### Non-planar Orthogonal Drawings with Fixed Topology [chapter]

Markus Chimani, Gunnar W. Klau, René Weiskircher
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a procedure for calculating the bend minimal shape of non-planar graphs with given topology. The method is an extension of the Simple-Kandinsky drawing standard -a simplification of the more complex Kandinsky standard. For both models, algorithms exist that guarantee bend minimality for planar graphs with given topology. They generate orthogonal drawings with equal node size where multiple edges can be attached to a single side of a node. In contrast to Kandinsky, Simple-Kandinsky
more &raquo; ... certain restrictions on the split up of such bundles. In this paper we extend the drawing standard to the class of non-planar graphs and present an algorithm that computes provably bend-minimal drawings within this standard. The extension treats edge crossings in a special way by letting them share identical grid points where appropriate. Hence it allows crossings of whole bundles of edges instead of single edges only. Besides having a reduced number of bends, drawings computed by our algorithm are easier to read and consume less area than those produced by the traditional approaches. Furthermore, we show a sharp upper bound of the bend count for the heuristic use of Simple-Kandinsky for non-planar graphs and present an extension of the new method that is able to draw non-planar clustergraphs.
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