The drawability problem for minimum weight triangulations
Theoretical Computer Science
Embedding problems for paths with direction constrained edges
Theoretical Computer Science
Dynamic Grid Embedding with Few Bends and Changes
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Embedding Problems for Paths with Direction Constrained Edges
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Orthogonal Drawings of Cycles in 3D Space (Extended Abstract)
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
GD'10 Proceedings of the 18th international conference on Graph drawing
Triangulations with circular arcs
GD'11 Proceedings of the 19th 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
Cauchy's theorem and edge lengths of convex polyhedra
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
On the usability of lombardi graph drawings
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating its angles; we also discuss minimality properties of the characterization. The characterization can be used: (1) to decide in linear time whether a given distribution of angles between the edges of a planar triangular graph can result in a planar drawing; (2) to reduce the problem of maximizing the minimum angle in a planar straight-line drawing of a planar triangular graph to a nonlinear optimization problem purely on a space of angles; (3) to give a characterization of the planar drawings of a triconnected graph through a system of equations and inequalities relating its angles; (4) to give a characterization of Delaunay triangulations through a system of equations and inequalities relating its angles; (5) to give a characterization of all the planar drawings of a triangular graph through a system of equations and inequalities relating the lengths of its edges; in turn, this result allows us to give a new characterization of the disc-packing representations of planar triangular graphs.