MATHEON TU-Berlin
Interests
  • Differential geometry and discrete differential geometry
  • Mathematical visualization / Computer graphics
  • Industrial/architectual geometry
  • Multitouch and tangible interfaces
  • Software development
Publications
(click on the image to download the full-text PDF)

Variational Methods for Discrete Surface Parameterization. Applications and Implementation. (Doctoral Thesis)
Stefan Sechelmann. Variational Methods for Discrete Surface Parameterization. Applications and Implementation, TU-Berlin, 2016, DOI: 10.14279/depositonce-5415


Discrete conformal maps: Boundary value problems, circle domains, Fuchsian and Schottky uniformization
Alexander I. Bobenko, Stefan Sechelmann, and Boris Springborn. Discrete conformal maps: Boundary value problems, circle domains, Fuchsian and Schottky uniformization. In A. I. Bobenko, editor, Advances in Discrete Differential Geometry. Springer, 2016.


DGD Gallery: Storage, sharing, and publication of digital research data
M. Joswig, M. Mehner, S. Sechelmann, J. Techter, and A.I. Bobenko. DGD Gallery: Storage, sharing, and publication of digital research data. In A. I. Bobenko, editor, Advances in Discrete Differential Geometry. Springer, 2016.


S-conical minimal surfaces. Towards a uni fied theory of discrete minimal surfaces.
Alexander I. Bobenko, Benno König, Tim Ho mann, and Stefan Sechelmann. S-conical minimal surfaces. Towards a uni fied theory of discrete minimal surfaces. preprint: http://www.discretization.de


Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns
Alexander Bobenko, Nikolay Dimitrov, and Stefan Sechelmann. Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns. preprint: arXiv:1510.04053


Surface panelization using periodic conformal maps
Thilo Rörig, Stefan Sechelmann, Agata Kycia, and Moritz Fleischmann, Surface panelization using periodic conformal maps,
Advances in Architectural Geometry 2014 (P. Block, J. Knippers, N.J. Mitra, and W. Wang, eds.), Springer, 2014, p. 365. Best Paper Award AAG 2014


Uniformization of discrete Riemann surfaces
Stefan Sechelmann, Uniformization of discrete Riemann surfaces, Discrete Differential Geometry (Alexander I. Bobenko, Richard Kenyon, Peter Schröder, and Günter M. Ziegler, eds.), vol. 9, Oberwolfach Reports, no. 3, European Mathematical Society, 2012, pp. 2105-2107.


Quasiisothermic Mesh Layout
S. Sechelmann, T. Rörig, and A. I. Bobenko. Quasiisothermic Mesh Layout.
In Hesselgren, L.; Sharma, S.; Wallner, J.; Baldassini, N.; Bompas, P.; Raynaud, J. (Eds.). Advances in Architectural Geometry 2012. 2012, 344 p. 285 illus. in color. ISBN 978-3-7091-1250-2


Topology Optimisation of Regular and Irregular Elastic Gridshells by means of a Non-linear Variational Method.
E. Lafuente E, S. Sechelmann, T. Rörig, and C. Gengnagel. Topology Optimisation of Regular and Irregular Elastic Gridshells by means of a Non-linear Variational Method.
In Hesselgren, L.; Sharma, S.; Wallner, J.; Baldassini, N.; Bompas, P.; Raynaud, J. (Eds.). Advances in Architectural Geometry 2012. 2012, 344 p. 285 illus. in color. ISBN 978-3-7091-1250-2


On the Materiality and Structural Behaviour of highly-elastic Gridshell Structures
E. Lafuente E, C. Gengnagel, S. Sechelmann, and T. Rörig. On the Materiality and Structural Behaviour of highly-elastic Gridshell Structures
In Gengnagel, C.; Kilian, A.; Palz, N.; Scheurer, F. (Eds.). Computational Design Modeling: Proceedings of the Design Modeling Symposium Berlin 2011 2012, XVI, 347 p. ISBN 978-3-642-23435-4



Discrete Minimal Surfaces, Koebe Polyhedra, and Alexandrov's Theorem. Variational Principles, Algorithms, and Implementation. (Diploma Thesis)

Discrete Riemann Surfaces

Riemann surfaces have been studied for a long time. Recently, the development of robust conformal mapping algorithms based on triangulaions has lead to significant interest in discrete versions of smooth theorems and constructions in the context of Riemann surfaces. In this section I present a selection of images from my research on the topic of discrete Riemann surfaces.

A Riemann surface can have quite different representations. I consider three kinds of representations in my work: Embeddings in 3-space, algebraic curves, and quotient spaces of the Euclidean plane, the hyperbolic plane, and the Riemann sphere. The latter beeing uniformizations of Fuchsian type or schottky type respectively.

Most of the algorithms for the calculation with discrete Riemann surfaces are available online as part of the VaryLab project.

VaryLab
VaryLab is all about mesh optimization, we say discrete surface optimization. That means you can modify a given mesh to have minimal energy in a certain sense. The energy in question is a combination of energies that are defined on the vertex positions of the input mesh. VaryLab implements various energies for discrete surfaces, e.g., planarity of faces, equal lengths of edges, curvature of parameter curves and many more.

Multitouch

I work together with the people of www.interactive-scape.com to create multi-touch applications.
jPETScTao
jPETScTao is the name for a Java project, that tries to make a part of the functionality of two numeric libraries PETSc and Tao accessible for Java programs. It utilizes the JNI to achieve that.
See

jPETScTao

for a detailed description.
Java Applications
Minimal Surfaces

Discrete Minimal Surfaces
This application calculates discrete minimal surfaces as described in my diploma thesis. The construction method follows the approach of Bobenko, Hoffmann, and Springborn. It uses the notion of discrete isothermic surfaces and their Cristoffel transform to define discrete minimal surfaces. The program is able to create surfaces with planar boundary curvature lines.
Alexandrov's polyhedron

Alexandrov's Polyhedron
In cooperation with Ivan Izmestiev I implemented an algorithm for constructing convex polyhedra with a given metric. The java webstart on the left is the main program which I used for testing and research purposes.


Teamgeist(TM) Polyhedron
The right program is an application of the alexandrov program. It calculates a polyhedron with predefined combinatorics and symetry of the Teamgeist(TM) soccer ball. I created this during the world soccer championchips. For a description and a java applet see A "Teamgeist" Polyhedron

Another polyhedron I created with the help of this tool is the Reuleaux Triangle Tetrahedron. This is a Tetrahedron with curved sides which are Reuleaux Triangles. Those triangles get slighly bent to fit together.

Koebe polyhedron

Koebe Polyhedron Editor
Together with Boris Springborn I created a visualization tool for Koebe Polyhedra. Click the image to start a Java Webstart application.

The left section is a graph designer. If the graph is 3-connected and enbedded the program calculates the corresponding polyhedron and displays a normalized representation in the righ section.

This is the first program I created for the geometry group. It contains numerical algorithms for nonlinear optimization of the convex functional involved. I use the MTJ library for linear solving and sparse matrix representation. The program is also part of my diploma thesis and is being described in detail in Chapter 1.
Last modified: Stefan Sechelmann 2016-07-28