Facts:Institute of Mathematics@TU-Berlin
DFG Research Center MATHEON mathematics for key technologies
Project F1: Discrete Surface Parametrizations
Blog: Notes on things
office: MA 879
phone: +49(0)30 314-29486
group: Geometry Group
Talks:Here a list of talks I gave.
jReality plugins jRWorkspace is a java plugin SDK. Originally designed as a plugin system for jReality it has become an indenpendent tool to build user interfaces of complex modular applications.
The plugin SDK is delivered together with the standard implementation of the plugin controller. Download the jRWorkspace plugin SDK from here:
Conformal maps plugins
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.
The first picture I am implementing a raytracing renderer. Right now it is able to render quadric surfaces like spheres or hyperboloids. The goal of this project is to implement and experiement with global illumination lighting and volume rendering. In the end this is going to be a rendering backend for the fabulous jReality scene graph engine. I'm still not sure which scene file format to use but the renderman format seems reasonable to me.
On the left side is (nearly) the first picture I created. It uses a reflection shader, raytraced shadows, and a slight phong lighing. The checker board texture is mandatory for a first raytracer picture I suspect.
Diploma Thesis The title of my diploma thesis is:
Discrete Minimal Surfaces, Koebe Polyhedra, and Alexandrov's Theorem. Variational Principles, Algorithms, and Implementation.I am describing the mathematics and implementation of applications I have been creating for the geometry group. Namely the Koebe polyhedron editor, the discrete minimal surface tool, and the alexandrov polyhedron editor. See the application section for further information about these programs.
Discrete Minimal Surface Gallery:I present some of the discrete minimal surfaces I created for my diploma thesis.
Schoen's I-6 Surface
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 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 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 marvelous 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.
Piano PlayingHere I publish the piano recordings I'm doing for fun and at home. Feel free to download and listen.
Last modified: Stefan Sechelmann 2012-07-24