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

C lli i D t ti Collision Detection

Sung-Eui Yoon (윤성의) (윤성의)

C URL Course 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 C llidi i i i y

• Minimum separation

Colliding primitives

p distance

• Compute a minimum

di t b t t distance between two

• bjects and report primitives

realizing the distance

3

realizing the distance

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
• r space partitioning hierarchies

6

Object vs. Space Partitioning Hierarchies Hierarchies

OPH: SPH:

• Object centric
• Space centric

j p

• Spatial redundancy
• Object redundancy
• e.g., BVHs
• e.g., kd-trees

e.g., BVHs e.g., kd trees

7

Modified from Prof. M. C. Lin’s slides

Object vs. Space Partitioning Hierarchies Hierarchies

OPH: SPH:

• Object centric
• Space centric

j p

• Spatial redundancy
• Object redundancy
• e.g., BVHs
• e.g., kd-trees

e.g., BVHs e.g., kd trees

8

Modified from Prof. M. C. Lin’s slides

Object vs. Space Partitioning Hierarchies Hierarchies

OPH: SPH:

• Object centric
• Space centric

j p

• Spatial redundancy
• Object redundancy
• e.g., BVHs
• e.g., kd-trees

e.g., BVHs e.g., kd trees

9

Modified from Prof. M. C. Lin’s slides

Object vs. Space Partitioning Hierarchies Hierarchies

OPH: SPH:

• Object centric
• Space centric

j p

• Spatial redundancy
• Object redundancy
• e.g., BVHs
• e.g., kd-trees

e.g., BVHs 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

AABB OBB Sphere Convex Hull 6-dop

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 A2 A3 B1 A2 A3 B2 B3 BVH1 BVH2 A1, B1 R fi d Refine one node A2, B1 A3, B1 ……

13

Bounding volume test tree (BVTT)

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

t

• Discrete checking
• Can miss collision if time step is large

t t+1

• Continuous checking
• Always identify collisions

y y

• Expensive