Robust cascading of operations on polyhedra

Elisha Sacks, Victor Milenkovic

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.

Original languageEnglish (US)
Pages (from-to)216-220
Number of pages5
JournalCAD Computer Aided Design
Issue number1
StatePublished - 2014


  • Geometric rounding
  • Robust computational geometry

ASJC Scopus subject areas

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


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