Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Automating the design of graphical presentations of relational information
ACM Transactions on Graphics (TOG)
On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
DAG—a program that draws directed graphs
Software—Practice & Experience
Area requirement and symmetry display in drawing graphs
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A node-positioning algorithm for general trees
Software—Practice & Experience
Visualizing and querying software structures
ICSE '92 Proceedings of the 14th international conference on Software engineering
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
Area-efficient upward tree drawings
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Systematic Programming: An Introduction
Systematic Programming: An Introduction
IEEE Software
Rigi: a model for software system construction, integration, and evolution based on module interface specifications
Visualizing object oriented software in three dimensions
CASCON '93 Proceedings of the 1993 conference of the Centre for Advanced Studies on Collaborative research: software engineering - Volume 1
Graph Theory With Applications
Graph Theory With Applications
Comparaison de la lisibilité des graphes en représentation noeuds-liens et matricielle
IHM 2004 Proceedings of the 16th conference on Association Francophone d'Interaction Homme-Machine
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Many systems, particularly those which present relational information, include a graph drawing function. Such systems have motivated a great deal of research on algorithms for drawing graphs; a recent survey lists over 250 references. Almost all this work has been oriented toward two-dimensional drawings. This paper describes an investigation of mathematically fundamental aspects of three-dimensional graph drawing. In particular we give three results concerning the space required for three-dimensional drawings.We showhow to produce a grid drawing of an arbitrary n-vertex graph with all vertices located at integer grid point, in an n × 2n × 2n grid, such that no pair of edges cross. This grid size is optimal to within a constant. We also show how to convert an orthogonal two-dimensional drawing in a H × V integer grid to a three-dimensional drawing with ⌈√H⌉ × ⌈√H⌉ × V volume. Using this technique we show, for example, that three-dimensional drawings of binary trees can be computed with volume ⌈√n⌉ × ⌈√n⌉ × ⌈logn⌉. We give an algorithm for producing drawings of rooted trees in which the z coordinate of a node represents the depth of the node in the tree; our algorithm minimizes the footprint of the drawing, that is, the size of the projection in the xy plane.Finally, we list significant unsolved problems in algorithms for three-dimensional graph drawing.