Facts
Institute of Mathematics@TUBerlinSFB / Transregio 109 Discretization in Geometry and Dynamics Project A01: Discrete Riemann Surfaces Github Profile Blog: Notes on things Ello Profile mail: sechel@math.tuberlin.de office: MA 879 phone: +49(0)30 31429486 Interests
Publications
(click on the image to download the fulltext PDF)
Discrete Minimal Surfaces of Koebe Type
Variational Methods for Discrete Surface Parameterization. Applications and Implementation. (Doctoral Thesis)
Discrete conformal maps: Boundary value problems, circle domains, Fuchsian and Schottky uniformization
DGD Gallery: Storage, sharing, and publication of digital research data
Sconical minimal surfaces. Towards a unified theory of discrete minimal surfaces.
Discrete Uniformization of Polyhedral Surfaces with Nonpositive Curvature and Branched Covers over the Sphere via Hyperideal Circle Patterns
Surface panelization using periodic conformal maps
Quasiisothermic Mesh Layout
Topology Optimisation of Regular and Irregular Elastic Gridshells by means of a Nonlinear Variational Method.
On the Materiality and Structural Behaviour of highlyelastic Gridshell Structures Talks
A list of talks in chronological order.
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 3space, 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. Fuchsian uniformization of the hyperelliptic curve $\mu^2=\lambda\cdot(\lambda^61)$. Riemann map of a slit square to the disk with circular boundary components. Uniformization of algebraic curve of Lawsons surface $\mu^2=\lambda^61$. Algebraic curve of Lawsons surface. Boundary and identifications of a fundamental domain. Schottky data for a genus 3 discrete Riemann surface. Fuchsian uniformization of genus 3 discrete Riemann surface given by Schottky data. Symmetric uniformization of Lawsons surface $\mu^2=\lambda^61$. Euclidean uniformization of a genus 2 surface with translational periods. Map to the corresponding algebraic curve with 6 branch points. Mercator projection. 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.
Visit us at http://www.varylab.com
Multitouch
I work together with the people of www.interactivescape.com to create multitouch 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 for a detailed description. Discrete SIsothermic Minimal Surfaces
Quadrilateral Boundary SchwarzP Surface Unsymmetric ScherkTower Schoen's I6 Surface Cubic Boundary Discrete Catenoid 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 3connected 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. Private
Piano Playing
Here I publish the piano recordings I'm doing for fun and at home. Feel free to
download and listen. For recording I use a
Seiler 132 Konzert
and the software sample Ivory.
Last modified: Stefan Sechelmann 20191203
