Quasiformal Dilatation of Projective Transformations and Discrete Conformal Maps

Stefan Born, Ulrike Bücking, Boris Springborn

Description

Quasiconformal dilatation of projective transformations of the real projective plane are shown. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. This result is used to analyze the dilatation of the circumcircle preserving piecewise projective interpolation between discretely conformally equivalent triangulations. It is shown that another interpolation scheme, angle bisector preserving piecewise projective interpolation, is in a sense optimal with respect to dilatation. These two interpolation schemes belong to a one-parameter family.

References

  • Stefan Born, Ulrike Bücking, and Boris Springborn.
    Quasiconformal Dilatation of Projective Transformations and Discrete Conformal Maps.
    Discrete & Computational Geometry, 57(2):305–317, 2017.
    arXiv:1505.01341.

Authors

Dr. Stefan Born   +

University: TU Berlin

Dr. Ulrike Bücking   +

Projects: A01
University: FU Berlin, Institut für Mathematik, 038
Address: Arnimallee 3, 14195 Berlin, GERMANY
Tel: +49 30 83866595
E-Mail: buecking[at]math.fu-berlin.de
Website: https://www.mi.fu-berlin.de/en/math/groups/ag-diskret-algebra-geom/members/Professoren/ulrike_buecking.html

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/

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