for Computer Graphics", Morgan Kaufmann Publisher 1996.
    Classical introductory book on wavelets, image compression, subdivision
  • H. Schumann, W. Müller: "Visualisierung - Grundlagen und allgemeine Methoden", Springer Verlag 2000.
  • W. Schroeder, K. Martin, B. Lorensen: "The Visualization Toolkit" Prentice Hall, 1998/2004.
    Outdated reference for the VTK library, covers a wide variety of aspects on visualisation with VTK
  • D. Cohen-Or, C. Greif et al.: "A Sampler of Useful Computational Tools for Applied Geometry,(...)", Taylor & Francis, 2015
  • M. Botsch et al.: "Polygon Mesh Processing", A K Peters, 2010
    Important aspects of modern geometry processing, data structures, smoothing, parametrization, simplification, deformation
  • T. K. Dey: "Curve and Surface Reconstruction", Cambridge Univ. Press, 2011
  • H. Edelsbrunner: "Geometry and Topology for Mesh Generation", Cambridge Univ. Press, 2006
    Triangulation methods, Delaunay triangulation, topological and combinatorial aspects

Useful Software:

  • JavaView: http://javaview.de/
    Visualization software and library, provides implementations of many geometric algorithms