# Fast Tetrahedral Meshing in the Wild

## TL;DR

The paper introduces fTetWild, a fast and robust tetrahedral meshing algorithm that converts triangle soups into high-quality meshes using floating-point arithmetic, improving speed and validity guarantees over previous methods.

## Contribution

fTetWild replaces rational triangle insertion with an incremental approach, enabling faster processing and guaranteed validity of tetrahedral meshes with floating-point coordinates.

## Key findings

- Significantly faster than previous methods
- Guarantees valid tetrahedral meshes with floating-point coordinates
- Successfully inserts all input triangles in practical tests

## Abstract

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach makes it possible to maintain a valid floating-point tetrahedral mesh at all algorithmic stages, eliminating the need for costly constructions with rational numbers used by TetWild, while maintaining full robustness and similar output quality. This allows us to improve on TetWild in two ways. First, our algorithm is significantly faster, with running time comparable to less robust Delaunay-based tetrahedralization algorithms. Second, our algorithm is guaranteed to produce a valid tetrahedral mesh with floating-point vertex coordinates, while TetWild produces a valid mesh with rational coordinates which is not guaranteed to be valid after floating-point conversion. As a trade-off, our algorithm no longer guarantees that all input triangles are present in the output mesh, but in practice, as confirmed by our tests on the Thingi10k dataset, the algorithm always succeeds in inserting all input triangles.