Planar shape manipulation using approximate geometric primitives

Victor Milenkovic, Elisha Sacks, Steven Trac

Research output: Contribution to journalArticlepeer-review


We present robust algorithms for set operations and affine transformations on curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is O(n log n + k) for an input of size n with k = O(n2) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms using sequences of six set operations and affine transforms on shapes bounded by algebraic curve segments of degree 1 to 6. We test generic and degenerate inputs.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalInternational Journal of Computational Geometry and Applications
Issue number1
StatePublished - Feb 2013


  • Robust computational geometry
  • planar shape manipulation
  • set operations
  • snap rounding

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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