Physics for Games Physics for Games Programmers Programmers Problem Problem

OverviewOverview

Squirrel Eiserloh

Technical DirectorRitual Entertainment

squirrel@eiserloh.netwww.ritual.comwww.algds.org

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Types of Problems Knowing when to cheat Simplifying things Giving shape to things Moving things around Simulation baggage Detecting (and resolving) collisions Sustained interactions Dealing with the impossible Making it fast enough

Knowing When To Cheat

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Knowing When to Cheat Discrete physics simulation falls

embarrassingly short of reality. “Real” physics is prohibitively

expensive... ...so we cheat. We need to cheat enough to be able to

run in real time. We need to not cheat so much that

things break in a jarring and unrecoverable way.

Much of the challenge is knowing how and when to cheat.

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Knowing When to Cheat

Ask: “Will the player notice?” “Will the player care?” “Will the results be predictable?” “Are we at least cheating in a consistent

way?” “Will the simulation break?”

If the simulation breaks, they will notice and they will care

Some crimes are greater than others

Simplifying Things

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Simplifying Things

Simplified bodies

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Simplifying Things

Simplified bodies Even more

simplified bodies

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Simplifying Things

Simplified bodies Even more

simplified bodies Convex bodies

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Simplifying Things

Simplified bodies Even more

simplified bodies Convex bodies Homogeneous

bodies

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Simplifying Things

Simplified bodies Even more

simplified bodies Convex bodies Homogeneous

bodies Rigid bodies

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Simplifying Things

Simplified bodies Even more

simplified bodies Convex bodies Homogeneous

bodies Rigid bodies Indestructible

bodies

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Simplifying Things

Movement is often assumed to be in a vacuum (ignoring air resistance)

Even when air resistance does get simulated, it is hugely oversimplified

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Simplifying Things

Collisions are often assumed to be perfect and elastic

That is, 100% of the energy before the collision is maintained after the collision

Think billiard balls

Giving Shape to Things

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Giving Shape to Things

N-sphere 2d: Disc 3d: Sphere

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Giving Shape to Things

N-sphere 2d: Disc 3d: Sphere

Simplex 2d: Triangle 3d: Tetrahedron

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Giving Shape to Things

N-sphere 2d: Disc 3d: Sphere

Simplex 2d: Triangle 3d: Tetrahedron

Convex Polytope 2d: Convex Polygon 3d: Convex

Polyhedron a.k.a. “Convex Hull” a.k.a. “Brush” (Quake)

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Giving Shape to Things

Discrete Oriented Polytope (DOP)

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Giving Shape to Things

Discrete Oriented Polytope (DOP)

Oriented Bounding Box (OBB)

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Giving Shape to Things

Discrete Oriented Polytope (DOP)

Oriented Bounding Box (OBB)

Axis-Aligned Bounding Box (AABB)

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Giving Shape to Things

Discrete Oriented Polytope (DOP)

Oriented Bounding Box (OBB)

Axis-Aligned Bounding Box (AABB)

Capsule

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Giving Shape to Things

Discrete Oriented Polytope (DOP)

Oriented Bounding Box (OBB)

Axis-Aligned Bounding Box (AABB)

Capsule Cylinder (3d only)

Moving Things Around

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Moving Things Around Kinematics

Describes motion Uses position,

velocity, momentum, acceleration

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Moving Things Around Kinematics

Describes motion Uses position,

velocity, momentum, acceleration

Dynamics Explains motion Uses forces ...and impulses

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Moving Things Around Kinematics

Describes motion Uses position,

velocity, momentum, acceleration

Dynamics Explains motion Forces (F=ma) Impulses

Rotation Torque Angular momentum Moment of inertia

Simulation Baggage

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Simulation Baggage

Flipbook syndrome

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Simulation Baggage

Flipbook syndrome Things can happen

in-between snapshots

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Simulation Baggage

Flipbook syndrome Things mostly

happen in-between snapshots

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Simulation Baggage

Flipbook syndrome Things mostly

happen in-between snapshots

Curved trajectories treated as piecewise linear

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Simulation Baggage

Flipbook syndrome Things mostly

happen in-between snapshots

Curved trajectories treated as piecewise linear

Terms often assumed to be constant throughout the frame

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Simulation Baggage (cont’d)

Error accumulates

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Simulation Baggage (cont’d)

Error accumulates Energy is not

always conserved Energy loss can be

undesirable Energy gain is evil

Simulations explode!

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Simulation Baggage (cont’d)

Error accumulates Energy is not

always conserved Energy loss can be

undesirable Energy gain is evil

Simulations explode!

Rotations are often assumed to happen instantaneously at frame boundaries

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Simulation Baggage (cont’d)

Error accumulates Energy is not always

conserved Energy loss can be

undesirable Energy gain is evil

Simulations explode!

