  We propose the first GPU algorithm for the 3D triangulation refinement
problem. For an input of a piecewise linear complex $\mathcal{G}$ and a
constant $B$, it produces, by adding Steiner points, a constrained Delaunay
triangulation conforming to $\mathcal{G}$ and containing tetrahedra mostly of
radius-edge ratios smaller than $B$. Our implementation of the algorithm shows
that it can be an order of magnitude faster than the best CPU algorithm while
using a similar amount of Steiner points to produce triangulations of
comparable quality.
