CO1301: Games Concepts Dr Nick Mitchell (Room CM 226) Material originally prepared by Gareth Bellaby Lecture 15 Particle Systems

Particle systems  A particle system is a simulation of phenomenon such as smoke, rain or fire as a set of discrete particles.  Discrete means separate.  The different type of effects are created by changing:  textures  blending  colour  physics of the system

Efficiency  Typically quads are used:  Faster than a model with depth.  Orientated towards the camera so that they always appear 3D.

Emitters  A particle system has an emitter.  Particles come out of the emitter.  They have an initial velocity.  They have a lifetime.  This could be dependent upon time (e.g. die after a certain point) or location (e.g. die when they hit the ground)  You could re-use a particle after it has died. A particle that has died is re-emitted. In this way the particles cycle around and around. A system has been created.

Basic physics of the system  The central concept is that particles have an initial velocity, and then gravity is then applied to them.  Gravity will change the velocity of the particle over time.  Different particles in the system will be moving at different speeds.  Gravity only affects the y-component.  You could apply other forces:  e.g. drag because of air resistance.  swirling because of wind.

Types of particle systems  The appropriate physics is applied to the particles.  No hard and fast rules:  It is a matter of aesthetics and the effect you want to achieve...

Fountain  Single point emitter.  Particles are emitted in a small fan.  Fast initial velocity.  Blue particles  Blend so that overlaid textures darken.  Physics is an initial velocity outwards. Gravity then pulls the particles downwards.  Gravity causes them to fall after a period.  Destroyed when hit the ground.

Smoke  Single point emitter  Grey particles.  Blend so that overlaid textures darken  Smoke gently rises (because smoke is light and the emitter is a heat source)  The air is hot so it rises and the smoke is light and gets carried along.  A small amount of gravity.  Destroyed after a certain amount of time.  Could use swirling, e.g. employ noise.

Rain  Surface emitter  Grey particle.  Maybe use a streak.  Blend with high transparency.  Probably little or no overlay.  Drop downwards with a constant velocity.

Fire  Red/yellow particles  Blend so that overlaid textures lighten.  Single emitter  Short lifetime.  Higher velocity.  Die quickly.

Explosion  Red/yellow particles  Single emitter.  May all be emitted at same time. Some may be delayed.  Emitted in all directions or in a wide fan.  High velocity.  See Steve Rabin, "Powerful Explosion Effects Using Billboard Particles", Game Programming Gems 5.

Particle maths  Velocity v is distance d divided by time t.

Particle maths  Constant acceleration is the rate of change in velocity:  So after a “period of time” the new velocity will be the old velocity plus the amount of change over that time period:

Particle maths  Need to look at velocity and acceleration  Velocity is units per second, e.g. metres per second  Acceleration is units per second per second, e.g. metres per second per second  This is important when taking time into account.  Using the frame time, apply the velocity but multiply the velocity by the frame time.

Particle maths  If we want to calculate the effect of acceleration:  calculate the new velocity using the frame time  apply the velocity and again multiply the velocity by the frame time.  Note the way that frame time is implicitly taken into account twice because it is units per second per second.

Programming: data structure  We could use an array to store all of the particles  The particles cycle around  We can use a dynamic data structure such as the STL class.  The class is like a dynamic array.  Dynamic in the sense that you can change it’s size on-the-fly at run-time.  It has nothing to do with the vectors of 3D graphics despite its name.  Why not research this yourself.  I may well add it to the summer work...

Euler integration  Stateful version.  Version you will use in the lab.

Euler integration  Expressed as a position

Varying the direction  Want all of the particles to have the same initial velocity.  Nice to have the particles "fan out" from the emitter.  Random element.  Offset in the along the x-axis.  Use the maths of right-angle triangles to calculate the components of the movement vector.

Varying the direction

Closed function  There is an alternative way of thinking about the maths of particle systems.  Stateless version.  Used by Luna in his chapter on particle systems.  Simple.  Drawback is that it only uses the one acceleration: so you can't apply other physics to the particles in mid-movement.

Closed function  Do not need to record the velocity frame by frame.  Simply need the starting velocity, acceleration and the time passed since the particle was at that starting velocity.

Closed function

Maths  Want to find the average velocity over a period of time. Acceleration is a constant. Therefore can do a simple average.  Average velocity is displacement over time

Maths  These are equivalent, so let's put them together.

Maths  Can substitute one of the earlier equations into this (from slide 13)

Other variants exist  May want sometimes to employ other variants.  Also useful to combine different accelerations.  See Latta and the maths books

References  Jeff Lander, "The Ocean Spray in Your Face",  Lutz Latta, "Building a Million Particle System." In GDC 2004 Proceedings,  Lutz Latta, "Everything about Particle Effects",  More articles at his site:  John van der Burg, "Building an Advanced Particle System". erburg_01.htm

References  Van Verth, Essential Mathematics for Games and Interactive Applications: A Programmer's Guide.  Wendy Stahler, Beginning Math and Physics for Game Programmers  NVidia developers site  ATI developers site