Provably Correct Floating-Point Implementation of a Point-in-Polygon Algorithm

  • Mariano M. MoscatoEmail author
  • Laura Titolo
  • Marco A. Feliú
  • César A. MuñozEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11800)


The problem of determining whether or not a point lies inside a given polygon occurs in many applications. In air traffic management concepts, a correct solution to the point-in-polygon problem is critical to geofencing systems for Unmanned Aerial Vehicles and in weather avoidance applications. Many mathematical methods can be used to solve the point-in-polygon problem. Unfortunately, a straightforward floating-point implementation of these methods can lead to incorrect results due to round-off errors. In particular, these errors may cause the control flow of the program to diverge with respect to the ideal real-number algorithm. This divergence potentially results in an incorrect point-in-polygon determination even when the point is far from the edges of the polygon. This paper presents a provably correct implementation of a point-in-polygon method that is based on the computation of the winding number. This implementation is mechanically generated from a source-to-source transformation of the ideal real-number specification of the algorithm. The correctness of this implementation is formally verified within the Frama-C analyzer, where the proof obligations are discharged using the Prototype Verification System (PVS).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Institute of AerospaceHamptonUSA
  2. 2.NASA Langley Research CenterHamptonUSA

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