TY - JOUR
T1 - Testing simple polygons
JF - Computational GeometryComputational Geometry
Y1 - 1997
A1 - Arkin, Esther M.
A1 - Belleville, Patrice
A1 - Mitchell, Joseph S. B.
A1 - Mount, Dave
A1 - Romanik, Kathleen
A1 - Salzberg, Steven
A1 - Souvaine, Diane
KW - probing
KW - Testing
KW - Verifying
AB - 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.
VL - 8
SN - 0925-7721
ER -