# Density-equalizing maps for simply-connected open surfaces

## TL;DR

This paper introduces a novel algorithm for creating flattening maps of simply-connected open surfaces in 3D, utilizing density diffusion principles to achieve various properties like area preservation, with applications in visualization and remeshing.

## Contribution

The paper presents a new density diffusion-based method for generating customizable flattening maps of open surfaces, enabling diverse mapping properties.

## Key findings

- Effective density-equalizing flattening maps produced
- Versatile mappings achieved by varying initial density
- Applications demonstrated in visualization and remeshing

## 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.