Drawing trees with perfect angular resolution and polynomial area
Christian A. Duncan,David Eppstein,Michael T. Goodrich,Stephen G. Kobourov,Martin Nöllenburg +4 more
- pp 183-194
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TLDR
What is achievable with straight-line drawings and what more is achievable is explored with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.Abstract:
We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, 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.read more
Citations
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Journal ArticleDOI
Drawing Trees with Perfect Angular Resolution and Polynomial Area
Christian A. Duncan,David Eppstein,Michael T. Goodrich,Stephen G. Kobourov,Martin Nöllenburg +4 more
TL;DR: The results explore what is achievable with straight-line drawings and what more is achieving with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.
Book ChapterDOI
Planar and poly-arc lombardi drawings
TL;DR: It is shown that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.
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2-D Layout for Tree Visualization: a survey
TL;DR: This is a survey of recent researches on 2D tree visualization approaches including different styles of node-link diagram, main variations of Treemap, some solutions designed especially for mobile devices, and several hybrid approaches.
Proceedings ArticleDOI
The graphs of planar soap bubbles
TL;DR: In this paper, the authors characterize the graphs formed by two-dimensional soap bubbles as being exactly the 3-regular bridgeless planar multigraphs and prove that this characterization remains invariant under Mobius transformations.
Book ChapterDOI
Pinning balloons with perfect angles and optimal area
Immanuel Halupczok,André Schulz +1 more
TL;DR: An algorithm for embedding unordered trees with straight lines and perfect angular resolution such that it can be covered with a disk of radius n3.0367, while having no edge of length smaller than 1.
References
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Journal ArticleDOI
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Journal ArticleDOI
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C. Wetherell,A. Shannon +1 more
TL;DR: Two naive tree drawers are surveyed, formalize aesthetics for tidy trees, and two algorithms which draw tidy trees are discussed, one of which may be shown to require the minimum possible paper width.
Book ChapterDOI
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