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Complex Logarithmic Views for Small Details in Large Contexts
September-October 2006 (vol. 12 no. 5)
pp. 845-852
ASCII Text
x 
 
Joachim Böttger, Michael Balzer, Oliver Deussen, "Complex Logarithmic Views for Small Details in Large Contexts," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 845-852, September-October, 2006.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2006.126,
author = {Joachim Böttger and Michael Balzer and Oliver Deussen},
title = {Complex Logarithmic Views for Small Details in Large Contexts},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {12},
number = {5},
issn = {1077-2626},
year = {2006},
pages = {845-852},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.126},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Complex Logarithmic Views for Small Details in Large Contexts
IS - 5
SN - 1077-2626
SP845
EP852
EPD - 845-852
A1 - Joachim Böttger,
A1 - Michael Balzer,
A1 - Oliver Deussen,
PY - 2006
KW - Detail in context
KW - complex logarithm
KW - conformal mappings
KW - analytic functions
KW - interaction.
VL - 12
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Commonly known detail in context techniques for the two-dimensional Euclidean space enlarge details and shrink their context using mapping functions that introduce geometrical compression. This makes it difficult or even impossible to recognize shapes for large differences in magnification factors. In this paper we propose to use the complex logarithm and the complex root functions to show very small details even in very large contexts. These mappings are conformal, which means they only locally rotate and scale, thus keeping shapes intact and recognizable. They allow showing details that are orders of magnitude smaller than their surroundings in combination with their context in one seamless visualization. We address the utilization of this universal technique for the interaction with complex two-dimensional data considering the exploration of large graphs and other examples.

[1] M. Balzer and O. Deussen, Exploring relations within software systems using treemap enhanced hierarchical graphs. In Proceedings of the IEEE International Workshop on Visualizing Software for Understanding and Analysis, pages 89–94. IEEE, 2005.
[2] M. Balzer and O. Deussen, Voronoi treemaps. In Proceedings of the IEEE Symposium on Information Visualization, pages 49–56. IEEE, 2005.
[3] T. Keahey and E. Robertson, Techniques for non-linear magnification transformations. In Proceedings of IEEE Symposium on Information Visualization, pages 38–45. IEEE, 1996.
[4] T. Keahey and E. Robertson, Nonlinear magnification fields. In Proceedings of IEEE Symposium on Information Visualization, pages 51–58. IEEE, 1997.
[5] J. Lamping and R. Rao, Laying out and visualizing large trees using a hyperbolic space. In Proceedings of the ACM Symposium on User Interface Software and Technology, pages 13–14. ACM, 1994.
[6] J. Mackinlay, G. Robertson, and S. Card, The perspective wall: Detail and context smoothly integrated. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pages 173–176. ACM, 1991.
[7] T. Needham, Visual Complex Analysis. Clarendon Press, 1997.
[8] G. Robertson and J. Mackinlay, The document lens. In Proceedings of the ACM Symposium on User Interface Software and Technology, pages 101–108. ACM, 1993.
[9] R. Spence and M. Apperley, Data base navigation: An office environment for the professional. In Readings in information visualization: Using vision to think, pages 333–340. Morgan Kaufmann, 1999.

Index Terms:
Detail in context, complex logarithm, conformal mappings, analytic functions, interaction.
Citation:
Joachim Böttger, Michael Balzer, Oliver Deussen, "Complex Logarithmic Views for Small Details in Large Contexts," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 845-852, Sept. 2006, doi:10.1109/TVCG.2006.126
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