Robust free space construction for a polyhedron with planar motion

Elisha Sacks, Nabeel Butt, Victor Milenkovic

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We present a free space construction algorithm for a polyhedron that translates in the xy plane and rotates around its z axis, relative to a stationary polyhedron. We employ the proven paradigm of constructing the configuration space subdivision defined by patches that comprise the configurations where the boundary features of the polyhedra are in contact. We implement the algorithm robustly and efficiently. The challenge is to detect degenerate predicates efficiently and to handle them correctly. We use our ACP (Adaptive Controlled Perturbation) robustness strategy to prevent degenerate predicates due to input in special position. The remaining cases are predicates that are identical to the zero polynomial because their arguments are derived from overlapping sets of input vertices. We detect and handle these cases with custom logic. We validate the implementation by computing maximum clearance paths.

Original languageEnglish (US)
Pages (from-to)18-26
Number of pages9
JournalCAD Computer Aided Design
StatePublished - Sep 2017


  • Configuration space
  • Path planning
  • Robust computational geometry

ASJC Scopus subject areas

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


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