Conformal Deformations of Discrete Surfaces

The Construction of a Discrete Differential Geometry Version of Certain Conformal Deformations

Two geometries can be considered equivalent if there exists an angle preserving transformation between them; this is a so called conformal transformation. In the smooth case, conformal equivalences are quite well understood. However, mimicking their construction in the discrete case brought up not only interesting properties and algorithms, but also interesting problems - first and foremost the question of how to construct conformal deformations with certain prescribed properties.

Scientific Details+

The goal of this project is to develop an exact Discrete Differential Geometry version of conformal deformations with prescribed mean curvature half-density. This will be based on the notion of conformal equivalence of triangle meshes introduced in B. Springborn, P. Schröder, and U. Pinkall. Conformal equivalence of triangle meshes , and provide an exact Discrete Differential Geometry version of the numerical methods developed in K. Crane, U. Pinkall, and P. Schröder. Spin transformations of discrete surfaces.



Master thesis
  • W.Y. Lam.
    Infinitesimal conformal deformations of triangulated surfaces.
    Master's thesis, Technische Universität Berlin, 2013.


Prof. Dr. Ulrich Pinkall   +

Projects: A05, C07
University: TU Berlin
E-Mail: pinkall[at]math.tu-berlin.de
Website: http://page.math.tu-berlin.de/~pinkall/

Dr. Albert Chern   +

Projects: A05, C07
University: TU Berlin
E-Mail: chern[at]math.tu-berlin.de