Legacy display Course

Selected Topics in Science and Technology:
Geometry Processing and Discrete Shells

The course will be given by Dr. Behrend Heeren.

Where/When: Tu 12.00-14.30 and Th 12.00-14.30, Room N0.003, starting on June, 13th!

News

• The second oral exam is on Wednesday, 6th of September in room Z2.069.

Topics

• numerical treatment of thin shell problems
• discrete surface modeling (e.g. via discrete differential geometry)
• numerical simulations of thin shell deformations
• efficient implementation by multiresolution schemes or differential representations
• operations in the shape space of discrete shells and applications in Computer Graphics

You can find more information here.

Script and further references

A scan of my handwritten notes is available here, a more detailed presentation can be found here (last update: July 26th).

So far, the course builds on the following references (which are also cited in the notes):

• Mario Botsch, Leif Kobbelt, Marc Pauly, Pierre Alliez, Bruno Levy, Polygon Mesh Processing, CRC Press, 2010.
• Klaus Hildebrandt, Konrad Polthier, Max Wardetzky, On the convergence of metric and geometric properties of polyhedral surfaces, Geom. Dedicata, 123:89–112, 2006.
• Max Wardetzky, Discrete Differential Operators on Polyhedral Surfaces - Convergence and Approximation, PhD thesis, Freie Universität Berlin, 2006.
• Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr, Discrete differential geometry operators for triangulated 2-manifolds, In Visualization and Mathematics III, pages 35–57. Springer Berlin Heidelberg, 2002.
• David Cohen-Steiner and Jean-Marie Morvan, Restricted Delaunay triangulations and normal cycle. In Proc. of Symposium on Computational Geometry, pages 312–321, 2003.
• Philippe G. Ciarlet and Christinel Mardare, An introduction to shell theory. In Differential geometry: theory and applications, volume 9 of Ser. Contemp. Appl. Math. CAM, pages 94–184. Higher Ed. Press, Beijing, 2008.
• Philippe G. Ciarlet, An Introduction to Differential Geometry with Applications to Elasticity. Springer, Dordrecht, 2005
• Sören Bartels, Numerical Methods for Nonlinear Partial Differential Equations, volume 47 of Springer Series in Computational Mathematics. Springer, 2015.
• Gero Friesecke, Richard D. James, Stefan Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Comm. Pure Appl. Math., 2002.
• Gero Friesecke, Richard D. James, Maria G. Mora, Stefan Müller, Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence, C. R. Math. Acad. Sci. Paris, 2003.
• Benedikt Wirth, Leah Bar, Martin Rumpf, Guillermo Sapiro, A continuum mechanical approach to geodesics in shape space, Int. J. Comput. Vis., 2011.
• Martin Rumpf and Benedikt Wirth, Discrete geodesic calculus in shape space and applications in the space of viscous fluidic objects, SIAM J. Imaging Sci., 2013.
• Martin Rumpf and Benedikt Wirth. Variational time discretization of geodesic calculus, IMA J. Numer. Anal., 2015.
• Behrend Heeren, Martin Rumpf, Max Wardetzky, Benedikt Wirth, Time-discrete geodesics in the space of shells, Comput. Graph. Forum, 2012.
• Behrend Heeren, Martin Rumpf, Peter Schröder, Max Wardetzky, Benedikt Wirth, Exploring the geometry of the space of shells, Comput. Graph. Forum, 2014.
• Eitan Grinspun, Anil N. Hirani, Mathieu Desbrun, Peter Schröder, Discrete shells, In Proc. of ACM SIGGRAPH/Eurographics Symposium on Computer animation, 2003.

Exam

The oral exam takes 30 minutes, you can choose a topic to start with.
Here you can find a list of guiding questions for the exam as well as some examples of suitable topics to start with.
The content of the exam is based on the lecture and my handwritten notes - the detailed latex notes are thought to be additional information.
In particular, sections and paragraphs with a star (*) have not been discussed in class (and are not required in the exam!).