Optimal Möbius Transformations for Information Visualization and Meshing

  • Marshall Bern
  • David Eppstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2125)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Marshall Bern
    • 1
  • David Eppstein
    • 2
  1. 1.Xerox PARCPalo AltoUSA
  2. 2.Dept. Inf. & Comp. Sci.UC IrvineUSA

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