1. Algorithmic Animation & Particle Systems

2. Key Frame Animation
Hand-drawn animation was straight-ahead (start at one position, and animate each small movement
Computer Animation is usually based on key frames – a frame for the starting position and a frame for the end position

3. Key Frame Animation
How do you calculate the frame positions in between key frames?
Interpolation: Approximation of a function between two known points

4. Why interpolation?
Attributes (position, size, color) change as a function over time
Function often given by physics f = ma
Why approximate a known function?
Solving function at certain point requires solving differential equations

5. Interpolation Idea: Don’t want to solve equation at each point
Approximate some points and connect them with
Lines
Arcs
Other functions (trig)

6. Euler Integration
Use first derivative to get the direction of the curve at a point.
Draw lines in direction of first derivative
Accuracy depends on the frequency with which you re-evaluate the derivative

7. Euler Integration

8. Linear Interpolation Use a line to connect 2 way points In C#:
Mathf.Lerp(from, to, percent)
Vector3.Lerp
Quaternion.Lerp
Color.Lerp

9. Example – Moving between way points
private Vector3 start; private Vector3 end; private float startTime; private float speed; void Start() { startTime = Time.time; } void Update() { float journeyLength = Vector3.Distance(start, end); float distCovered = (Time.time - startTime)* speed; float fracJourney = distCovered / journeyLength; transform.position = Vector3.Lerp(start, end, fracJourney);

10. More on Approximation Collision Detection:
Can’t always calculate every collision
Isolate groups of things that may collide
Approximate the result

11. Example: Hair

12. Example: Springs Hooke’s law: f = – kx k is “springiness” constant
x is extension
Also know f = ma
Spring forces act on other elements(& other springs)

13. Particle Systems Create one simple object
Objects follow rules of behavior
Many instances of the simple object create an interesting overall effect

14. Examples:
Small spheres
Fireworks
Waterfalls

15. Particle Systems:
Springs
Hair
Cloth

16. Distributed Computation
De-centralized control
Aggregate behavior emerges
Simple rules for the individual lead to complex behavior for the group
Often very natural-looking

17. Distributed Computation Examples
Braitenberg Vehicles
Light lover
Light fear
Aggression
Traffic
Patterns

18. Distributed Computation Examples
Boids: three rules
Separation
Alignment
Cohesion

19. Distributed Computation Examples
Fish
Virtual Fishtank
Xiaoyuan Tu

20. Artificial Life Ants Know “home” Look for food
If they find food source, pick it up and head home
Drop pheromones – chemicals “smelled” by antennae
Result: All food gets taken home

21. Artificial Life Termites Rules Result: food in one place
If you reach food and don’t have any, pick some up
If you reach food and have some already, put it down
Move randomly
Result: food in one place

22. Artificial Life Creatures Random joints with degrees of freedom
Try to move
Learn to move from one place to the other