On-line graph algorithms with SPQR-trees
Proceedings of the seventeenth international colloquium on Automata, languages and programming
A polynomial time circle packing algorithm
Discrete Mathematics
Optimal Möbius Transformations for Information Visualization and Meshing
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Computational Geometry: Theory and Applications
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Steinitz theorems for orthogonal polyhedra
Proceedings of the twenty-sixth annual symposium on Computational geometry
Drawing trees with perfect angular resolution and polynomial area
GD'10 Proceedings of the 18th international conference on Graph drawing
Planar and poly-arc lombardi drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
Force-Directed lombardi-style graph drawing
GD'11 Proceedings of the 19th international conference on Graph Drawing
Planar lombardi drawings of outerpaths
GD'12 Proceedings of the 20th international conference on Graph Drawing
The graphs of planar soap bubbles
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe---Andreev---Thurston circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Möbius transformations, defined using three-dimensional hyperbolic geometry. We also use circle packing to construct planar Lombardi drawings of a special class of 4-regular planar graphs, the medial graphs of polyhedral graphs, and we show that not every 4-regular planar graph has a planar Lombardi drawing. We have implemented our algorithm for 3-connected planar cubic graphs.