An optimal algorithm for the separating common tangents of two polygons

TY - GEN

T1 - An optimal algorithm for the separating common tangents of two polygons

AU - Abrahamsen, Mikkel

N1 - Conference code: 31

PY - 2015/6/1

Y1 - 2015/6/1

N2 - We describe an algorithm for computing the separating common tangents of two simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies to the same side of the line. A separating common tangent of two polygons is a tangent of both polygons where the polygons are lying on different sides of the tangent. Each polygon is given as a read-only array of its corners. If a separating common tangent does not exist, the algorithm reports that. Otherwise, two corners defining a separating common tangent are returned. The algorithm is simple and implies an optimal algorithm for deciding if the convex hulls of two polygons are disjoint or not. This was not known to be possible in linear time and constant workspace prior to this paper. An outer common tangent is a tangent of both polygons where the polygons are on the same side of the tangent. In the case where the convex hulls of the polygons are disjoint, we give an algorithm for computing the outer common tangents in linear time using constant workspace.

AB - We describe an algorithm for computing the separating common tangents of two simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies to the same side of the line. A separating common tangent of two polygons is a tangent of both polygons where the polygons are lying on different sides of the tangent. Each polygon is given as a read-only array of its corners. If a separating common tangent does not exist, the algorithm reports that. Otherwise, two corners defining a separating common tangent are returned. The algorithm is simple and implies an optimal algorithm for deciding if the convex hulls of two polygons are disjoint or not. This was not known to be possible in linear time and constant workspace prior to this paper. An outer common tangent is a tangent of both polygons where the polygons are on the same side of the tangent. In the case where the convex hulls of the polygons are disjoint, we give an algorithm for computing the outer common tangents in linear time using constant workspace.

U2 - 10.4230/LIPIcs.SOCG.2015.198

DO - 10.4230/LIPIcs.SOCG.2015.198

M3 - Conference article

SN - 1868-8969

VL - 34

SP - 198

EP - 208

JO - Leibniz International Proceedings in Informatics

JF - Leibniz International Proceedings in Informatics

T2 - International Symposium on Computational Geometry (SoCG 2015)

Y2 - 22 June 2015 through 25 June 2015

ER -