Density-Equalizing Maps for Simply-Connected Open Surfaces


G. P. T. Choi and C. H. Rycroft, “Density-Equalizing Maps for Simply-Connected Open Surfaces,” Submitted.
Density-Equalizing Maps for Simply-Connected Open Surfaces


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.