Let B be a set of n unit balls in R3. We present a linear-size data structure for storing B that can determine in (Equation presented) time whether a query line intersects any ball of B and report all k such balls in additional O(k) time. The data structure can be constructed in O(n log n) time. (The O∗(·) notation hides subpolynomial factors, e.g., of the form O(nε), for arbitrarily small ε > 0, and their coefficients which depend on ε.) We also consider the dual problem: Let L be a set of n lines in R3. We preprocess L, in O∗(n2) time, into a data structure of size O∗(n2) that can determine in O∗(1) time whether a query unit ball intersects any line of L, or report all k such lines in additional O(k) time.
|Title of host publication||39th International Symposium on Computational Geometry, SoCG 2023|
|Editors||Erin W. Chambers, Joachim Gudmundsson|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - 1 Jun 2023|
|Event||39th International Symposium on Computational Geometry, SoCG 2023 - Dallas, United States|
Duration: 12 Jun 2023 → 15 Jun 2023
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||39th International Symposium on Computational Geometry, SoCG 2023|
|Period||12/06/23 → 15/06/23|
Bibliographical notePublisher Copyright:
© Pankaj K. Agarwal and Esther Ezra; licensed under Creative Commons License CC-BY 4.0.
- Intersection searching
- cylindrical range searching
- partition trees
- union of cylinders