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Computer Science 385.3
Term 1, 2006
Tutorial 3
Assignment 4 – Special Effects
Assignment 4 – Special Effects
Implement Special Effects for your virtual world.
A Few Options:
-Particle Systems
-Spring-Mass System
-L-Systems, Fractals
-Advanced Geometry (NURBs)
-True Transparancy
-Shadows
Assignment 4 – Special Effects
Particle Systems:
-Simple animations can simulate many effects.
-Demos: fireworks, ParticleCannon
-Store information on a set of particles, and use some sort of
simulation to move them through the world.
particle
{
vector position; // current x,y,z position
vector velocity; // current direction of particle
vector force; // the force acting on the particle.
int alive; // indicates how long particle has been active
int lifespan; // indicates how long particle will exist
float mass; // mass of particle, useful for calculations
rgb color; // color of the particle.
}
Assignment 4 – Special Effects
Particle Systems:
-Must use some sort of integration to simulate the motion
of the particles.
Euler integration should be called at each timestep:
euler_update()
{
for each particle
{
currentParticle.position += timestep * currentParticle.velocity;
currentParticle.velocity += timestep * currentParticle.force/mass;
}
}
Assignment 4 – Special Effects
Particle Systems:
-Can use different sets of dynamics to apply force to the
particles, in order to simulate effects like ballistic motion,
spreading, anti-gravity, or many more.
Perform Ballistic Motion at each timestep:
ballistic_motion()
{
for each particle
{
particle.age += timestep;
if (particle.age > particle.lifespan)
{
expire(particle);
}
else
{
Apply gravity to the particle.
}
}
}
Assignment 4 – Special Effects
Particle Systems:
Can achieve a wide variety of effects, including:
-Rain
-Snow
-Fountains
-Sparks
-Smoke
-Spring-Mass
-Demos: particle
Assignment 4 – Special Effects
Spring-Mass System:
-Specific instance of a particle system where the
particles are treated as masses that are attached
together by springs. Can be used to model cloth, bone
structures, etc.
-Demo: springs
spring
{
float k;
// spring constant
float restLength; // rest length of the spring
}
The attached spring will apply forces on the masses at both ends.
Equation: Spring Force = -k * distance (distance from rest position).
Assignment 4 – Special Effects
Spring-Mass System:
-Use a different set of dynamics to calculate the forces
on each mass, based on the spring values.
spring_motion()
{
for each spring
{
// find the distance between the two masses;
vector difference = vector_difference(mass1.position, mass2.position);
float length = vector_length(difference);
force = -1*currentSpring.k * (length – currentSpring.restLength);
// normalize the difference vector to find out amount in each x,y component.
normalize(difference);
mass1.force += difference * force;
}
euler_update();
damping();
}
Assignment 4 – Special Effects
L-Systems:
Replacement grammars that have proven effective in
modeling trees and other plantlife. Similar to Turtle Graphics
(Logo), can map tokens to drawing primitives, such as lines.
-Demo: lsys
Tokens can include:
F : move a set distance in the current direction.
+/- : change current direction a set angle.
@/# : change current angle in 3-dimensions.
[/] : push/pop current state on the stack
Assignment 4 – Special Effects
L-Systems:
L-Systems also require replacement rules, which are all
applied simultaneously to the current string of tokens.
Probabilities and random values can be used to determine
which rule is used when more than one applies.
Replacement Rules could include:
F -> FFF -> F[-F][F][+F]
-Demo: Trees
Assignment 4 – Special Effects
Advanced Geometry:
Can specify parametric equations for curves in order to
achieve better control and aesthetic qualities. There are
other more advanced curves, such as splines, bezier
curves and NURBs that use a combination of endpoints
and control points to achieve smooth curves.
-OpenGL provides some functionality for these features;
see the notes for further details.
-Demo: splines
Assignment 4 – Special Effects
True Transparency:
By default, OpenGL's depth test will cull occluded objects
and ensure that only the nearest polygons are displayed.
Transparency can be achieved by pulling information out
of the depth buffer and blending color information from
all objects at a specific location.
This blending function is based on the transparency of the
occluding polygons.
Assignment 4 – Special Effects
Shadows:
Z-Buffer is notoriously poor for providing support for
shadows; only hard shadows can be achieved.
OpenGL offers this functionality using the stencil buffer.
-Demo: Shadows