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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Trade-Offs in Planar Polyline Drawings
verfasst von : Stephane Durocher, Debajyoti Mondal
Erschienen in: Graph Drawing
Verlag: Springer Berlin Heidelberg
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Angular resolution, area and the number of bends are some important aesthetic criteria of a polyline drawing. Although trade-offs among these criteria have been examined over the past decades, many of these trade-offs are still not known to be optimal. In this paper we give a new technique to compute polyline drawings for planar triangulations. Our algorithm is simple and intuitive, yet implies significant improvement over the known results. We present the first smooth trade-off between the area and angular resolution for 2-bend polyline drawings of any given planar graph. Specifically, for any given
n
-vertex triangulation, our algorithm computes a drawing with angular resolution
r
/
d
(
v
) at each vertex
v
, and area
f
(
n
,
r
), for any
r
∈ (0,1], where
d
(
v
) denotes the degree at
v
. For
r
< 0.389 or
r
> 0.5,
f
(
n
,
r
) is less than the drawing area required by previous algorithms;
f
(
n
,
r
) ranges from 7.12
n
2
when
r
≤ 0.3 to 32.12
n
2
when
r
= 1.