Collision Detection. Pu Jiantao.
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1 Collision Detection Pu Jiantao
2 Content Introduction CD with rays Dynamic CD using BSP Trees Hierarchical Method OBBTree Method Some Other Topics
3 Introduction Collision Collision is a fundamental task in virtual reality: (1) Haptic rendering (force-- --feedback); (2) Physically-based simulation; (3) Virtual training ( Medical, drivers ); (4) Robot technique; (5) Computer games
4 Introduction Three Topics Related to Collision: (1) Collision detection (2) Collision determination (3) Collision response
5 Introduction Good CD Algorithms should satisfy: (1) Interactive rate for large-scale scene; (2) No requirement of geometric shape; (3) Applied for dynamic scene; (4) Fast creation of bounding box;
6 Introduction Different kinds of colliding bodies: Three levels of difficulity: (1) Convex rigid bodies; (2) General rigid bodies; (3) Deformable bodies;
7 Introduction If the scenario contains n moving objects and m static objects, the number of test needed done is : n nm
8 Introduction Strategies: (1) Spatial partitioning; (2) Multiphase algorithms; (3) Categorize objects (static, dynamic..);
9 Multi-phase detection strategy Detect possible collision between objects: ie,, Cull things which can not collide Detect colliding surfaces and determine point of contact
10 Multi-phase detection strategy Bounding volumes
11 Rays Method Approximate an object with a set of rays
12 Dynamic CD using BSP Trees Determine collisions between the geometry described by a BSP tree and a collider
13 Dynamic CD using BSP Trees A sphere does not approximate a character in a game very well, while cylinder does to some extend
14 Dynamic CD using BSP Trees e = n ( t p ) o
15 Dynamic CD using BSP Trees Pseudo code Pseudo code for finding the impact poin by traversing BSP tree. Check if empty or not in the BSP tree Shifting the dividing plane of BSP tree to find correct impact point. Potential inaccuracy and beveling
16 Dynamic CD using BSP Trees Inaccuracies can occur using this method. The right sphere collides correctly, while the left sphere detects a collision too early. To the right, this is solved by introducing an extra bevel plane
17 Features. Hierarchical Method Interactive rates with models consisting of a large number of polygons, both when far away and close together Handling polygon soup. Possible to undergo rigid-body motion Efficient BV fitting
18 Hierarchical Method Hierarchy Building Bottom-up (BOXTREE) Top-down (divide and conquer) Incremental tree-insertion
19 Hierarchical Method Evaluating the performance of CD algorithms t = n v c v + n p c p + n u c u Where n v : number of BV/BV overlap tests c v : cost for a BV/BV overlap test n p : number of primitive pairs tested for overlap c p : cost for testing whether two primitives overlap n u : number of BVs updated due to the model s s motion c u : cost for updating a BV Better hierarchical decomposition of model : Lower value of n v, n p, n u Better methods for determining whether two things overlaps Lower value of c, c
20 OBBTree Method At siggraph 96, Gottschalk et al. presented a paper called OBBTree:: A Hierarchical Structure for Rapid Interference Detection
21 Why OBBTree? OBBTree Method OBBTree: A tight-fitting hierarchical structure and an efficient overlap-testing algorithm for interference detection amongst complex models undergoing rigid motion
22 Overlap Test OBBTree Method
23 OBBTree Method Hierarchical Building Building the OBBTree: Recursively partition the bounded polygons and bound the resulting groups
24 Some Other Topics Front Tracking It uses temporal coherence for speeding up collision queries
25 Some Other Topics Time-Critical Collision Detection The detection task must be finished in a certain time
26 Some Other Topics Distance Query To the left, two convex objects A and B are shown. To construct A- B, first move A and B so that one reference point is at origin. Then B is reflected, as shown in the middle, and the chosen reference point on B is put on the surface of A and then the reflected B is swept around A. In this way, A-B is created
27 Some Other Topics Distance Query (cont.) GTK Algorithm
28 Some Other Topics Deformed Objects Obviously, there are other sorts of motion, such as waves on the water or a piece of cloth swaying in the wind. The hybrid bottom-up/top-down tree update method
29 Some Other Topics Collision Response Collision response for a sphere approaching a plane. To the left the velocity vector V is divided into two components, Vn and Vp. To the right, pergectly elastic collision is shown, where the new velocity is V =Vp-Vn. For a less elastic collision, the length of Vn could be decreased
30 The End
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