1. Interpolation and Basic Techniques
Keyframing
Speed control along curve
Animation languages
Representing and interpolating orientations
Free form deformations
Global deformations
Path following

2. Curves Explicit form: y = f(x) Implicit form: 0 = f(x,y) x = f(u)
Parametric form:
y = g(u)
Good for testing points or good for generating points?

3. