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Visibility Algorithms in the Plane
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  • Cited by 71
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Sitchinava, Nodari and Strash, Darren 2018. Graph Drawing and Network Visualization. Vol. 10692, Issue. , p. 88.

    Ashok, Pradeesha Fomin, Fedor V. Kolay, Sudeshna Saurabh, Saket and Zehavi, Meirav 2018. Exact Algorithms for Terrain Guarding. ACM Transactions on Algorithms, Vol. 14, Issue. 2, p. 1.

    Nouri Bygi, M. and Ghodsi, M. 2018. Weak visibility queries of line segments in simple polygons and polygonal domains. International Journal of Computer Mathematics, Vol. 95, Issue. 4, p. 721.

    Cleve, Jonas and Mulzer, Wolfgang 2018. LATIN 2018: Theoretical Informatics. Vol. 10807, Issue. , p. 346.

    Altahir, Altahir Abdalla Asirvadam, Vijanth Sagayan Hamid, Nor Hisham B. Sebastian, Patrick Saad, Nordin B. Ibrahim, Rosdiazli B. and Dass, Sarat C. 2018. Optimizing Visual Sensor Coverage Overlaps for Multiview Surveillance Systems. IEEE Sensors Journal, Vol. 18, Issue. 11, p. 4544.

    Sheshkalani, Ali Narenji and Khosravi, Ramtin 2018. Verification of visibility-based properties on multiple moving robots in an environment with obstacles. International Journal of Advanced Robotic Systems, Vol. 15, Issue. 4, p. 172988141878665.

    Toll, Wouter Van Iv, Atlas F. Cook Kreveld, Marc J. Van and Geraerts, Roland 2018. The Medial Axis of a Multi-Layered Environment and Its Application as a Navigation Mesh. ACM Transactions on Spatial Algorithms and Systems, Vol. 4, Issue. 1, p. 1.

    Maheshwari, Anil Nandy, Subhas C. Pattanayak, Drimit Roy, Sasanka and Smid, Michiel 2018. Geometric Path Problems with Violations. Algorithmica, Vol. 80, Issue. 2, p. 448.

    Banyassady, Bahareh Korman, Matias and Mulzer, Wolfgang 2018. Computational Geometry Column 67. ACM SIGACT News, Vol. 49, Issue. 2, p. 77.

    Saha, Sourav Mandal, Ankita Sheth, Paras Narnoli, Harshita and Mahapatra, Priya  Ranjan  Sinha  2017. Computational Intelligence, Communications, and Business Analytics. Vol. 776, Issue. , p. 284.

    Inkulu, R. and Thakur, Nitish P. 2017. Algorithms and Discrete Applied Mathematics. Vol. 10156, Issue. , p. 205.

    Toan, Tran Quoc Sorokin, A. A. and Trang, Vo Thi Huyen 2017. Using modification of visibility-graph in solving the problem of finding shortest path for robot. p. 1.

    Emadi, Hamid Gao, Tianshuang and Bhattacharya, Sourabh 2017. Visibility-Based Target-Tracking Game: Bounds and Tracking Strategies. IEEE Robotics and Automation Letters, Vol. 2, Issue. 4, p. 1917.

    Bahoo, Yeganeh Banyassady, Bahareh Bose, Prosenjit Durocher, Stephane and Mulzer, Wolfgang 2017. WALCOM: Algorithms and Computation. Vol. 10167, Issue. , p. 308.

    Diwan, Ajit Arvind and Roy, Bodhayan 2017. Algorithms and Discrete Applied Mathematics. Vol. 10156, Issue. , p. 156.

    Sheshkalani, Ali Narenji Khosravi, Ramtin and Mohammadi, Mayssam 2017. Towards Autonomous Robotic Systems. Vol. 10454, Issue. , p. 51.

    Altahir, Altahir Abdalla Asirvadam, Vijanth Sagayan Hamid, Nor Hisham B. Sebastian, Patrick Saad, Nordin B. Ibrahim, Rosdiazli B. and Dass, Sarat C. 2017. Optimizing Visual Surveillance Sensor Coverage Using Dynamic Programming. IEEE Sensors Journal, Vol. 17, Issue. 11, p. 3398.

    Aichholzer, Oswin Kusters, Vincent Mulzer, Wolfgang Pilz, Alexander and Wettstein, Manuel 2017. An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings. International Journal of Computational Geometry & Applications, Vol. 27, Issue. 01n02, p. 57.

    Cardinal, Jean and Hoffmann, Udo 2017. Recognition and Complexity of Point Visibility Graphs. Discrete & Computational Geometry, Vol. 57, Issue. 1, p. 164.

    Fox-Epstein, Eli Tóth, Csaba D. and Winslow, Andrew 2016. Diffuse Reflection Radius in a Simple Polygon. Algorithmica, Vol. 76, Issue. 4, p. 910.


Book description

A human observer can effortlessly identify visible portions of geometric objects present in the environment. However, computations of visible portions of objects from a viewpoint involving thousands of objects is a time consuming task even for high speed computers. To solve such visibility problems, efficient algorithms have been designed. This book presents some of these visibility algorithms in two dimensions. Specifically, basic algorithms for point visibility, weak visibility, shortest paths, visibility graphs, link paths and visibility queries are all discussed. Several geometric properties are also established through lemmas and theorems. With over 300 figures and hundreds of exercises, this book is ideal for graduate students and researchers in the field of computational geometry. It will also be useful as a reference for researchers working in algorithms, robotics, computer graphics and geometric graph theory, and some algorithms from the book can be used in a first course in computational geometry.


'… the book gives a good overview of visibility algorithms in the plane, concentrating on basic algorithms but also covering the state of the art.'

Source: Mathematical Reviews

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