TU Berlin Fakultät II
Institut für Mathematik

Geometry II (SoSe 11)



Geometry Group



Vergangene Semester


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Geometry II:
Discrete Differential Geometry

(Summer 2011)

Lecture Alexander Bobenko Tue 12-14 MA 848
Thu 12-14 MA 848
Tutorial Thilo Rörig Wed 10-12 MA 848
Thu 10-12 MA 848

This is a course of the Berlin Mathematical School held in English.


Next possible date for oral exams is 23.08.2011. Please contact Fr. Janik for details.
No Lecture and tutorial this week (June 20 - June 23)
Exercise sheet 8 will be available on Friday 10.06. -- Sorry. Enjoy your thursday :-)
Error in Ex. 7.3: The Delaunay triangulation maximizes the minimal angle.
No tutorial on Thu 02.06. because of public holiday.
References concerning cotan-Laplace operator and intrinsic Delaunay triangulations below.
Error in Exercise 4 sheet 3. The cross-ratio is not preserved, but only its absolute value.
Error in Hint to exercise 3 on sheet 2. See corrected version online
No lecture on Tuesday 19.04. Tutorials start on Wednesday 20.04.
The first lecture will be on Tuesday 12.4, the first Tutorial on Wednesday 20.04.


Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. Discrete differential geometry aims at the development and application of discrete equivalents of the geometric notions and methods of differential geometry. The latter appears then as a limit of refinements of the discretization. Polyhedral surfaces are one of the main topics of this course. Current progress in this field is to a large extent stimulated by its relevance for computer graphics.


  • A. Bobenko, B. Springborn, A discrete Laplace-Beltrami operator for simplicial surfaces, pdf
  • U. Pinkall, K. Polthier, Computing Discrete Minimal Surfaces and Their Conjugates pdf
  • A. Bobenko, U. Pinkall, B. Springborn, Discrete conformal maps and ideal hyperbolic polyhedra, arXiv

Exercise sheets

The exercise sheets can be found here.

Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.

Office Hours

Office hours Alexander Bobenko TBA MA 881
Thilo Rörig Tue 10-12 MA 874

Thilo Rörig . 20.07.2011.