Effcient Collision Detection for Animation and Robotics potx

[...]... obstacles before an actual collision occurs Similarly, in computer animation, interactions among objects are simulated by modeling the contact constraints and impact dynamics Since prompt recognition of possible impacts is a key to successful response to collisions in a timely fashion, a simple yet e cient algorithm for collision detection is important for fast and realistic animation and simulation... computing the interaction forces and other penalty functions in motion planning Collision detection is usually coupled with an appropriate response to the collision The collision response is generally application dependent and many algorithms have been proposed for di erent environments like motion control in animation by Moore and Wilhelm 63 , physical simulations by Bara , Hahn, Pentland and Williams 3, 43,... necessary for computer animation; while others do not easily produce the exact collision points and contact normal direction for collision response 34 In one of the earlier animation papers addressing the issue of collision detection, Moore and Wilhelms 63 mentioned the method based on the Cyrus-Beck clipping algorithm 74 , which provides a simple, robust alternative but runs in On m  time for m polyhedra... with respect to the origin The collision detection algorithm is based only on local features of the polyhedra or control polytope of spline patches and does not require the position of the other features to be updated for the purpose of collision detection at every instant 19 2.2.2 System of Algebraic Equations Our algorithm for collision detection for algebraic surface formulates the problem of nding... Assume A and B are closed and bounded, therefore, compact The distance between objects A and B is the shortest Euclidean distance dAB : 2 3 dAB = p2A;q2B j p , q j inf and let PA 2 A, PB 2 B be such that dAB =j PA , PB j then PA and PB are a pair of closest points between objects A and B For each pair of features fA and fB  from objects A and B, rst we nd the pair of nearest points say PA and PB... technique can be used for dynamic collision detection, physical simulation, planning in three-dimensional space, and other robotics problems It forms the heart of the motion planning algorithm described in Chapter 6 In Chapter 4, we will discuss how we can use the incremental distance computation algorithm in Chapter 3 for dynamic collision detection between non-convex polytopes and objects with curved... reality applications and it has been extensively studied in robotics, computational geometry, and computer graphics for more than a decade 3, 4, 11, 13, 17, 41, 43, 45, 51, 53, 63 Yet, there is no practical, e cient algorithm available yet for general geometric models to perform collision detection in real time Recently, Pentland has listed collision detection as one of the major bottlenecks towards real... modeling by Turk 85 Since simplicity and ease of implementation is considered as one of the important factors for any practical algorithm in the computer graphics community, most collision detection algorithms used for computer animation are rather simple but not necessary e cient The simplest algorithms for collision detection are based upon using bounding volumes and spatial decomposition techniques... information which is needed in path planning for robots The static collision detection problem is often studied and then later extended to a dynamic environment However, the choice of step size can easily a ect the outcome of the dynamic algorithms If the position and orientation of the objects is known in advance, the collision detection can be solved as a function of time A related problem to collision. .. resulting space and can therefore be slow A similar method using interval arithmetic and subdivision has been presented for collision detection by Du 29 Du has extended it to dynamic environments as well However, for commonly used spline patches computing and representing the implicit representations is computationally expensive as stated by Ho mann 46 Both algorithms, 29, 46 , expect a closed form expression