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
- visualization of vectorfields
- visualization software and important examples
|Instructor||Prof. Dr. Konrad Polthier, Henriette Lipschütz|
|Room||Arnimallee 6 Lecture:|
|Start||Apr 20, 2020 | 10:00 AM|
|end||Jul 16, 2020 | 12:00 PM|
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.
B.Sc. in mathematics or computer science
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Outdated reference for the VTK library, covers a wide variety of aspects on visualisation with VTK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
- JavaView: http://javaview.de/
Visualization software and library, provides implementations of many geometric algorithms
- JavaView Wiki: http://www.mi.fu-berlin.de/w/AGGeom/JavaView
Documentation, tutorials, installation
- JavaView JavaDoc API: http://javaview.de/doc/reference/index.html
JavaDoc API reference for JavaView
- Eclipse: https://eclipse.org/downloads/
Universal programming environment, especially for the Java language
- Maya Student Version: http://www.autodesk.com/education/free-software/maya
High-end 3D modelling, animation and rendering software
- GhostView: http://pages.cs.wisc.edu/~ghost/
Classical PostScript viewer