Abstract We present a Minkowski sum algorithm for polyhedra based on convolution. We develop robust CPU and GPU implementations, using our ACP strategy to eliminate degeneracy and to enforce a user-specified backward error bound. We test the programs on 45 inputs with an error bound of 10-8. The CPU program outperforms prior work, including non-robust programs. The GPU program using 2688 CUDA cores exhibits a median speedup factor of 36, which increases to 68 on the 6 hardest tests. For example, it computes a Minkowski sum with a million features in 20 seconds.
- GPU algorithms
- Minkowski sums
- Robust computational geometry
ASJC Scopus subject areas
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering