Approximation Algorithms for Finding Best Viewpoints

We address the problem of finding viewpoints that preserve the relational structure of a three-dimensional graph drawing under orthographic parallel projection. Previously, algorithms for finding the best viewpoints under two natural models of viewpoint "goodness" were proposed. Unfortunately, the inherent combinatorial complexity of the problem makes finding exact solutions is impractical. In this paper, we propose two approximation algorithms for the problem, commenting on their design, and presenting results on their performance.

[1]  R. H. J. M. Otten,et al.  The Annealing Algorithm , 1989 .

[2]  David R. Wood Two-Bend Three-Dimensional Orthogonal Grid Drawing of Maximum Degree Five Graphs , 1998 .

[3]  Myron L. Braunstein,et al.  5 – Slant Perception , 1976 .

[4]  Colin Ware,et al.  Evaluating stereo and motion cues for visualizing information nets in three dimensions , 1996, TOGS.

[5]  Steven K. Feiner,et al.  Computer graphics: principles and practice (2nd ed.) , 1990 .

[6]  Pankaj K. Agarwal Intersection and decomposition algorithms for planar arrangements , 1991 .

[7]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

[8]  Kozo Sugiyama,et al.  Layout Adjustment and the Mental Map , 1995, J. Vis. Lang. Comput..

[9]  Prosenjit Bose,et al.  Drawing Nice Projections of Objects in Space , 1999, J. Vis. Commun. Image Represent..

[10]  Arne Frick,et al.  Fast Interactive 3-D Graph Visualization , 1995, GD.

[11]  Annalisa Massini,et al.  On Three-Dimensional Layout of Interconnection Networks , 1997, Graph Drawing.

[12]  Satoru Kawai,et al.  A simple method for computing general position in displaying three-dimensional objects , 1988, Comput. Vis. Graph. Image Process..

[13]  Myron L. Braunstein,et al.  Depth perception through motion , 1976 .

[14]  Peter Eades,et al.  Finding the Best Viewpoints for Three-Dimensional Graph Drawings , 1997, GD.

[15]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[16]  Edward M. Reingold,et al.  Graph drawing by force‐directed placement , 1991, Softw. Pract. Exp..

[17]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.