CGGC seminar (talk #195)
Date:  Wednesday 05/12/2012 (note special day)
Time: 11:30 am (note special time)
Room: Taub 401 (note special hall)
Speaker: Ofir Weber (Computer Science, Haifa University)
Title:   Computing Extremal Quasiconformal Maps
Abstract: Conformal maps are widely used in geometry processing applications. They are
smooth, preserve angles, and are locally injective by construction. However, conformal maps
do not allow for boundary positions to be prescribed. A natural extension to the space of
conformal maps is the richer space of quasiconformal maps of bounded conformal distortion.
Extremal quasiconformal maps, that is, maps minimizing the maximal conformal distortion, have
a number of appealing properties making them a suitable candidate for geometry processing
tasks. Similarly to conformal maps, they are guaranteed to be locally bijective; unlike
conformal maps however, extremal quasiconformal maps have sufficient flexibility to allow for
solution of boundary value problems. Moreover, in practically relevant cases, these solutions
are guaranteed to exist, are unique and have an explicit characterization.
We present an algorithm for computing piecewise linear approximations of extremal
quasiconformal maps for genus-zero surfaces with boundaries, based on Teichmüller's
characterization of the dilatation of extremal maps using holomorphic quadratic
differentials.We demonstrate that the algorithm closely approximates the maps when an
explicit solution is available and exhibits good convergence properties for a variety of
boundary conditions.
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