Kinetic Collision Detection for Disks and Spheres

Please enable javascript in your browser.

Alimizaei, Pouria | 2013

1135 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44862 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Abam, Mohammad Ali
Abstract:
Motion is an impartible component of our physical environment and the most obvious consequence of motion is collision. Diverse applications of collision detection algorithms in various real world simulated environments have led to numerous solutions to this problem from different aspects of computer science. Within computational geometry, kinetic data structure is the well-known framework to detect collisions of moving objects.This thesis will look into the problem of collision detection for a number of disjoint disks moving freely in 2D plane. To this end, we will provide a kinetic data structure (KDS) that uses O(n) storage and under the assumption of pseudo algebraic motion plans, processes O(n^2 ) events in the worst case. Each event can be handled in O(log⁡n ) time. We will also propose a KDS for collision detection between spheres which has size O(n log^3⁡n), processes O(n^2) events in the worst case but the time to process each event is O(log^4⁡n)
Keywords:
Computational Geometry ; Kinetic Data Structure ; Collision Detection ; Disjoint Disks ; Disjoint Spheres