Localized geometric query problems

Authors:
John Augustine;Sandip Das;Anil Maheshwari;Sabhas C. Nandy;Sasanka Roy;Swami Sarvattomananda
Affiliations:
Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India;Indian Statistical Institute, Kolkata, India;School of Computer Science, Carleton University, Ottawa, Canada;Indian Statistical Institute, Kolkata, India;Chennai Mathematical Institute, Chennai, India;School of Mathematical Sciences, Ramakrishna Mission Vivekananda University, Belur, India
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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Abstract

A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects P in the plane, so that for any arbitrary query point q, the largest circle that contains q but does not contain any member of P, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.