Density-equalizing maps for simply-connected open surfaces
For researchers in geometry processing and visualization, this provides a flexible method for surface flattening with controlled density, though it is an incremental extension of existing density-equalizing map techniques.
The paper proposes a density diffusion-based algorithm for flattening simply-connected open surfaces, enabling area-preserving parameterizations and other mappings with prescribed density distributions. Experiments demonstrate effectiveness for data visualization and surface remeshing.
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.