# A tetrahedral space-filling curve for non-conforming adaptive meshes

arXiv: https://arxiv.org/abs/1509.04627 · HTML: https://mlsanity.com/paper/1509.04627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid](https://mlsanity.com/paper/2511.16273/) (2025)

## Abstract (arXiv)

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neighbors of a mesh element in constant time, as well as the next and previous element in the space-filling curve and whether a given element is on the boundary of the root simplex or not. Our presentation concludes with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.