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