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arXiv · 1009.0581

Drawing Trees with Perfect Angular Resolution and Polynomial Area

Christian A. Duncan·David Eppstein·Michael T. Goodrich·Stephen G. Kobourov·Martin Nöllenburg
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Abstract

We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2π/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution. 3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straight-line drawings and what more is achievable with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.

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Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G. Kobourov, Martin Nöllenburg. 2015-09-10. Drawing Trees with Perfect Angular Resolution and Polynomial Area. https://doi.org/10.1007/s00454-012-9472-y

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