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Visualization of data on unfolded hypercubes

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Abstract

We present a new method to visualize data of the form y = f(x 1, x 2, x 3, x 4) that can be extended to n-dimensions. The essence of the method consists of slicing the data until the dimensions of the slices are reduced to n = 4 and then “unfold” the data into 3D space. Specifically, we map a visual representation of y onto the boundaries of a hypercube or other polytope and unfold those boundaries into 3D space. The display of the data provides a structural representation of 2D slices which can be adjusted and manipulated, allowing geometric properties like connectivity to be easily studied.

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References

  • Aguilera Ramírez A., Pérez Aguila R (2002) Presenting methods for unraveling the first two regular 4D polytopes (4D simplex and the hypercube). In: Proceedings of the first international symposium on, Cyber Worlds, IEEE, pp 439–446

  • Asimov D (1985) The grand tour: a tool for viewing multidimensional data. SIAM J Sci Stat Comput 6(1):128–143

    Article  MathSciNet  MATH  Google Scholar 

  • Bajaj CL, Pascucci V, Rabbiolo G, Schikore DR (1998) Hypervolume visualization: a challenge in simplicity. In: Proceedings of the 1998 IEEE symposium on volume visualization, pp 95–102

  • Banchoff T (1990) Beyond the third dimension: geometry, computer graphics and higher dimensions. Scientific American Library, New York

    MATH  Google Scholar 

  • de Oliveira MCF, Levkowitz H (2003) From visual data exploration to visual data mining: a survey. IEEE Trans Visual Comput Graph 9(3):378–394

    Article  Google Scholar 

  • dos Santos SR, Brodlie KW (2002) Visualizing and investigating multidimensional functions. In: Proceedings of the symposium on data visualisation 2002 (VISSYM ’02). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, pp 173–182

  • Feiner S, Beshers C (1990) Worlds within worlds: metaphors for exploring n-dimensional virtual worlds. In: Symposium on user interface software and technology, Proceedings of the 3rd annual ACM SIGGRAPH symposium on User interface software and technology, Snowbird, Utah, United States, pp 76–83

  • Hanson A, Heng PA (1992a) Illuminating the fourth dimension. IEEE Comput Graph Appl 12:54–62

    Article  Google Scholar 

  • Hanson A, Heng PA (1992b) Four-dimensional views of 3D scalar fields. In: IEEE Visualization, Proceedings of the 3rd conference on Visualization ’92, pp 84–91

  • Inselberg A, Dimsdale B (1990) Parallel coordinates: a tool for visualizing multi-dimensional geometry. In: IEEE visualization proceedings of the 1st conference on visualization ’90, pp 361–370

  • Love AL, Pang A, Kao DL (2005) Visualizing spatial multivalue data. IEEE Comput Graphics Appl 25(3):69–79

    Article  Google Scholar 

  • Mihalisin T, Timlin J, Schwegler J (1991) Visualizing multivariate functions, data, and distributions. IEEE Comput Graph Appl 11(3):28–35

    Article  Google Scholar 

  • Miller J, Gavosto EA (2004) The immersive visualization probe for exploring n-dimensional spaces. IEEE Comput Graph Appl :2–11

  • Turney P (1984) Unfolding the tesseract. J Recreat Math 17(1):1–16

    MathSciNet  MATH  Google Scholar 

  • van Wijk J.J., van Liere R. (1993) HyperSlice—visualization of scalar function of many variables. In: Proceeding of the IEEE conference on visualization (Visualization 93), pp 119–125

  • Vos FM, van Gelder RE, Serlie IWO et al (2003) Three-dimensional display modes for CT colonography: Conventional 3D virtual colonoscopy versus unfolded cube projection.. Radiology 228(3):878–885

    Article  Google Scholar 

Download references

Acknowledgments

We thank Wonpil Im from the Center for Bioinformatics from the University of Kansas for providing us with his data (Sect. 5.2) and for meeting us to discuss visualization needs. The Hurricane Isabel data were produced by the Weather Research and Forecast (WRF) model, courtesy of NCAR and the US National Science Foundation. We also wish to thank the anonymous reviewers for their suggestions which led to a much improved paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Estela A. Gavosto

  2. Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, KS, 66045, USA

    James R. Miller

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  1. Estela A. Gavosto
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  2. James R. Miller
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Correspondence to Estela A. Gavosto.

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Gavosto, E.A., Miller, J.R. Visualization of data on unfolded hypercubes. J Vis 16, 85–94 (2013). https://doi.org/10.1007/s12650-012-0148-8

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  • DOI: https://doi.org/10.1007/s12650-012-0148-8

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