Transcript Chapter 14 - Cengage Learning

CHAPTER 14
Physics Modeling
© 2008 Cengage Learning EMEA
LEARNING OBJECTIVES
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In this chapter you will learn about:
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The fundamentals of physics
Time
Position
Mass and weight
Velocity
Acceleration
Force
Momentum
Physics modeling and implementation
Linear momentum
Gravitational pull
Trajectory paths
Friction
Object collisions
Implementing a particle system
FUNDAMENTALS OF PHYSICS
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Video games originally featured a very small
amount of physics simulation, with games like
Breakout (released by Atari in 1976)
incorporating a limited degree of collision
detection and response to simulate the
destruction of bricks upon collision with a ball,
as well as the bouncing of this ball upon impact
with the movable paddle.
FUNDAMENTALS OF PHYSICS
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During the 1990s, concepts such as gravity and the
fundamental laws of physics were steadily finding their
way into games.
It wasn’t, however, until the release of games like Valve
Software’s Half Life 2 that true physics simulation really
contributed to the overall game play experience.
– Half Life 2 included numerous physics-based puzzles where the
player, for example, had to use gravity by removing bricks from
one end of a pulley system to lower the other end, etc.
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Physics has thus found its way into games for the
realistic simulation of object-player interaction as well as
for the animation of objects based on exerted forces and
environmental resistance.
FUNDAMENTALS OF PHYSICS
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One interesting development in the world
of physics is dedicated Physics Processing
Units or PPUs.
FUNDAMENTALS OF PHYSICS
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Most physics simulations are based on Newton’s laws of
motion – three laws describing the relationship between
the forces influencing a rigid body and the resulting
motion of this body.
Newton’s laws of motion can be summarized as follows:
1 The first law: law of inertia:
- A body in motion will remain in motion unless a net force is
exerted upon it.
2 The second law: law of acceleration:
- The net force of a particle is the rate of change of its linear
momentum.
- Momentum is the mass of the body multiplied by its velocity.
- The force on a body is thus its mass multiplied by its
acceleration (F = ma).
3 The third law: law of reciprocal actions:
- To every action there is an equal and opposite reaction.
FUNDAMENTALS OF PHYSICS
Computer games will rarely implement physics
or Newton’s laws of motion down to the letter.
 Doing so will leave little if any processing power
for the game’s AI, networking, game loop, etc.
 We will thus rather outline the physics needed
and simulate the required effects as close to real
life as possible, hence creating an extremely
close approximation but using a lot of
optimizations and assumptions to simplify the
original laws of motion.
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Time
Time is perhaps the most critical part of any
simulation – an abstract concept spanning
science, philosophy and art.
 Time in the real word is, of course, a basic
concept and a core element of the human
intellectual structure.
 In physics, time is considered a fundamental
quantity meaning that it can’t be defined in
terms of other quantities such as force or
momentum because these concepts are already
defined in terms of time.
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Time
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When designing an algorithm for use in a simple game
(such as the Breakout example previously discussed) it is
more common to define time around the game’s frame
rate than in terms of seconds, minutes, hours, and so
forth.
– For most of these games, one frame is normally taken as one
second or one time-step.
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More advanced games, such as 3D first-person shooters,
require a real time system operating independently from
the game’s frame rate.
Using real time (seconds) as opposed to virtual time
(frames) is required when modeling movement and
forces without the end result being unrealistically
influenced by changes in the game’s frame rate.
Position
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Each point in 3D space can be identified in
terms of an x-, y- and z-coordinate – the
point’s spatial position.
Mass and Weight
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Mass is a fundamental concept describing an
object’s atomic mass or the amount of matter
used to make up an object.
– The physical concept of mass must not be confused
with the weight of an object.
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Weight is directly proportional to the amount of
gravitational pull exerted upon the mass of an
object, for example, a person might weigh 80
kilograms on earth but will only weigh about 14
kilograms on the moon.
– The mass of this person will however remain
constant.
Velocity
Velocity can be described as the rate of
change of an object’s position. Velocity,
measured in meters per second (m/s), has
both magnitude (speed) and direction,
and is thus described as a vector quantity.
