Why Physics?

• More interactivity

• Looks cool (explosions)

• More realistic

• More variety and easier animations (rag doll physics for death animations)

• Better gameplay (space fighter, driving games)

Game Physics

• What is meant by Physics in games (old)?– Collision Detection (testing)

• But want the physical effect of hitting an immovable object.

• Also needed to provide the input (forces) for physical simulations (equations) of moveable or deformable objects.

– More intelligent (automated) interpolation• Particle systems – Artistically defined generation

with Newtonian-based controls.

Game Physics

• What is meant by Physics in games (new)?– Fluid dynamics– Deformable models– Ragdoll (non-scripted)

articulation– (More) Accurate simulation

Dead Reckoning

• Given the current state of a single entity, integrate it in time assuming there are no other influences.

• The state consists of:– Position– Velocity– Acceleration (optional)– Angular Momentum (optional)

Collisions

• Collision Detection– Collision detection is a geometric problem– Given two moving objects defined in an initial and

final configuration, determine if they intersected at some point between the two states

• Collision Response– The response to collisions is the actual physics

problem of determining the unknown forces (or impulses) of the collision

Collision Detection

• ‘Collision detection’ is really a geometric intersection detection problem

• Main subjects– Intersection testing (triangles, spheres, lines…)– Optimization structures (octree, BSP…)– Pair reduction (reducing N2 object pair testing)

Intersection Testing

• General goals: given two objects with current and previous orientations specified, determine if, where, and when the two objects intersect

• Alternative: given two objects with only current orientations, determine if they intersect

• Sometimes, we need to find all intersections. Other times, we just want the first one. Sometimes, we just need to know if the two objects intersect and don’t need the actual intersection data.

Collision Detection

Complicated for two reasons1. 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

Collision Detection

Two basic techniques1. Overlap testing

• Detects whether a collision has already occurred

2. Intersection testing• Predicts whether a collision will occur in the future

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

Overlap Testing:Useful Results

• Useful results of detected collision– Time collision took place– Collision normal vector

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 te r a tio n 1F o r w ar d 1 /2

I te r a tio n 2Bac k w ar d 1 /4

I te r a tio n 3F o r w ar d 1 /8

I te r a tio n 4F o r w ar d 1 /1 6

I te r a tio n 5Bac k w ar d 1 /3 2

I n itia l O v er lapT es t

t0.5t0.4375 t0.40625

BB B

A

A

A

AA A

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 t2

b u lle t

w in d o w

Intersection Testing

• Predict future collisions

• When predicted:– Move simulation to time of collision– Resolve collision– Simulate remaining time step

Intersection Testing:Swept Geometry

• Extrude geometry in direction of movement• Swept sphere turns into a “capsule” shape

t0

t1

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

Intersection Testing:Sphere-Sphere Collision

• Smallest distance ever separating two spheres:

• If

there is a collision

2

222

BAd

BA

22QP rrd

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

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

Dealing with Complexity

Two issues1. Complex geometry must be simplified

2. Reduce number of object pair tests

Collision Detection Methods

Many different methods We will focus on two of them:

– Grid method: good for many simple moving objects of about the same size (e.g., many moving discs with similar radii)

– Bounding Volume Hierarchy (BVH) method: good for few moving objects with complex geometry

Grid Method

d

Subdivide space into a regular grid cubic of square bins

Index each object in a bin

Grid Method

d

Running time is proportional tonumber of moving objects

Enclose objects into bounding volumes (spheres or boxes) Check the bounding volumes first

Bounding Volume Hierarchy Method

Enclose objects into bounding volumes (spheres or boxes) Check the bounding volumes first Decompose an object into two

Bounding Volume Hierarchy Method

Enclose objects into bounding volumes (spheres or boxes) Check the bounding volumes first Decompose an object into two Proceed hierarchically

Bounding Volume Hierarchy Method

Enclose objects into bounding volumes (spheres or boxes) Check the bounding volumes first Decompose an object into two Proceed hierarchically

Bounding Volume Hierarchy Method

• BVH is pre-computed for each object

Bounding Volume Hierarchy Method

BVH in 3D

Collision Detection

Two objects described by their precomputed BVHs

A

B C

D E F G

A

B C

D E F G

Collision Detection

AA

Search tree

AA

pruning

Collision Detection

AA

CCCBBCBB

Search tree

AA

A

B C

D E F G

Collision Detection

CCCBBCBB

AA

Search tree

pruning

A

B C

D E F G

Collision Detection

CCCBBCBB

AA

Search tree

GEGDFEFD

G DIf the pieces contained in G and D

overlap collision

A

B C

D E F G

Performance

Several thousand collision checks per second for 2 three-dimensional objects each described by 500,000 triangles, on a 1-GHz PC

Desirable Properties of BVs and BVHs

BVs: Tightness Efficient testing Invariance

BVH: Separation Balanced tree ?

Desirable Properties of BVs and BVHs

BVs: Tightness Efficient testing Invariance

BVH: Separation Balanced tree

Spheres

Invariant Efficient to test But tight?

Axis-Aligned Bounding Box (AABB)

Axis-Aligned Bounding Box (AABB)

Not invariant Efficient to test Not tight

Oriented Bounding Box (OBB)

Invariant Less efficient to test Tight

Oriented Bounding Box (OBB)

Comparison of BVs

Sphere

AABB OBB

Tightness - -- +

Testing + + o

Invariance

yes no yes

No type of BV is optimal for all situations

Why a Physics Engine?