Rotations are often assumed to happen instantaneously at frame boundaries

Numerical nightmares!

Collision Detection

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Collision Detection

We need to determine if A and B intersect

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Collision Detection

We need to determine if A and B intersect

Worse yet, they could be (and probably are) in motion

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Collision Detection

We need to determine if A and B intersect

Worse yet, they could be (and probably are) in motion

If they did collide, we probably also need to know when they collided

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Collision Response

...and we need to figure out how to resolve the collision

Sustained Interactions

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Sustained Interactions

Surface contact

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Sustained Interactions

Surface contact Edge contact

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Sustained Interactions

Surface contact Edge contact Contact points

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Sustained Interactions

Surface contact Edge contact Contact points

Different solutions

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Sustained Interactions

Surface contact Edge contact Contact points

Different solutions Stacking

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Sustained Interactions

Surface contact Edge contact Contact points

Different solutions Stacking Friction

Static & Kinetic

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Sustained Interactions

Surface contact Edge contact Contact points

Different solutions Stacking Friction

Static & Kinetic Constraints & Joints

Dealing With the Impossible

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Dealing With the Impossible

Interpenetration

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Dealing With the Impossible

Interpenetration Tunneling

Tunneling(Sucks)

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Tunneling

Small objects tunnel more easily

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Tunneling (cont’d)

Possible solutions Minimum size requirement?

Inadequate; fast objects still tunnel

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Tunneling (cont’d)

Fast-moving objects tunnel more easily

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Tunneling (cont’d)

Possible solutions Minimum size requirement?

Inadequate; fast objects still tunnel Maximum speed limit?

Inadequate; since speed limit is a function of object size, this would mean small & fast objects (bullets) would not be allowed

Smaller time step? Helpful, but inadequate; this is essentially the

same as a speed limit

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Tunneling (cont’d)

Besides, even with min. size requirements and speed limits and a small timestep, you still have degenerate cases that cause tunneling!

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Tunneling (cont’d)

Tunneling is very, very bad – this is not a “mundane detail” Things falling through world Bullets passing through people or walls Players getting places they shouldn’t Players missing a trigger boundary

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Tunneling (cont’d)

Interpenetration Tunneling Rotational

tunneling

Making It Fast Enough

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Making It Fast Enough

Don’t be too particular too soon Avoid unnecessary

work

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Making It Fast Enough

Don’t be too particular too soon Avoid unnecessary

work Eschew n-squared

operations Avoid the

“everything vs. everything” case

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Making It Fast Enough

Don’t be too particular too soon Avoid unnecessary

work Eschew n-squared

operations Avoid the

“everything vs. everything” case

Try using simulation islands or other methods to divide and conquer

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Simulation Islands

Consider: 1000 objects, 1

island 1000x1000 checks = 1 Million checks

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Simulation Islands

Consider: 1000 objects, 1

island 1000x1000 checks = 1 Million checks

Verses: 1000 objects,

divided into 10 islands of 100

10 x (100x100) checks

= 100,000 checks 1/10th as many!

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Simulation Islands

Simulation islands can “go to sleep” when they become stable i.e. when forces and

motion remain unchanged

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Simulation Islands

Simulation islands can “go to sleep” when they become stable i.e. when forces and

motion remain unchanged

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Simulation Islands

Simulation islands can “go to sleep” when they become stable i.e. when forces and

motion remain unchanged

When an object enters the island’s bounds...

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Simulation Islands

Simulation islands can “go to sleep” when they become stable i.e. when forces and

motion remain unchanged

When an object enters the island’s bounds...

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Simulation Islands

Simulation islands can “go to sleep” when they become stable i.e. when forces and

motion remain unchanged

When an object enters the island’s bounds...

...the island wakes up

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Simulation Islands

Add the newcomer to this simulation island

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Simulation Islands

Add the newcomer to this simulation island

...and put it back to sleep once it stabilizes

This is just one of many ways to reduce complexity

We’ll be covering several others later on

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Making It Fast Enough

Can also exploit work previously done Make “educated assumptions” using:

Temporal/frame coherence: Things tend not to have changed a whole lot in the 15ms or so since the previous frame, so save the previous frame’s results!

Spatial coherence: Things tend to miss each other far more often than they collide, and only things in the same neighborhood can collide with each other

Summary

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Summary The nature of simulation causes us

real problems... problems which can’t be ignored

So we cheat And we simplify things And even then, it can get quite

complex...

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Summary (cont’d)

Problems we’re concerned with: How should we choose to represent physical

bodies? How should we simulate and compute motion? How can we prevent energy build-up? How do we cope with floating point error? How can we detect collisions – especially when

large numbers of objects are involved? How should we resolve penetration? How should we handle contact? How can we prevent tunneling? How do we deal with non-rigid bodies?

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Questions?

Feel free to reach me by email at:

squirrel@eiserloh.net or

squirrel@ritual.com