1. Collision Detection

2. The problem can be defined as
Intro
The problem can be defined as
if, where and when
two objects intersect.

3. Collision Detection
Collision detection, as used in the games community, usually means intersection detection of any form
Intersection detection is the general problem: find out if two geometric entities intersect – typically a static problem
Subtle point: Collision detection is about the algorithms for finding collisions in time as much as space

4. Classification of Collision Detection
Type of objects
convexity/concavity
rigid/deformable
polygons/curves
1-Dimensional/2D/3D/N-D
static/dynamic
Time of collision
discrete/continuous
exact/approximate
Motion of objects
linear/non-linear
predictable/dynamic
bounded/unbounded
angular motion
Other factors
realtime/off-line
number of objects
allowable error margin
frame vs. path

5. Choosing an Algorithm
The geometry of the colliding objects is the primary factor in choosing a collision detection algorithm
“Object” could be a point, or line segment
Object could be specific shape: a sphere, a triangle, a cube, …
Objects can be concave/convex, solid/hollow, deformable/rigid, manifold/non- manifold

6. Collision Detection in the Video Game Package
For pair (j, k) of Sprites:
if the boundingBox(j) does not intersect boundingBox(k), return no intersection
let m be the intersection of j and k
if m is empty, return no intersection
otherwise, return intersection
This algorithm uses a simple test for intersection when possible (intersection of bounding boxes), and a more exact test when the bounding box fails to determine intersection.

7. Collision Detection in the Video Game Package
What this collision detection is not good at doing:
determining path intersections (important for fast moving objects or low model frame rates)
determining time/location of first intersection
predicting intersections
handling a large number of Sprites

8. Part 1: Bounding Volumes
Reduce complexity of collision computation by substitution of the (complex) original object with a simpler object containing the original one.

9. Bounding Volumes
The original objects can only intersect if the simpler ones do. Or better: if the simpler objects do NOT intersect, the original objects won’t either.

10. Different BVs used in game programming:
Bounding Volumes
Different BVs used in game programming:
Axes Aligned Bounding Boxes (AABB)
Oriented Bounding Boxes (OBB)
Spheres
k-Discrete Oriented Polytopes (k DOP)
Sphere
OBB
k-DOP
AABB

11. Oriented Bounding Box (OBB)
Bounding Volumes
Oriented Bounding Box (OBB)
Align box to object such that it fits optimally in terms of fill efficiency
Computationally expensive
Invariant to rotation
Complex intersection check

12. Separating Axes Theorem
Bounding Volumes
The overlap test is based on the
Separating Axes Theorem
(S. Gottschalk. Separating axis theorem. Technical Report TR96-024,Department
of Computer Science, UNC Chapel Hill, 1996)
Two convex polytopes are disjoint iff there exists a separating axis orthogonal to a face of either polytope or orthogonal to an edge from each polytope.

13. Bounding Volumes
Each box has 3 unique face orientations, and 3 unique edge directions. This leads to 15 potential separating axes to test (3 faces from one box, 3 faces from the other box, and 9 pairwise combinations of edges).

14. Not invariant to rotation
Bounding Volumes
K-DOP
Easy to compute
Good fill efficiency
Simple overlap test
Not invariant to rotation

15. k-DOPs are used e.g. in the game
Bounding Volumes
k-DOPs are used e.g. in the game
‘Cell Damage’
(XBOX, Pseudo Interactive, 2002)

16. Part 2: Collision on different scales:
Bounding Volumes
Part 2: Collision on different scales:
Hierarchies

17. Hierarchies
Idea:
To achieve higher exactness in collision detection, build a multiscale BV representation of the object

18. Hierarchies

19. Each node contains all primitives of its subtree
Hierarchies
Simple example:
Binary tree
Each node contains all primitives of its subtree
Leaves contain single primitive

20. Hierarchies

21. Hierarchies

22. Hierarchies

23. How to create a hierarchy tree
Hierarchies
How to create a hierarchy tree
Top down:
Use single BV covering whole object
Split BV
Continue recursively until each BV contains a single primitive

24. Start with BV for each primitive
Hierarchies
Bottom up:
Start with BV for each primitive
Merge

25. Example for top down using OBBs :
Hierarchies
Example for top down using OBBs :

26. Hierarchies
Comparison AABB / OBB

27. Part 3: Collision between
Multiple Objects
Part 3: Collision between
Multiple Objects

28. Grid Method: Create 3d grid volume overlay
Multiple Objects
Grid Method:
Create 3d grid volume overlay
Only check collision between objects sharing at least one cell

29. Multiple Objects
2D example

30. Sort and Sweep Create single AABB for each object
Multiple Objects
Sort and Sweep
Create single AABB for each object
Project BVs onto coordinate axes
Create a sorted list of start and endpoints for each coordinate axis, hence store the intervals created by each object
(Cont’d)

31. If startpoint of object i is hit, insert i into ‘active list’
Multiple Objects
Traverse each list
If startpoint of object i is hit, insert i into ‘active list’
If endpoint of object i is hit, remove i from ‘active list’
If 2 objects i1,i2 are active at the same time they overlap in the dimension processed
Objects overlapping in all single dimensions overlap in world

32. S3 S1 E3 S2 E1 E2 S1 S2 E1 S3 E2 E3 Multiple Objects X Y 3 1 2
OVERLAP 1,2 s1 s2 e1 s3 e2 e3

33. Note: sort and sweep for a single step is relatively expensive.
Multiple Objects
Note: sort and sweep for a single step is relatively expensive.
Since not all objects are transformed for the next frame, the list is not created newly for each frame, but updated.