Robust polyhedral Minkowski sums with GPU implementation

Min Ho Kyung, Elisha Sacks, Victor Milenkovic

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Article number2332
Pages (from-to)48-57
Number of pages10
JournalCAD Computer Aided Design
StatePublished - Jun 4 2015


  • GPU algorithms
  • Minkowski sums
  • Robust computational geometry

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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