 We use the following formula to
mathematically describe velocity (v):
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Acceleration
Acceleration is the rate of change of
velocity. Acceleration, measured in meters
per second2 (m/s2), has both magnitude
and direction, and is thus also described
as a vector quantity.
 We use the following formula to
mathematically describe acceleration (a):
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Force
Force is the physical action exerted upon an
object to accelerate it.
 There is thus a relationship between the mass of
the object, the force exerted upon it and the
resulting acceleration; and according to
Newton’s second law of motion, we can calculate
the force (F) on a body by multiplying its mass
(m) with its acceleration (a), resulting in the
following equation:
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Force
Momentum
Momentum is the product of mass and
velocity, i.e. a property inherent to objects
in motion.
 We use the following formula to
mathematically describe momentum (P):
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PHYSICS MODELING AND
IMPLEMENTATION
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Simulating Newtonian physics through the use of
quantities such as mass, acceleration, velocity, friction,
momentum, and force allows for the prediction of object
behaviour under certain conditions.
Physics modeling is generally implemented as part of a
physics engine.
Physics engines are classified into two classes: real-time
engines such as the Havok physics engine and highprecision physics engines such as those used by
scientists.
– Real-time physics engines ‘approximate’ physics modeling to
balance computational accuracy with the speed of the
simulation.
– Scientific physics engines are employed by organizations like
NASA and universities for various simulations
PHYSICS MODELING AND
IMPLEMENTATION
Linear Momentum
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Action-oriented games without collisions would simply
not work. Whether it’s a projectile fired from a weapon
striking a monster, a car skidding across the Daytona
Speedway or the player activating a switch; without the
ability to simulate one object striking another we would
simply not ‘have game.’
At the core of collision simulation is the conservation and
transfer of momentum.
Linear Momentum
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A well-known example demonstrating the
conservation and transfer of momentum is
Newton’s cradle – a device consisting of
five (or more) pendulums neighbouring
one another.
Gravitational Pull
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When looking at any early 1990s side-scrolling game,
such as Super Mario World or Commander Keen, one can
quickly see the effect of gravity on the player.
– For example, jumping vertically into the air is quickly followed by
the game character returning to its previous position.
– This is an early example of gravity in games, with modern
games modeling gravity much more closely.
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Gravity is the natural phenomenon where objects attract
each other due to each object being surrounded by a
gravitational field.
Simulating gravity in games does not
generally require advanced calculations
that involve the universal gravitational
constant or the exact mass of an object.
Gravitational Pull
[see the textbook for an example and detailed discussion].
Trajectory Paths
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Without accurate projectile simulation, we
would not be able to model bomb drops
from aeroplanes, a kickoff in a football
game, or the trajectory of a baseball after
being hit by a batter.
Trajectory Paths
Trajectory can be described as the path or
course travelled by an object.
 Calculating this path often requires the
consideration of gravitational forces,
aerodynamic factors, wind shear, etc.
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– For most game-based implementations we’ll
assume uniform gravity while negating wind
and other aerodynamic factors.
[see the textbook for an example and detailed discussion].
Friction
Friction, stemming from electromagnetic
forces between atomic particles, is an
energy-consuming force between two
objects in contact.
 The most common form of friction is
known as Coulomb friction.
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[see the textbook for
an example and
detailed discussion].
Introduction to Object Collisions
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The game Asteroids illustrates the basic problem
of collision detection and response in one of the
simplest forms possible.
Introduction to Object Collisions
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The game Breakout features a ball that can either
bounce from the boundaries of the game window or
movable paddle while also destroying bricks upon
collision.
Bouncing the ball off the screen boundaries requires very
basic collision detection mainly because we already know
where the boundaries of the screen are while at the
same time only considering collisions with two horizontal
and two vertical edges.
Also, an object such as the
ball in Breakout will always
reflect at an angle equal and
opposite to its initial incoming
angle.
Introduction to Object Collisions
[see the textbook for an example
and detailed discussion].
PARTICLE SYSTEMS
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A particle system is a graphics subsystem
used to simulate certain natural
phenomena such as fire, smoke, sparks,
explosions, dust, magic spells, trail effects,
etc.
PARTICLE SYSTEMS
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Particle systems are usually implemented
using three stages:
– the setup stage
– the simulation stage
– the rendering stage.
[see the textbook for an
example and detailed
discussion].