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Planar Polyline Drawings via Graph Transformations

Algorithmica, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huaming Zhang, Zhang Huaming
exaly   +3 more sources

Graphs That Admit Polyline Drawings with Few Crossing Angles

SIAM Journal on Discrete Mathematics, 2012
We consider graphs that admit polyline drawings where all crossings occur at the same angle $\alpha\in (0,\frac{\pi}{2}]$. We prove that every graph on $n$ vertices that admits such a polyline drawing with at most two bends per edge has $O(n)$ edges. This result remains true when each crossing occurs at an angle from a small set of angles.
Radoslav Fulek, Csaba Tóth
exaly   +3 more sources

Optimal Area Algorithm for Planar Polyline Drawings

2002
We present a linear time algorithm based on Schnyder trees that produces planar polyline drawings. These drawings have the optimal area (4(n-1)2/9) and width ([2(n-1/3]), and have at most n-2 bends, where n is the number of vertices of the graph. Moreover, at most one bend per edge is needed.
Bonichon, Nicolas   +2 more
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Planar Polyline Drawings with Good Angular Resolution

1998
We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree n on a (2n - 5) × (3/2n - 7/2) grid with at most 5n - 15 bends and minimum angle > 2/d. In the constructed drawings, every edge has at most three bends and length O(n).
Carsten Gutwenger, Petra Mutzel
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Layered Polyline Drawings of Planar Graphs.

A k-layer polyline drawing of a planar graph G is a planar drawing of G on a set L of k parallel lines such that each vertex is mapped to a point on L and each edge is mapped to a polygonal chain with the endpoints and bends lying on L. In the fixed embedding setting, the output drawing maintains the given planar embedding, whereas in the variable ...
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Polyline simplification based on the artificial neural network with constraints of generalization knowledge

Cartography and Geographic Information Science, 2022
Xianyong Gong, Jiawei Du
exaly  

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