TY - JOUR

T1 - Circle shooting in a simple polygon

AU - Agarwal, Pankaj K.

AU - Sharir, Micha

PY - 1993/1

Y1 - 1993/1

N2 - Consider the following problem: Given a simple n-gon P, preprocess it so that for a query circle π and a point s on π, one can quickly compute Φ(P, π, s), the first intersection point between P and π as we follow π from s in clockwise direction. We show that P can be preprocessed, in time O(n log3n), into a data structure of size O(n log3n), so that, for a query circle π, Φ(P, π, s) can be computed in O(log4n) time. We apply the circle shooting algorithm to report all K intersections between a set of m circular arcs and another set of n circular arcs in time O((m√n + n√m)log2.5(m + n) + (K + m + n)log4(m + n)).

AB - Consider the following problem: Given a simple n-gon P, preprocess it so that for a query circle π and a point s on π, one can quickly compute Φ(P, π, s), the first intersection point between P and π as we follow π from s in clockwise direction. We show that P can be preprocessed, in time O(n log3n), into a data structure of size O(n log3n), so that, for a query circle π, Φ(P, π, s) can be computed in O(log4n) time. We apply the circle shooting algorithm to report all K intersections between a set of m circular arcs and another set of n circular arcs in time O((m√n + n√m)log2.5(m + n) + (K + m + n)log4(m + n)).

UR - http://www.scopus.com/inward/record.url?scp=0003500940&partnerID=8YFLogxK

U2 - 10.1006/jagm.1993.1004

DO - 10.1006/jagm.1993.1004

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AN - SCOPUS:0003500940

SN - 0196-6774

VL - 14

SP - 69

EP - 87

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 1

ER -