• Physics simulation is hard

• Requires very stable integrator

• Articulated bodies especially take difficult math

• Optimization is important

• Spring systems explode easily

Major Features

• Collision detection

• Newtonian forces and collision response

• Buoyant forces

• Friction

• Articulation and jointed characters (rag doll)

• Prebuilt objects for simulation

Physics Toolkits

• ODE (Open Dynamics Engine)• Ageia PhysX• Newton Game Dynamics• Havok• Havok FX• Tokamak Game Physics

Rigid Body Dynamics

• What is involved in this:

• http://www.youtube.com/watch?v=NM0bY_IFoes&feature=related

More Complicated?

• What about this one?

• http://www.youtube.com/watch?v=Q7HLWrldgLQ&feature=related

Ragdoll Physics

• YouTube

• http://www.youtube.com/watch?v=gbuA-HEbROk

• Demo

• http://www.2dplay.com/ragdoll-physics-2/ragdoll-physics-2-play.htm

Fluid Dynamics

• Water and other fluids are governed by the Navier Stokes equations.– http://gameplanets.blogspot.com/2007/06/phy

sics-simulations.html

• nVidia demo– http://www.youtube.com/watch?v=wWlaD_2g

sIM&feature=related

Cloth Simulation

• Surface-like objects such as a cape on your super-hero or a flag.– http://youtube.com/watch?v=11L97NM2eiU&f

eature=related

Physics – Do we need it?

• Is it worth the cost?

• Why not just fake it?

Real-time Graphics Methods• Real-time graphics is all about hackery

• It’s impossible to get a realtime, high-fidelity global illumination rendering

• The questions you should ask:– What effects do I want in my game?– What corners am I willing to cut?

Billboards• A billboard is a flat object that faces something

– There are lots of different billboarding methods, but we’ll stick with the easiest, most used one

• Take a quad and slap a texture on it. Now we want it to face the camera. How do we do that?

• Bread and butter of older 3d games and still used extensively today– Monsters (think Doom)– Items– Impostors (LOD)– Text– Faked smoke, fire, explosions, particle effects, halos, etc.– #*$&ing lens flares

• Bad news: Little to no shading

Light Mapping• We’d like soft lighting and soft shadows but the fixed function

pipeline won’t let us have our way. Plus, real lighting is slow once we involve multiple lights.

• Hmm…– Most of our world geometry is static– We can blend multiple textures together in multiple passes

(multitexturing)– Radiosity is good at diffuse – Radiosity is view independent

Light Mapping

• Let’s precompute the global illumination (sans specular) using radiosity, store it in a light map, and blend that with the detail texture– That’s the gist of it. Implementing it can be tricky. – Don’t need to use radiosity either

• Fun Fact: id software used tohave a SGI Origin 2000 (16 x 180mhz, 1.2GB RAM) to crunch maps. They sold it on ebay in 2000.

• Note: probably should be called dark mapping…

No Light Mapping

Quake 3: Arena nvnews.net

Light Mapping!

Quake 3: Arena nvnews.net

Low-Poly Modeling• Trying to make effective, complex models that a game engine can handle is

extremely difficult

• For the longest time games were just forced to have blocky looking models

• Thanks to normal mapping, now we can make really low poly models look incredibly complex

Low-Poly Modeling

• This requires that the artist make a normal map

• She can draw the normal map manually• Or create two versions of the model, one

complex and one simplified, and use an automated tool to generate the normal map that represents the “differences” of the two models

Keyframed Animation• Same idea as keyframes in traditional animation• A keyframe represents position and orientation at a point

in time– Break the model into chunks (head, torso, etc.) and each chunk

has vectors/matrices associated with it– Keyframes specify the values of those matrices at specific points

in time and their geometry– Interpolate position and rotation (quaternions again) between

those time periods. – Quake 3 is keyframed and uses ~ 15 keyframes/sec– Uses a lot of memory because you need to store the geometry

at each keyframe, but keyframing is fast

Skeletal Animation• The model has a skeleton and the skeleton is animated, not

the model• Every vertex on the “skin” is connected to a bone so when

the bone moves so does the skin. This is done with hierarchy and matrix transforms (sound familiar?)

• This involves transforming vertices so we can do this in a vertex shader (blend registers)

• Skeleton allows for realistic physics simulation on the model• Keyframing is almost dead. Doom III, Half-Life 2, and other

new games all use skeletal animation.• The memory cost of keyframing was so high that Quake 3

was almost changed to skeletal animation at the last minute• Related: facial animation

Motion Capture• Elegant hack• If you’ve seen decent human animation in a game, it’s

mocap. Video games are the biggest market for motion capture and now the movie industry is getting into it.

• “Motion capture actor” is actually a legitimate profession now

• Tom Hanks, that guy who did Gollum in LOTR

Note: Former MLB pitcher John Rocker

Material Libraries• Technical Directors and Artists at a game company now have the

luxury of creating material libraries – whole sets of shaders and associated texture maps that can be used to enrich in-game models

• 3D movie production, especially at places like Pixar, always work with material libraries, allowing people to focus solely on shader production

• This frees the 3D and 2D artists to focus on art, not technology

Doom III

Halo 2

Black and White 2