On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Drawing graphs in the plane with high resolution
SIAM Journal on Computing
On the Angular Resolution of Planar Graphs
SIAM Journal on Discrete Mathematics
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
A linear-time algorithm for drawing a planar graph on a grid
Information Processing Letters
Handbook of discrete and computational geometry
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
A Technique for Drawing Directed Graphs
IEEE Transactions on Software Engineering
Optimizing Area and Aspect Ratio in Straight-Line Orthogonal Tree Drawings
GD '96 Proceedings of the Symposium on Graph Drawing
Planar Drawings and Angular Resolution: Algorithms and Bounds (Extended Abstract)
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Fast Layout Methods for Timetable Graphs
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Planar straight-line drawing in an O(n)×O(n) grid with angular resolution Ω(1/n)
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Curvilinear graph drawing using the force-directed method
GD'04 Proceedings of the 12th international conference on Graph Drawing
On the density of maximal 1-planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We describe a unified framework of aesthetic criteria and complexity measures for drawing planar graphs with polylines and curves. This framework includes several visual properties of such drawings, including aspect ratio, vertex resolution, edge length, edge separation, and edge curvature, as well as complexity measures such as vertex and edge representational complexity and the area of the drawing. In addition to this general framework, we present algorithms that operate within this framework. Specifically, we describe an algorithm for drawing any n- vertex planar graph in an O(n) 脳 O(n) grid using polylines that have at most two bends per edge and asymptotically-optimal worst-case angular resolution. More significantly, we show how to adapt this algorithm to draw any n-vertex planar graph using cubic B茅zier curves, with all vertices and control points placed within an O(n) 脳 O(n) integer grid so that the curved edges achieve a curvilinear analogue of good angular resolution. All of our algorithms run in O(n) time.