Game Physics

1
Game Physics
2
Introduction to Game Physics

• Traditional Game Physics
• Particle system
• Rigid body dynamics
• Flexible body dynamics
• Some State-of-art Topics
• Car physics
• Fluid dynamics
• Rag-doll physics
• Physics
• Rigid body kinematics
• Newtons Laws
• Forces
• Momenta
• Energy

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Basic Concepts from Physics (1/2)

• Newtons Laws
• 1st Law
• ????,?????????
• 2nd Law
• F ma mdv/dt
• 3rd Law
• ????????
• Forces
• Gravity / Spring forces / Friction / Viscosity
• Torque
• ? r X F
• Equilibrium

4
Basic Concepts from Physics (2/2)

• Momenta
• Linear momentum
• Angular momentum
• Moment of inertia

5
Particle Dynamics

• Particles are objects with
• Mass
• Position
• Velocity
• Respond to forces
• But no spatial extent (no size!)
• Point mass
• Based on Newton Laws
• f ma
• x f / m
• v f / m, x v

..
.
.
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Basic Particle System
typedef struct float m / mass /
float x / position / float v /
velocity / float f / force accumulator
/ Particle typedef struct Particle p
/ array of pointers to particles / int n
/ number of particles / float t /
simulation clock / ParticleSystem
states
Particle n time

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/ gather states from the particles / void
ParticleGetState(ParticleSystem p, float dst)
int i for (i 0 i lt p-gtn i)
(dst) p-gtpI-gtx0 (dst)
p-gtpI-gtx1 (dst) p-gtpI-gtx2
(dst) p-gtpI-gtv0 (dst)
p-gtpI-gtv1 (dst) p-gtpI-gtv2

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/ scatter states into the particles / void
ParticleSetState(ParticleSystem p, float src)
int i for (i 0 i lt p-gtn i)
p-gtpi-gtx0 (src) p-gtpi-gtx1
(src) p-gtpi-gtx2 (src)
p-gtpi-gtv0 (src) p-gtpi-gtv1
(src) p-gtpi-gtv2 (src)
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/ calculate derivative, place in dst / void
ParticleDerivative(ParticleSystem p, float
dst) int i ClearForce(p)
ComputeForce(p) for (i 0 i lt p-gtn i)
(dst) p-gtpi-gtv0 (dst)
p-gtpi-gtv1 (dst) p-gtpi-gtv2
(dst) p-gtpi-gtf0/p-gtpi-gtm
(dst) p-gtpi-gtf1/p-gtpi-gtm
(dst) p-gtpi-gtf2/p-gtpi-gtm
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/ Euler Solver / void EulerStep(ParticleSystem
p, float DeltaT) ParticleDeriv(p, temp1)
ScaleVector(temp1, DeltaT) ParticleGetState(p,
temp2) AddVector(temp1, temp2, temp2)
ParticleSetState(p, temp2) p-gtt DeltaT
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Rigid Body Dynamics

• Mass of a Body
• Mass center
• Force
• Linear momentum
• P(t) M v(t)
• Velocity (v)
• Torque
• Angular momentum
• L(t) I w(t)
• Local rotation (w)
• Inertia Tensor
• Reference
• www-2.cs.cmu.edu/afs/cs/user/baraff/www/pbm

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Flexible Body Dynamics (1/2)

• Particle-Spring Model
• F k x
• Not a stress-strain model
• Lack of Elasticity, Plasticity,
  Viscous-Elasticity
• Can be unstable

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Flexible Body Dynamics (2/2)

• Finite Element Method
• Solver for ODE/PDE
• Boundary conditions
• Energy equation
• Stress-strain model
• Very complicated computing process
• Conservation of Energy

14
Advanced Topics in Game Physics

• Fracture Mechanics (??????)
• Fluid Dynamics (????)
• Car Dynamics (?????)
• Rag-doll Physics (??????)

15
Game FX
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Introduction to Game FX

• Improve the Visual Sound Game Effects
• Includes
• Combat FX
• Environment FX
• Character FX
• Scene FX
• Sound FX
• FX Editor Needed
• General 3D animation can not do it
• Key-frame system is nor working
• FX animation is always
• Procedurally
• Related to the previous frame
• Small Work But Large Effect

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FX Editing Tool
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Combat FX

• During the Combat
• Weapon motion blur
• Weapon effect
• Skill effect
• After the Combat
• Damage effect
• FX Editor

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Combat FX Example
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Motion Blur Image Solution

• Computer Animation
• Image solution
• Blending rendered image sequence
• Render too many frames
• Divide the frames
• Average
• Done!

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Motion Blur Geometry Solution

• In Games, Use Transparent Objects to Simulate the
  Motion Blur
• False Motion Blur
• Tracking the motion path of the object
• Connecting them as a triangular mesh
• Use time-dependent semi-transparency to simulate
  the blur
• The path can be smoothed using Catmull-Rom spline
• Local stability of the curve

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FX Uses Texture Animation

• Almost All Game FXs Use this Trick
• Geometry Object on which the Texture Animation
  Playing
• Billboard
• 3D Plate
• Cylinder
• Sphere
• Revolving a cross section curve
• Texture Sequence with Color-key
• Semi-transparent Textures
• Alpha blending
• Source color added to background
• Demo!!!!

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Particle System for FXs in Combat

• The FXs
• Fire / exposure / smoke / dust
• Initial Value Time dependency
• Combined with Billboard FX
• Billboard to play the texture animation
• Particle system to calculate the motion path
• Gravity is the major force used
• Emitter pattern
• Single emitter
• Area emitter
• Emitter on vertices
• Demo !!!

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Environment FX

• Weather
• Use particle system
• Rain
• Snow
• Wind
• Fog
• Traditional fog
• From near to far
• Hardware standard feature
• Volume fog
• Layered fog
• Use vertex shader
• Day Night

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Character FX

• Fatality
• Case by case and need creative solutions
• Rendering Effects on Skins
• Environment mapping
• Bump map
• Normal map
• Multiple texture map
• Flexible body
• Flexible body dynamics
• Fur
• Real-time fur rendering

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Scene FX Sky Box

• Use a very large box or dome-like model to
  surround the whole game scene
• Use textures on the box or dome as the backdrop
• Use multiple textures and texture coordinates
  animation to simulate the moving of the clouds

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Scene FX Lens Flare

• Runtime calculate the position and orientation of
  the camera with the sun
• Put textures to simulate the lens flare

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Scene FX Light Scattering

• Atmospheric Light Scattering
• Caused by dust, molecules, or water vapor
• These can cause light to be
• Scattered into the line of sight (in-scattering)
• Scattered out of the line of sight
  (out-scattering)
• Absorbed altogether (absorption)

• Skylight and sun light
• Can be Implemented by Vertex Shader

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Scene FX Light Scattering Examples
With scattering
Without scattering