Chapter 4.2 Collision Detection and Resolution
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Transcript of Chapter 4.2 Collision Detection and Resolution
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Chapter 4.2Collision Detection and Resolution
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Collision DetectionComplicated for two reasons
1. Geometry is typically very complex, potentially requiring expensive testing
2. Naïve solution is O(n2) time complexity, since every object can potentially collide with every other object
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Collision DetectionTwo basic techniques
1. Overlap testing Detects whether a collision has already
occurred2. Intersection testing
Predicts whether a collision will occur in the future
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Overlap Testing Facts
Most common technique used in games Exhibits more error than intersection
testing Concept
For every simulation step, test every pair of objects to see if they overlap
Easy for simple volumes like spheres, harder for polygonal models
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Overlap Testing:Useful Results Useful results of detected collision
Time collision took place Collision normal vector
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Overlap Testing:Collision Time Collision time calculated by moving
object back in time until right before collision Bisection is an effective technique
B B
t1
t0.375
t0.25
B
t0
I ter a tio n 1F o rw ard 1 /2
I ter a tio n 2Bac k w ar d 1 /4
I ter a tio n 3F o rw ar d 1 /8
I ter a tio n 4F o r w ar d 1 /1 6
I ter atio n 5Bac k w ard 1 /3 2
I n it ia l O v er lapT es t
t0.5t0.4375 t0.40625
BB B
A
A
A
AA A
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Overlap Testing:Limitations Fails with objects that move too fast
Unlikely to catch time slice during overlap Possible solutions
Design constraint on speed of objects Reduce simulation step size
t0t -1 t1 t2b u lle t
w in d o w
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Intersection Testing Predict future collisions When predicted:
Move simulation to time of collision Resolve collision Simulate remaining time step
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Intersection Testing:Swept Geometry Extrude geometry in direction of
movement Swept sphere turns into a “capsule”
shapet0
t1
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Intersection Testing:Sphere-Sphere Collision
Q 1
Q 2
P 1
P 2
P
Q
t= 0
t= 0
t= 1
t= 1
t
,2
2222
B
rrΑBt QP
BAΒΑ .QQPPB
QPA
1212
11
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Intersection Testing:Sphere-Sphere Collision Smallest distance ever separating
two spheres:
If there is a collision
2
222
BAd BA
22QP rrd
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Intersection Testing:Limitations Issue with networked games
Future predictions rely on exact state of world at present time
Due to packet latency, current state not always coherent
Assumes constant velocity and zero acceleration over simulation step Has implications for physics model and
choice of integrator
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Dealing with ComplexityTwo issues
1. Complex geometry must be simplified
2. Reduce number of object pair tests
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Dealing with Complexity:Simplified Geometry Approximate complex objects with
simpler geometry, like this ellipsoid
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Dealing with Complexity:Minkowski Sum By taking the Minkowski Sum of
two complex volumes and creating a new volume, overlap can be found by testing if a single point is within the new volume
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Dealing with Complexity:Minkowski Sum
Y}B and :{ XABAYX
X Y =YX X Y =
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Dealing with Complexity:Minkowski Sum
t0
t1
t0
t1
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Dealing with Complexity:Bounding Volumes Bounding volume is a simple
geometric shape Completely encapsulates object If no collision with bounding volume,
no more testing is required Common bounding volumes
Sphere Box
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Dealing with Complexity:Box Bounding Volumes
Ax is -Alig n ed Bo u n d in g Bo x O r ien ted Bo u n d in g Bo x
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Dealing with Complexity:Achieving O(n) Time ComplexityOne solution is to partition space
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Dealing with Complexity:Achieving O(n) Time ComplexityAnother solution is the plane sweep
algorithm
C
B
R
A
x
y
A0 A 1 R 0 B0 R 1 C 0 C 1B1
B0
B1A1
A0
R 1
R 0
C 1
C 0
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Terrain Collision Detection:Height Field Landscape
T o p - D o wn Vie w
P e r sp e c t iv e Vie w
T o p - D o wn Vie w ( h e igh t s a dde d)
P e r sp e c t iv e Vie w ( h e igh t s a dde d)
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Terrain Collision Detection:Locate Triangle on Height Field
Q
R
Q
Q z > Q x
Q z < = Q x
z
x
R z > 1 - R x
R z < = 1 - R x
R
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Terrain Collision Detection:Locate Point on Triangle Plane equation: A, B, C are the x, y, z components
of the plane’s normal vector Where
with one of the triangles vertices being
Giving:
0 DCzByAx
0PND
0P 00 PNNNN zyx zyx
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Terrain Collision Detection:Locate Point on Triangle The normal can be constructed by
taking the cross product of two sides:
Solve for y and insert the x and z components of Q, giving the final equation for point within triangle:
0201 PPPPN
y
zzxxy N
PNQNQNQ 0
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Terrain Collision Detection:Locate Point on Triangle Triangulated Irregular Networks
(TINs) Non-uniform polygonal mesh
Barycentric Coordinates
P 1
P 2
P 0
Q
P o in t = w 0P 0 + w 1P 1 + w 2P 2
Q = ( 0 )P 0 + ( 0 .5 )P 1 + (0 .5 )P 2
R = ( 0 .3 3 )P 0 + ( 0 .3 3 )P 1 + ( 0 .3 3 )P 2R
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Terrain Collision Detection:Locate Point on Triangle Calculate barycentric coordinates for
point Q in a triangle’s plane
If any of the weights (w0, w1, w2) are negative, then the point Q does not lie in the triangle
2
12
121
212
22
212
22
12
1 1VSVS
VVVV
VV VV
VVww
022
011
0
PPVPPVPQS
210 1 www
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Collision Resolution:Examples Two billiard balls strike
Calculate ball positions at time of impact Impart new velocities on balls Play “clinking” sound effect
Rocket slams into wall Rocket disappears Explosion spawned and explosion sound effect Wall charred and area damage inflicted on nearby
characters Character walks through wall
Magical sound effect triggered No trajectories or velocities affected
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Collision Resolution:Parts Resolution has three parts
1. Prologue2. Collision3. Epilogue
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Collision Resolution:Prologue Collision known to have occurred Check if collision should be ignored Other events might be triggered
Sound effects Send collision notification messages
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Collision Resolution:Collision Place objects at point of impact Assign new velocities
Using physics or Using some other decision logic
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Collision Resolution:Epilogue Propagate post-collision effects Possible effects
Destroy one or both objects Play sound effect Inflict damage
Many effects can be done either in the prologue or epilogue
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Collision Resolution:Resolving Overlap Testing1. Extract collision normal2. Extract penetration depth3. Move the two objects apart4. Compute new velocities
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Collision Resolution:Extract Collision Normal Find position of objects before impact Use two closest points to construct the
collision normal vector
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Collision Resolution:Extract Collision Normal Sphere collision normal vector
Difference between centers at point of collision
t0
t0
t0 . 2 5
t0 . 5
t0 . 2 5
t0 . 5
t0 . 7 5
t0 . 7 5
t1
t1
C o llis io n
N o rm a l
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Collision Resolution:Resolving Intersection Testing Simpler than resolving overlap
testing No need to find penetration depth or
move objects apart Simply
1. Extract collision normal2. Compute new velocities