# Density-equalizing maps for simply-connected open surfaces

arXiv: https://arxiv.org/abs/1704.02525 · HTML: https://mlsanity.com/paper/1704.02525/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2017.

## Built on by (most cited first, 6 of 6)

- [A unifying framework for n-dimensional quasi-conformal mappings](https://mlsanity.com/paper/2110.10437/) (2021)
- [Learning-based density-equalizing map](https://mlsanity.com/paper/2506.10027/) (2025)
- [Free-Boundary Quasiconformal Maps via a Least-squares Operator in Diffeomorphism Optimization](https://mlsanity.com/paper/2511.11679/) (2025)
- [Adaptive area-preserving parameterization of open and closed anatomical surfaces](https://mlsanity.com/paper/2111.04265/) (2021)
- [Resolution-free neural surrogates for geometric parameterization and mapping with spatially varying fields](https://mlsanity.com/paper/2605.28551/) (2026)
- [Learning Task-Aware Sampling with Shared Saliency through Density-Equalizing Mappings](https://mlsanity.com/paper/2606.12869/) (2026)

## Abstract (arXiv)

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in ℝ3. 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.