Quasiconformal Dilatation of Projective Transformations and Discrete Conformal Maps

We consider the quasiconformal dilatation of projective transformations of the real projective plane. 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. We apply this result to analyze the di...

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Bibliographic Details
Published inDiscrete & computational geometry Vol. 57; no. 2; pp. 305 - 317
Main Authors Born, Stefan, Bücking, Ulrike, Springborn, Boris
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2017
Springer Nature B.V
Subjects
Combinatorics
Computational Mathematics and Numerical Analysis
Dilatation
Equivalence
Interpolation
Mathematics
Mathematics and Statistics
Optimization
Pencils
Shape
Transformations
Transformations (mathematics)
52C26
Piecewise projective
Discrete complex analysis
Optimal quasiconformal mapping
30C62
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Summary:We consider the quasiconformal dilatation of projective transformations of the real projective plane. 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. We apply this result to analyze the dilatation of the circumcircle preserving piecewise projective interpolation between discretely conformally equivalent triangulations. We show 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.
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ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-016-9854-7