Planar shape manipulation using approximate geometric primitives

Victor Milenkovic, Elisha Sacks, Steven Trac

Research output: Contribution to journalArticle

Abstract

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
Volume23
Issue number1
DOIs
StatePublished - Feb 2013

Fingerprint

Manipulation
Robust Algorithm
Algebraic curve
Affine transforms
Affine transformation
Computational Complexity
Refinement
Transform
Output
Computational complexity

Keywords

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

ASJC Scopus subject areas

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

Cite this

Planar shape manipulation using approximate geometric primitives. / Milenkovic, Victor; Sacks, Elisha; Trac, Steven.

In: International Journal of Computational Geometry and Applications, Vol. 23, No. 1, 02.2013, p. 1-27.

Research output: Contribution to journalArticle

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