Density-equalizing maps for simply-connected open surfaces

@article{Choi2018DensityequalizingMF,
  title={Density-equalizing maps for simply-connected open surfaces},
  author={Gary Pui-Tung Choi and Chris H. Rycroft},
  journal={ArXiv},
  year={2018},
  volume={abs/1704.02525}
}
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… 

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