@article {521036, title = {Density-Equalizing Maps for Simply Connected Open Surfaces}, journal = {SIAM Journal on Imaging Sciences}, volume = {11}, number = {2}, year = {2018}, pages = {1134-1178}, abstract = {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 flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings 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.}, url = {https://doi.org/10.1137/17m1124796}, author = {Gary P. T. Choi and Chris H. Rycroft} }