Efficient Techniques For Weighted Random Distributions In Game Particle Systems

Balancing Randomness in Particle Effects

True randomness in particle effects can often cause undesirable visual results. Spikes in density, gaps in coverage, and irregular behavior over time can damage the believability and stability of effects. Implementing weighted random distributions allows artists to guide randomness towards more predictable results.

Weighted random rolls are most applicable when controlling spatial density, lifetime variation, size ranges, rotation speed, and other particle attributes. By intelligently tuning the probability curves of these distributions, randomness is balanced with artistic control.

Defining the Problem Space

Unbounded randomness applied to particle effects often manifests as visible issues:

Table of Contents

Sparse density with large visible gaps
Spiky density with clusters and irregularity
Quickly changing behavior over the lifetime of the emitter

These visual artifacts damage believability and perceived quality. They originate from the mathematical properties of true random number generators. Most RNG algorithms aim for maximal entropy and randomness by avoiding any correlations or patterns.

Weighted random distributions provide control over the output curve shape. Common use cases include:

Smoothing spatial density of particles
Reducing lifetime and size variation
Clamping rotation rates and velocity magnitudes

Skillful use of weighted randomness balances performance constraints with artistic goals. The techniques discussed aim to grant more predictability and stability to particle effects.

Implementing Weighted Distribution

Weighted randomness is implemented by skewing the statistical distribution of random values. Higher weights make certain outcomes more likely. Consider this C++ example:

float GetWeightedValue() 
{
  float roll = GetRandom(0, 1);
  
  if (roll < 0.2) return 0.0f;
  else if (roll < 0.5) return 0.33f; 
  else if (roll < 0.9) return 0.66;
  else return 1.0f;
}

This outputs one of four fixed values, with probabilities 20%, 30%, 40%, and 10%. By tuning cutoff points higher probabilities steer the random roll towards desirable results.

For particle attributes like lifetime and velocity, this technique prevents extreme outlier values. Smooth ranged gradients are also possible by interpolating between sample points.

Choosing appropriate weight values involves experimentation. Consider which roll values have the most visual impact. Assign higher weights to clamp down on extremes. Smooth transitions using intermediary steps.

Strategies for Tuning Weights

Exaggerate weights towards extremes during early prototyping
Observe particle behavior over long time periods to identify defects
Adjust weight bias progressively to converge on desired results
Use an exponential scale for finer control over narrow ranges
Clamp problematic attributes before applying other weighting

Review effects in real-time while tuning weights. Minor tweaks can solve dense clusters, gaps, and instability over time. Gradual refinement balances overall randomness with desired aesthetic qualities.

Optimizing Lookup Performance

Weighted distribution requires additional sampling and comparisons per roll. Performance costs scale linearly with particle counts. Optimizations include:

Using Pre-calculated Tables

Store lookup tables mapping random inputs to weighted outputs. This offsets sampling costs to a one-time precompute:

float gVelocityCurve[256];

void InitLookupTable() {
  for (int i = 0; i < 256; i++) {
    float roll = i/255.0f; 
    gVelocityCurve[i] = GetWeightedVelocity(roll);
  }
} 

float GetVelocityForParticle() {
  int index = Random(0, 255);
  return gVelocityCurve[index];     
}

Table size scales quality but consumes memory. Sample sparsely for lower precision and reduced memory overhead.

Caching Results

Cache previous lookup results since particles often share attributes. Reuse caches based on emitter ID:

float lastEmitter1Velocity;

float GetVelocityForEmitter1Particle() {

  if (UseCachedValue(0.9f))  
    return lastEmitter1Velocity;
  
  lastEmitter1Velocity = LookupVelocity();
  return lastEmitter1Velocity;     
}

Probability of cache hits will vary. Balance between computational savings and cache invalidation costs.

Minimizing Unnecessary Rolls

Avoid recalculating attributes which don't frequently change:


struct Particle {
  float baseSize; 
  float size;
};

void UpdateParticle(Particle p) {
  
  if (p.lifetimePercent < 0.5f) {
    // Only vary size over first half of lifetime
    p.size = p.baseSize * LookupRandomSize(); 
  }
}

Amortize lookups over multiple frames or emitter cycles when possible. Apply intermittently and interpolate between values.

Case Studies

Weighted curves excel for effects with known desirable attributes. Three examples include:

Explosions with Radial Falloff

Explosion density should peak at the center and smoothly trail off towards the outer radii:

float weight = RemapValue(particleDistance, 0, 80, 1, 0); 
float actual Lifetime = Lerp(2.0, 8.0, weight);
float velocity = Lerp(fast, slow, weight);

Distance based weights visually hide particles further away. Interpolating lifetime and velocity scales down power towards the edges.

Non-homogeneous Smoke Plumes

Smoke density varies erratically in real turbulence. Artists temper this variance while retaining authenticity:

float turbulence = max(0, Perlin3D(position) - 0.5);  

float baseWeight = InverseLerp(-0.2, 0.2, turbulence);           
float sizeMultiplier = Lerp(2.0, 0.5f, baseWeight);

Perlin noise shifted towards zero provides input to scale size. Higher density emerges in turbulent volumes without spike outliers.

Rain Particle Size Variation

Droplet size impacts perceived rainfall intensity. A narrow distribution clamps perceived intensity:

const float sizes[] = {0.5, 1.0, 1.3, 1.5}; 
const float weights[] = {0.4, 0.3, 0.2, 0.1};

...

int index = LookupWeighted(weights);
float size = sizes[index];

Strongly biased sampling to smaller sizes mimics light to moderate rainfall. Expand and skew table for heavy downpour effects.

Achieving Believable Results

Balancing realism with stability leads to credible particle effects. Additional techniques include:

Perceptual Considerations

Leverage known visual and perceptual limits in weighting schemes:

Clamp range of intense attributes like velocity and energy
Smooth spatial gaps by narrowing emitted angle ranges
Lower contrast of distant particles by limiting size ranges

Grade attribute ranges relative to emitter proximity. Distant viewers perceive smoothed aggregate behaviors.

Maintaining Artistic Control

Retain intuitive ease of authoring by exposing curve parameters:

Expose per-attribute smoothing amounts
Visualize probability distributions in UI
Animate weightings over particle lifetime

Provide tweakable bias sliders instead of hard-coded constants. Iterate based on real-time feedback.

Debugging and Profiling

Verify effects of randomness tuning using analysis tools:

Visualize statistical output like standard deviation
Provide histogram spectrum analysis of key attributes
Overlay emitter draw bounds to pinpoint gaps
Color code particles by age to find instability over time

Quantitative and visual analytics accelerate finding and resolving defects from excessive randomness.

Conclusion

Weighted random distributions enable artists to guide particles towards desirable aggregate behaviors. By skewing probabilities and smoothing outliers, believable randomness is achieved with high performance. Mastering these techniques allows practical effects otherwise too expensive or unstable under pure randomness.