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Volumetric Density-Equalizing Reference Map with Applications

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Abstract

The density-equalizing map, a technique developed for cartogram creation, has been widely applied to data visualization but only for 2D applications. In this work, we propose a novel method called the volumetric density-equalizing reference map for computing density-equalizing map for volumetric domains. Given a prescribed density distribution in a volumetric domain in \(\mathbb {R}^3\), the proposed method continuously deforms the domain, with different volume elements enlarged or shrunk according to the density distribution. With the aid of the proposed method, medical and sociological data can be visualized via deformations of 3D objects. The method can also be applied to adaptive remeshing and shape modeling. Furthermore, by exploiting the time-dependent nature of the proposed method, applications to shape morphing can be easily achieved. Experimental results are presented to demonstrate the effectiveness of the proposed method.

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The data are available from the corresponding author on request.

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Acknowledgements

This work was supported in part by the Croucher Foundation (to G. P. T. Choi), the Harvard Quantitative Biology Initiative and the NSF-Simons Center for Mathematical and Statistical Analysis of Biology at Harvard, Award Number #1764269 (to G. P. T. Choi), and the Applied Mathematics Program of the U.S. Department of Energy (DOE) Office of Science Advanced Scientific Computing Research under contract DE-AC02-05CH11231 (to C. H. Rycroft). We thank Dr. Anselm Hui (Prince of Wales Hospital) for useful discussion on medical data visualization.

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Authors and Affiliations

  1. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

    Gary P. T. Choi & Chris H. Rycroft

  2. Mathematics Group, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Chris H. Rycroft

Authors
  1. Gary P. T. Choi
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  2. Chris H. Rycroft
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Correspondence to Gary P. T. Choi.

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Choi, G.P.T., Rycroft, C.H. Volumetric Density-Equalizing Reference Map with Applications. J Sci Comput 86, 41 (2021). https://doi.org/10.1007/s10915-021-01411-4

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  • DOI: https://doi.org/10.1007/s10915-021-01411-4

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