Flocking

1. Flocking References: http://www.red3d.com/cwr/boids/ xxx

2. What is it? • A way to simulate "herds": • Flock of birds • Flock of fish • Herd of wildebeest • A group of enemies First image: http://www.hanskellner.com/2007/03/02/dusk-flock-of-birds-video/ Second image: http://www.environment.ucla.edu/podcasts/article.asp?parentid=4002 Third image: http://virtualiansanity.blogspot.com/2010/09/lion-king-favorite-scenes.html Fourth image: http://en.wikipedia.org/wiki/Resident_Evil_4

3. Boid Representation • A generic term for a flocking character • Position () • 2D: a 2-vector (x, y) • 3D: a 3-vector (x, y, z) • Orientation • 2D: an angle (0=right, 90=up, etc) • 3D: • an angle (if your character is always generally upright) • quaternion • rotation matrix • Euler angles • … • Linear Velocity: the speed the object is moving () • 2D: a 2-vector (Δx, Δy); Usually in units/s • 3D: a 3-vector (Δx, Δy, Δz); Usually in units/s • Rotational Velocity: the speed the object is rotating • Only needed if you have independent steering. • A rotation amount per second. • Rotation matrices are hard to use here. • Quaternions are especially nice for this.

4. Boid Representation, cont. • Independent Steering? • For most characters, the orientation should match the direction of the linear velocity • Need a refresher on the math? • Sometimes, you do want a separate facing direction… • [optional] Max Speed (a scalar) • Useful to keep speed under control • Refresher (with vectors)? Image: http://www.atariage.com/screenshot_page.html?SoftwareLabelID=906

5. Steering • Adjustments to current position / orientation • Two parts: • Linear (a force, ) • Update the position / velocity like this: • (this is Newton-Euler-1 Integration; Other approaches include Runga-Kutta-4 integration, Verlet integration, …) • Note: Unless Δt is infinitely small (which it isn't), the new position won't be exactly where it would be in real life.

6. Steering, cont. • Rotational (a torque, T) • Only needed if you have independent steering • In 2D • Recall: • θ = orientation (an angle) • δ = rotational velocity (angles / s) • T = rotational acceleration (angles / s2)

7. Steering, cont. • Rotational (a torque, T) • In 3D (I'm using quaternions for orientation, etc) • Recall: • Q = orientation (a quaternion) = [w, ] • δ = rotational velocity (a quaternion, rotation is in angles/s) • T = rotational acceleration (a quaternion, rotation is in angles / s2) • Note, to "combine" two quaternions you multiply (like you do with matrices), not add.

8. Flocking overview • Every frame: • Generate 0 or more steerings (force vectors) • From a set of low-level behaviors • Seek • Flee • Wander • Avoid-another-boid • Align • Obstacle-avoid • Each force vector is created considering only that behavior • Combine these steerings into a single force vector • Apply it using the position-/velocity-update formula.

9. Low-level behavior: Seek max_accel

10. Low-level behavior: Flee max_accel

11. Low-level Behavior: Wander • Approach #1: • Add random.uniform(-m, m) to heading. • Generate a force vector in this direction • Problem: tends to be "jittery" • Approach #2: • Every few seconds generate a new seek target. • Problem: can be abrupt. • Approach #3: • Place a target n units in the heading direction • Add random.uniform(-m,m) to it's rotation • This is relative to the heading direction • Seek towards this target • Usually a little less "jittery" • Even though the target itself is "jittery"

12. Low-level behavior: Avoid-another-boid • Simple: • If within n units, flee • More advanced: • Predict if we'll collide, and if so steer to avoid • "Problem" cases: • Moving parallel to each other -- no collision! • Intersecting paths, but no hit. • Calculating the correction force vector. • Can also consider a "cone of vision"

13. Low-level behavior: Align • Given: a direction vector. • Simple -- just accelerate in this direction!

14. Low-level Behavior: Obstacle Avoid • One approach: Usually you want to modulate the force based on distance.

15. Blending • Often, you have more than 1 steering force: • E.g. We want to take a meandering path towards a target: • Wander ~ 50% • Seek ~50% • Linear Blending • w1 + w2 + … + wn should equal 1.0 • Why?

16. Blending, cont. • Problems: • Contradictory forces (Equlibria) • Oscillating: • If you gradually adjust weights, this shouldn't happen. • Near-sightedness • E.g. taking the wrong route in a maze. • Combine this with A* to get around this. • Behaviors that should take precedence: • E.g. Wall-avoid if we're close; otherwise, 0.5 wander, 0.5 seek. • Use a decision tree.