Kristoffer Josefsson

Dipl. Math. Kristoffer Josefsson

Geometry group at Institute of Mathematics at TU-Berlin

Mail: josefsso@math.tu-berlin.de
Phone: +49-30-314-29273
Room: MA 877
Curriculum Vitae: cv.pdf
Master Thesis: exjobb_d4vt_article.pdf

Research interests:

Polyhedral surfaces and discretizations of classical phenomena of differential geometry, in particular mean curvature functions on Delaunay triangulated polyhedra.
Discrete developing maps, nets of polyhedra and unfoldings.
Curvature of polygons and polyhedral surfaces, representations of discrete meshes from curvature and the Minkowski problem.
Isometric deformations of quad-meshes and relations to integrable systems.
Applications of discrete differential geometry in architectural design.

Discrete differential geometry and kinematics in architectural design

Matheon

Java Applications:

DForm editor (beta)

DForm editor This is a tool for modelling D-Forms, a concept introduced by Tony Wills. These are modelled by gluing two shapes with equal circumference at their boundaries. This program requires Java 5.

Instructions (to be expanded):
Right click on the left editor to insert two shapes, change to the desired settings in the dialog and press compute. By right-clicking the shapes and going to "controller", one can change subdivision levels. It is also possible to load and save shapes.

Example files with suggestions:

clip.polygon: Subdivision level: 4, first shape cubic-, second circular subdivision (see above, or screenshot).

heart.polygon: Subdivision level 3, first shape cubic-, second circular subdivision (screenshot).

cross.polygon: Subdivision level 2, first circular-, second bisecting circular subdivision (screenshot).

Relevant literature:

Alexandrov's theorem, weighted Delaunay triangulations, and mixed volumes by Alexander I. Bobenko, Ivan Izmestiev, 2006. Preprint: arXiv:math/0609447v1 [math.DG]
Computational Line Geometry by H. Pottmann and J. Wallner, Springer-Verlag, Berlin u.a. 2001, ISBN 3-540-42058-4, 565 pp. 264 figs., 17 in color.
Geometric Folding Algorithms: Linkages, Origami, Polyhedra by Erik D. Demaine and Joseph O'Rourke. Cambridge University Press, July 2007. xii+472 pages. ISBN 978-0-521-85757-4.

Discrete minimal surfaces

Discrete minimal surface Updated - now requires Java 1.6+

This is a tool for generating discrete minimal surfaces.
(Description to be written)

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Relevant literature:

Computing Discrete Minimal Surfaces and Their Conjugates by Ulrich Pinkall and Konrad Polthier, Experiment. Math. Volume 2, Issue 1 (1993), 15-36. Preprint at http://www-sfb288.math.tu-berlin.de/~konrad/articles/diri/diri_jem.pdf
A discrete Laplace-Beltrami operator for simplicial surfaces by Alexander I. Bobenko and Boris A. Springborn, 2006. Preprint: arXiv:math/0503219v3 [math.DG]
Discrete Differential-Geometry Operators for Triangulated 2-Manifolds by Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr, 2002. Preprint at http://www.multires.caltech.edu/pubs/diffGeoOps.pdf

Last modified: September 22, 2008