  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.
