Testing simple polygons

Esther M. Arkin, Patrice Belleville, Joseph S.B. Mitchell, David Mount, Kathleen Romanik, Steven Salzberg, Diane Souvaine

Research output: Contribution to journalArticle


We consider the problem of verifying a simple polygon in the plane using "test points". A test point is a geometric probe that takes as input a point in Euclidean space, and returns "+" if the point is inside the object being probed or "-" if it is outside. A verification procedure takes as input a description of a target object, including its location and orientation, and it produces a set of test points that are used to verify whether a test object matches the description. We give a procedure for verifying an n-sided, non-degenerate, simple target polygon using 5n test points. This testing strategy works even if the test polygon has n + 1 vertices, and we show a lower bound of 3n + 1 test points for this case. We also give algorithms using O(n) test points for simple polygons that may be degenerate and for test polygons that may have up to n + 2 vertices. All of these algorithms work for polygons with holes. We also discuss extensions of our results to higher dimensions.

Original languageEnglish (US)
Pages (from-to)97-114
Number of pages18
JournalComputational Geometry: Theory and Applications
Issue number2
StatePublished - Jul 1997


  • Probing
  • Testing
  • Verifying

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Fingerprint Dive into the research topics of 'Testing simple polygons'. Together they form a unique fingerprint.

  • Cite this

    Arkin, E. M., Belleville, P., Mitchell, J. S. B., Mount, D., Romanik, K., Salzberg, S., & Souvaine, D. (1997). Testing simple polygons. Computational Geometry: Theory and Applications, 8(2), 97-114. https://doi.org/10.1016/S0925-7721(96)00015-6