Videos, and Games
Discrete Differential Geometry
This is a basic course of the Berlin Mathematical School
and lectures will be held in English. The tutorials will be held
in English or German, depending on the students attending each
will be offered 9-12h on Thu. 8 Nov.
for the Delaunay triangulation algorithms is these
lecture notes from ETH Zürich; see Chapters 6 and 7.
be no lecture on Wednesday, 4.7.
hours this week are by appointment only (not on Thursday as
usual), please write an email.
Here are the
references mentioned in today's tutorial:
"The Laplace Equation" (Smooth theory of Dirchlet boundary
value problems, Hölder continuity for domains explained in 1.17),
Polthier, "Computing discrete minimal surfaces and their
conjugates" (Reference [cotan-minimal] for the simplicial
minimal surface algoithm in the script)
et al., "Discrete Laplace operators: No free lunch"
We will talk about
aspects of the second reference in next week's tutorial!
taking questions for the last tutorial on July 16th. Please send
an email with topics you would like to have covered or questions
about any of the topics from this semester.
some further references mentioned in the tutorial (not relevant
for the exam):
Izmestiev et al., "There
is no triangulation of the torus with vertex degrees 5,6,... "
Günther et al., "Smooth
polyhedral surfaces" (proof spherical area of Gauss map
equals discrete Gaussian curvature)
find Conway's Zip Proof here.
allowed to hand in the following exercises after the due dates:
Ex. 5.1 -> June
Ex. 6.2 ->
We will cover the
topic "elastic rods" in the tutorial on Monday.
office hours tomorrow will be from 10:15-12.
derivation of the Euler-Lagrange eq.I recommend to have a look into
V.I.Arnold, Mathematical Methods of Classical Mechanics, Springer,
2nd ed., p. 55 ff. (or take a copy in the lecture tomorrow)
- There is no lecture on Wed 18 Apr; the first lecture will be
on Thursday 19 April.
- There are no tutorials on Mon 16 Apr; tutorials and office
hours will start in the second week.
Classical differential geometry studies smooth curves and
surfaces, for instance in terms of their curvatures. This course
will consider analogous notions and results for discrete (usually
polygonal) curves and discrete (usually polyhedral) surfaces.
Specific topics will include:
- Curvatures of discrete curves, discrete elastic curves
- Curvatures of discrete surfaces, special parametrizations and
classes of surfaces
- Discrete conformal and harmonic maps, the discrete Laplace
operator, Delaunay triangulations, circle packings, discrete
conformal equivalence, discrete Riemann surfaces, variational
- Alexander I. Bobenko, Lecture
notes from the Summer 2014 version of this course.
- John M. Sullivan, Curves of Finite
Total Curvature, in Discrete Differential Geometry,
Birkhäuser, 2008, pp. 137–161.
- John M. Sullivan, Curvatures
of Smooth and Discrete Surfaces, in Discrete
Differential Geometry, Birkhäuser, 2008, pp. 175–188.
- Sheet 1,
due 30 April
- Sheet 2,
due 7 May
- Sheet 3,
due 14 May
- Sheet 4,
due 23 May
- Sheet 5,
due 28 May
- Sheet 6,
due 4 June
- Sheet 7,
due 11 June
- Sheet 8,
due 18 June
- Sheet 9,
due 25 June
- Sheet 10,
due 2 July
- Sheet 11,
due 9 July
Homework policy and exam information
- To get a certificate for the tutorial and thus qualify to
take the oral exam, you need to satisfactorily complete 60% of
the homework assignments.
- The exercises are to be done in groups of two people and
handed in at one of the tutorials each Monday.
- Oral exams
will be offered 10-12h on 25 July and 27 July.
It will also be possible to take the exam in late September or in