# Computing Three-dimensional Constrained Delaunay Refinement Using the GPU

## TL;DR

This paper introduces the first GPU-based algorithm for 3D constrained Delaunay refinement, significantly accelerating the process while maintaining triangulation quality comparable to CPU methods.

## Contribution

It presents a novel GPU algorithm for 3D triangulation refinement that outperforms existing CPU algorithms in speed with similar quality.

## Key findings

- GPU algorithm is an order of magnitude faster than CPU algorithms
- Produces triangulations with similar Steiner point count and quality
- Effective for complex 3D geometries

## Abstract

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.