# Conformal Equivalence of Triangle Meshes

Ulrich Pinkall, Peter Schröder, Boris Springborn

### Description

A new algorithm for conformal mesh parameterization is presented here. It is based on a precise notion of discrete conformal equivalence for triangle meshes which mimics the notion of conformal equivalence for smooth surfaces. The problem of finding a flat mesh that is discretely conformally equivalent to a given mesh can be solved efficiently by minimizing a convex energy function, whose Hessian turns out to be the well known $cot$-Laplace operator. This method can also be used to map a surface mesh to a parameter domain which is flat except for isolated cone singularities.
Examples are shown of how these can be placed automatically in order to reduce the distortion of the parameterization.

### References

#### Prof. Dr. Ulrich Pinkall   +

Projects: A05, C07
University: TU Berlin, Institut für Mathematik, MA 822
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31424607
E-Mail: pinkall[at]math.tu-berlin.de
Website: http://page.math.tu-berlin.de/~pinkall/

#### Prof. Dr. Boris Springborn   +

Projects: A01
University: TU Berlin, Institut für Mathematik, MA 871
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31423617
Fax: +49 30 31479282
E-Mail: boris.springborn[at]tu-berlin.de
Website: http://page.math.tu-berlin.de/~springb/