Circle shooting in a simple polygon

Pankaj K. Agarwal, Micha Sharir

Research output: Contribution to journalArticlepeer-review


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)).

Original languageEnglish
Pages (from-to)69-87
Number of pages19
JournalJournal of Algorithms
Issue number1
StatePublished - Jan 1993


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