TY - JOUR
T1 - Testing simple polygons
AU - Arkin, Esther M.
AU - Belleville, Patrice
AU - Mitchell, Joseph S.B.
AU - Mount, David
AU - Romanik, Kathleen
AU - Salzberg, Steven
AU - Souvaine, Diane
N1 - Funding Information:
* Corresponding author. J Partially supported by National Science Foundation Grants ECSE-8857642 and CCR-9204585. 2 Partially supported by Postgraduate and Postdoctoral fellowships from the National Science and Engineering Research Council of Canada. 3 Partially supported by grants from Hughes Research Laboratories, Boeing Computer Services, Air Force Office of Scientific Research contract AFOSR-91-0328, and by National Science Foundation Grants ECSE-8857642 and CCR-9204585. 4 Partially supported by NSF Grants CCR-89-08901 and CCR-93-10705 and by grant JSA 91-5 from the Bureau of the Census. 5 Partially supported by AFOSR Grant F49620-93-1-0039. 6 Supported in part by National Science Foundation Grant IRI-9116843. 7 Supported in part by National Science Foundation Grant CCR-91-04732.
PY - 1997/7
Y1 - 1997/7
N2 - 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.
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.
KW - Probing
KW - Testing
KW - Verifying
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U2 - 10.1016/S0925-7721(96)00015-6
DO - 10.1016/S0925-7721(96)00015-6
M3 - Article
AN - SCOPUS:0343411878
SN - 0925-7721
VL - 8
SP - 97
EP - 114
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 2
ER -