Testing simple polygons

TitleTesting simple polygons
Publication TypeJournal Articles
Year of Publication1997
AuthorsArkin EM, Belleville P, Mitchell JSB, Mount D, Romanik K, Salzberg S, Souvaine D
JournalComputational GeometryComputational Geometry
Type of Article10.1016/S0925-7721(96)00015-6
ISBN Number0925-7721
Keywordsprobing, Testing, Verifying

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.