2.3 Particle Dynamics
A particle's position in each succeeding frame can be computed by knowing its velocity (speed and direction of movement). This can be modified by an acceleration force for more complex movement, e.g., gravity simulation.
A particle's color can be modified by a rate-of-color-change parameter, its opacity by a rate-of-opacity-change parameter, and its size by a rate-of-size-change parameter. These rates of change can be global, i.e. the same for all particles, or they can be stochastic for each particle.
2.4 Particle Extinction
When a particle is created it can be given a lifetime in frames. After each frame, this is decremented and when the lifetime is zero, the particle is destroyed. Another mechanism might be that when the color/opacity are below a certain threshold the particle is invisible and is destroyed. When a particle has left the region of interest, e.g., is a certain distance from its origin, it could be destroyed.
2.5 Particle Rendering
Particles can obscure other particles behind them, can be transparent, and can cast shadows on other particles. They can also interact with other, conventionally modeled primitives. In this system the authors made two assumptions. The first was that the particle systems do not intersect with other primitives (so the rendering system only has to handle particles). The other objects in a scene are rendered separately and then composited with the particle system images. If the particles do interact with other objects, e.g., go behind them, then the images are divided into sub-images which are composited.
A second approximation is that the particles are light sources, that additively combine according to their color and opacity values. This eliminates the hidden surface problem since particles do not obscure each other but just add more light to a given pixel. It also eliminates shadows.