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Methods for Searching Mutual Visible Intervals on Moving Objects

Workshop in Dhaka introduces MVI-tree and MVI-list to efficiently find mutual visible intervals between moving convex polygons. The goal is to determine mutual visibility among moving objects at any time, tackling problems like searching and constructing data structures. Evaluation shows that MVI-tree method outperforms the naive algorithm.

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Methods for Searching Mutual Visible Intervals on Moving Objects

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  1. Methods for Searching Mutual Visible Intervals on Moving Objects 2007.Feb.12 Y.Kusakari,Y.Sugimoto,J.Notoya,M.Kasai Akita Prefectural University Workshop in Dhaka

  2. Introduction Problems Data Structures Mutual visible Intervals Search Tree（MVI-tree） Mutual visible Intervals Search List（MVI-list） Conclusion Future Works Contents Workshop in Dhaka

  3. Mutual Visibility of Moving objects. A person and a car are Mutual visible. A person and a car are not Mutual visible. Workshop in Dhaka

  4. Motivation：RoboCup • Simulation League： Succor Field：2D Euclidean Space. Player：Convex region • Pass succeed iff the sender can see the receiver ( iff the Mutual visibility exists). • Player moves depending on the time. Find the “mutual visible intervals” between moving objects efficiently. Workshop in Dhaka

  5. RoboCup （Simulation League） Figure Overview of the field. Workshop in Dhaka

  6. Mutual Visible Intervals of two Moving Convex polygons Input:Two convex polygons velocity representative point Mutual Visible-Intervals： Workshop in Dhaka

  7. Mutual Visible Intervals for various times. Workshop in Dhaka

  8. Finding the Mutual visible intervals for two moving convex polygons at any time. Two methods(data structures) Mutual Visible Intervals search tree（MVI-tree） Mutual Visible Intervals search list（MVI-list） Goal Workshop in Dhaka

  9. Problem1:Finding MVI ：# of vertices INPUT： Initial configuration Velocities Query time OUTPUT： Workshop in Dhaka

  10. Naïve algorithm INPUT： 1.Calculate the configuration at time . Initial configuration 2. Find two iso-common tangents. Velocities Query time OUTPUT： Workshop in Dhaka

  11. Naïve algorithm Workshop in Dhaka

  12. Problem2:Searching MVI ：# of vertices INPUT： ：# of searching Initial configuration Velocities Sequence of query times OUTPUT： Sequence of MVIs. Workshop in Dhaka

  13. Naïve algorithm ：# of searching INPUT： For each time , Initial configuration 1.Calculate the configuration at time . Velocities 2.Find iso-common tangent of . Sequence of query times Repeat times. OUTPUT： Workshop in Dhaka

  14. Data Structure Outline of Our Method ：# of searching INPUT： Initial configuration AlgorithA (construct) Algorithm B (query) Velocities Sequence of query times Repeat times. OUTPUT： Workshop in Dhaka

  15. Introduction Problems Data Structures Mutual visible Intervals Search Tree（MVI-tree） Mutual visible Intervals Search List（MVI-list） Conclusion Future Works Contents Workshop in Dhaka

  16. MVI-tree Mutual Visible-Intervals search tree ：# of vertices Balanced Tree time ・・・ ・・・ ・・・ ・・・ : a changing time when MVI changes Workshop in Dhaka

  17. Changing MVI Moving object Straight line Static object Workshop in Dhaka

  18. Workshop in Dhaka

  19. Workshop in Dhaka

  20. Extension and MVI Position of Representative Point The moving object touches an extension of an edge of . Workshop in Dhaka

  21. Positions of representative points Transform from positions of representative points to changing times. Workshop in Dhaka

  22. Searching MVI using MVI-tree A root- leaf path. Balanced Tree Time ・・・ ・・・ ・・・ ・・・ : a changing time ：# of vertices Workshop in Dhaka

  23. :# of vertices :# of searching Time Complexity • Naïve algorithm • Searching an MVI sequence • MVI-tree Method • Constructing an MVI-tree • Searching an MVI sequence Workshop in Dhaka

  24. Experimental result（F=1） Workshop in Dhaka

  25. Experimental result（F=100） Workshop in Dhaka

  26. The number of searching ：Constructing MVI-tree ：Finding MVI using MVI-tree ：The naïve method Fmin Workshop in Dhaka

  27. MVI-tree method is superior to the naïve method if . Evaluation of MVI-tree Workshop in Dhaka

  28. Introduction Problems Data Structures Mutual visible Intervals Search Tree（MVI-tree） Mutual visible Intervals Search List（MVI-list） Conclusion Future Works Contents Workshop in Dhaka

  29. P-list(one of MVI-list) -The vertex list of polygon is given counterclockwise -Vertices becomes terminal p as the same order. Workshop in Dhaka

  30. Constructing MVI-list • P-list(one of the MVI-list): • A sequence of pairs . This sequence is automatically sorted as the time. : a changing time when p changes. : a vertex as in . Workshop in Dhaka

  31. Searching MVI using MVI-list • Using binary search algorithm onMVI-lists. Workshop in Dhaka

  32. :# of vertices :# of searching Time Complexity • Naïve algorithm • Searching a sequence of MVIs • MVI-tree • Constructing MVI-tree • Searching a sequence of MVIs • MVI-list • Constructing MVI-list • Searching a sequence of MVIs Workshop in Dhaka

  33. Experimental result（F=1) Constructing MVI-list Searching MVI using MVI-ist The naïve algorithm Time (s) # of vertices Workshop in Dhaka

  34. Experimental result（F=10) Constructing MVI-list Searching MVIs using MVI-list The naïve algorithm Time (s) # of vertices Workshop in Dhaka

  35. The number of searching Fmin ：Constructing MVI-list ：Finding MVI using MVI-list ：Finding MVI using naïve method # of vertices Workshop in Dhaka

  36. Evaluation MVI-list • MVI-list method is superior to naïve method if . Cf. MVI-tree Workshop in Dhaka

  37. Conclusion • Two Methods for searching MVIs are presented. • MVI-tree method take time . • MVI-list method take time . • By experimental results, MVI-list method is superior to MVI-tree method in time. Workshop in Dhaka

  38. Future works • Mutual visibility of 3 or more Moving objects. • Mutual visible region of Convex polytops in 3 D. • Extended the motion: • Accelerated motion; • Rotational motion; • … Workshop in Dhaka

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