Trees with convex faces and optimal angles

Authors:
Josiah Carlson;David Eppstein
Affiliations:
Computer Science Department, University of California, Irvine;Computer Science Department, University of California, Irvine
Venue:
GD'06 Proceedings of the 14th international conference on Graph drawing
Year:
2006

Citing 2
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Drawing trees with perfect angular resolution and polynomial area

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Optimal 3D angular resolution for low-degree graphs

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Bounds on the complexity of halfspace intersections when the bounded faces have small dimension

Proceedings of the twenty-seventh annual symposium on Computational geometry

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Abstract

We consider drawings of trees in which all edges incident to leaves can be extended to infinite rays without crossing, partitioning the plane into infinite convex polygons. Among all such drawings we seek the one maximizing the angular resolution of the drawing. We find linear time algorithms for solving this problem, both for plane trees and for trees without a fixed embedding. In any such drawing, the edge lengths may be set independently of the angles, without crossing; we describe multiple strategies for setting these lengths.