### Abstract

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 language | English (US) |
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Pages (from-to) | 97-114 |

Number of pages | 18 |

Journal | Computational Geometry: Theory and Applications |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1997 |

### Keywords

- Probing
- Testing
- Verifying

### ASJC Scopus subject areas

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

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## Cite this

*Computational Geometry: Theory and Applications*,

*8*(2), 97-114. https://doi.org/10.1016/S0925-7721(96)00015-6