# Data-Driven Space-Filling Curves

arXiv: https://arxiv.org/abs/2009.06309 · HTML: https://mlsanity.com/paper/2009.06309/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Analogous to Evolutionary Algorithm: Designing a Unified Sequence Model](https://mlsanity.com/paper/2105.15089/) (2021)
- [Neural Space-filling Curves](https://mlsanity.com/paper/2204.08453/) (2022)
- [Versatile Ordering Network: An Attention-based Neural Network for Ordering Across Scales and Quality Metrics](https://mlsanity.com/paper/2412.12759/) (2024)

## Abstract (arXiv)

We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to existing methods. We achieve such data coherency by calculating a Hamiltonian path that approximately minimizes an objective function that describes the similarity of data values and location coherency in a neighborhood. Our extended variant even supports multiscale data via quadtrees and octrees. Our method is useful in many areas of visualization, including multivariate or comparative visualization, ensemble visualization of 2D and 3D data on regular grids, or multiscale visual analysis of particle simulations. The effectiveness of our method is evaluated with numerical comparisons to existing techniques and through examples of ensemble and multivariate datasets.