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Title: Density-Equalizing Maps for Simply Connected Open Surfaces

Abstract

Here in this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in $$\mathbb{R}^3$$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

Authors:
 [1];  [2]
  1. Harvard Univ., Cambridge, MA (United States). Paulson School of Engineering and Applied Sciences
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1525278
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Imaging Sciences
Additional Journal Information:
Journal Volume: 11; Journal Issue: 2; Journal ID: ISSN 1936-4954
Publisher:
Society for Industrial and Applied Mathematics
Country of Publication:
United States
Language:
English

Citation Formats

Choi, Gary P. T., and Rycroft, Chris H. Density-Equalizing Maps for Simply Connected Open Surfaces. United States: N. p., 2018. Web. doi:10.1137/17M1124796.
Choi, Gary P. T., & Rycroft, Chris H. Density-Equalizing Maps for Simply Connected Open Surfaces. United States. doi:10.1137/17M1124796.
Choi, Gary P. T., and Rycroft, Chris H. Mon . "Density-Equalizing Maps for Simply Connected Open Surfaces". United States. doi:10.1137/17M1124796. https://www.osti.gov/servlets/purl/1525278.
@article{osti_1525278,
title = {Density-Equalizing Maps for Simply Connected Open Surfaces},
author = {Choi, Gary P. T. and Rycroft, Chris H.},
abstractNote = {Here in this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.},
doi = {10.1137/17M1124796},
journal = {SIAM Journal on Imaging Sciences},
number = 2,
volume = 11,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
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