Quasiconformal Dilatation of Projective Transformations and Discrete Conformal Maps

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• 作者：Stefan Born ; Ulrike Bücking ; Boris Springborn
• 关键词：Piecewise projective ; Optimal quasiconformal mapping ; Discrete complex analysis
• 刊名：Discrete & Computational Geometry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：57
• 期：2
• 页码：305-317
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Computational Mathematics and Numerical Analysis;
• 出版者：Springer US
• ISSN：1432-0444
• 卷排序：57

文摘

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.