# David Eppstein - Publications

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**A Möbius-invariant power diagram and its applications to soap
bubbles and planar Lombardi drawing**.

D. Eppstein.

Invited talk at EuroGIGA Midterm
Conference, Prague, Czech Republic, 2012.

*Discrete
Comput. Geom.* 52 (3): 515–550, 2014 (Special issue for SoCG 2013).
This talk and journal paper combines the results from
"Planar Lombardi drawings for
subcubic graphs" and "The graphs of
planar soap bubbles".
It uses three-dimensional hyperbolic geometry to define a partition of
the plane into cells with circular-arc boundaries, given an input
consisting of (possibly
overlapping) circular disks and disk complements, which remains
invariant under Möbius transformations of the input. We use this
construction as a tool to construct planar Lombardi drawings of
all 3-regular planar graphs; these are graph drawings in which the edges
are represented by circular arcs meeting at equal angles at each vertex.
We also use it to characterize the graphs of two-dimensional soap bubble
clusters as being exactly the 2-vertex-connected 3-regular planar graphs.

Publications –
David Eppstein –
Theory Group –
Inf. & Comp. Sci. –
UC Irvine

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