C lli i Collision Detection D t ti Sung-Eui Yoon ( ) ( ) C - PowerPoint PPT Presentation

C lli i Collision Detection D t ti Sung-Eui Yoon ( 윤성의 ) ( 윤성의 ) C Course URL: URL http://jupiter.kaist.ac.kr/~sungeui/SGA/

Course Administration Course Administration ● Make progresses on your chosen topic Make progresses on your chosen topic ● Write down toward the mid-term report, whose deadline is Nov-6 deadline is Nov-6 ● Presentation schedule 2

Proximity Queries Proximity Queries ● Collision detection Collision detection ● Checks whether there is collision between objects collision between objects ● Reports colliding primitives if any y Colliding primitives C llidi i i i ● Minimum separation p distance ● Compute a minimum di t distance between two b t t objects and report primitives realizing the distance realizing the distance 3

Collision Detection Collision Detection ● Main component of: Main component of: ● Dynamic simulation for game & movies ● Navigation and path planning ● Navigation and path planning ● Virtual prototyping 4

Time Complexity Time Complexity ● Naïve method between two objects Naïve method between two objects ● O(n * m), where n and m are # of triangles of two objects two objects ● Can be very slow even for small models ● Can we do better? ● Employ culling techniques Employ culling techniques 5

Hierarchical Representations Hierarchical Representations ● Bounding volumes Bounding volumes ● A proxy containing primitives ● Should be tight and easy to ● Should be tight and easy to check for collision ● Provide culling Provide culling ● Recursively represent models ● Provide hierarchical culling Provide hierarchical culling ● Object partitioning hierarchies or space partitioning hierarchies 6

Object vs. Space Partitioning Hierarchies Hierarchies OPH: SPH: - Object centric j - Space centric p - Spatial redundancy - Object redundancy - e.g., BVHs e.g., BVHs - e.g., kd-trees e.g., kd trees 7 Modified from Prof. M. C. Lin’s slides

Object vs. Space Partitioning Hierarchies Hierarchies OPH: SPH: - Object centric j - Space centric p - Spatial redundancy - Object redundancy - e.g., BVHs e.g., BVHs - e.g., kd-trees e.g., kd trees 8 Modified from Prof. M. C. Lin’s slides

Object vs. Space Partitioning Hierarchies Hierarchies OPH: SPH: - Object centric j - Space centric p - Spatial redundancy - Object redundancy - e.g., BVHs e.g., BVHs - e.g., kd-trees e.g., kd trees 9 Modified from Prof. M. C. Lin’s slides

Object vs. Space Partitioning Hierarchies Hierarchies OPH: SPH: - Object centric j - Space centric p - Spatial redundancy - Object redundancy - e.g., BVHs e.g., BVHs - e.g., kd-trees e.g., kd trees 10 Modified from Prof. M. C. Lin’s slides

Bounding Volume Hierarchies Bounding Volume Hierarchies ● Each node has bounding volumes Each node has bounding volumes ● Leaf node has k primitives; typically, k is 1 . . .. BVH 11

Trade off in Choosing BV’s Trade-off in Choosing BV s Sphere OBB AABB 6-dop Convex Hull increasing complexity & tightness of fit decreasing cost of overlap tests + BV update 12 Excerpted from Prof. M. C. Lin’s slides

BVH Based Collision Detection BVH-Based Collision Detection A1 B1 A2 A2 A3 A3 B2 B3 BVH1 BVH2 A1, B1 R fi Refine one node d A3, B1 A2, B1 …… Bounding volume test tree (BVTT) 13

Hierarchy Construction Hierarchy Construction ● Top-down vs. bottom-up approach Top down vs bottom up approach ● Top-down methods ● Recursively partition primitives into two sub- sets sets ● Bottom up methods ● Bottom-up methods ● Merges nearby primitives into BV nodes 14

Continuous Collision Detection Continuous Collision Detection ● Discrete checking ● Discrete checking t t ● Can miss collision if time step is large t+1 ● Continuous checking ● Always identify collisions y y ● Expensive