Drawing Trees with Perfect Angular Resolution and Polynomial Area
Drawing Trees with Perfect Angular Resolution and Polynomial Area
复制标题
以完美的角度分辨率和多项式面积绘制树木
DOI：
10.1007/s00454-012-9472-y
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发表时间：
2010
影响因子：
0.8
通讯作者：
M. Nöllenburg
中科院分区：
文献类型：
--
作者：
C. A. Duncan;D. Eppstein;M. Goodrich;S. Kobourov;M. Nöllenburg
我们研究的方法，绘制树木与完美的角分辨率，即，每个节点的角度等于。我们证明了：1.任何无序树都有一个具有完美角分辨率和多项式面积的无交叉直线图; 2.任何具有完美角分辨率的无交叉直线图都有一个需要指数面积的有序树; 3.任何有序树都有一个具有完美角分辨率和多项式面积的无交叉Lombardi风格图（每个边用圆弧表示）.
We study methods for drawing trees with perfect angular resolution, i.e., with angles at each nodeequal to. 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-freeLombardi-styledrawing (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.