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Optimal Möbius Transformations for Information Visualization and Meshing

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Algorithms and Data Structures (WADS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2125))

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Abstract

We give linear-time quasiconvex programming algorithms for finding a Möbius transformation of a set of spheres in a unit ball or on the surface of a unit sphere that maximizes the minimum size of a transformed sphere. We can also use similar methods to maximize the minimum distance among a set of pairs of input points. We apply these results to vertex separation and symmetry display in spherical graph drawing, viewpoint selection in hyperbolic browsing, element size control in conformal structured mesh generation, and brain flat mapping.

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Author information

Authors and Affiliations

  1. Xerox PARC, 3333 Coyote Hill Rd., Palo Alto, CA, 94304, USA

    Marshall Bern

  2. Dept. Inf. & Comp. Sci., UC Irvine, CA, 92697-3425, USA

    David Eppstein

Authors
  1. Marshall Bern
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  2. David Eppstein
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Candada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. Center for Geometric Computing, Brown University, Providence, RI, 02912-1910, USA

    Roberto Tamassia

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© 2001 Springer-Verlag Berlin Heidelberg

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Bern, M., Eppstein, D. (2001). Optimal Möbius Transformations for Information Visualization and Meshing. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_3

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  • DOI: https://doi.org/10.1007/3-540-44634-6_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42423-9

  • Online ISBN: 978-3-540-44634-7

  • eBook Packages: Springer Book Archive

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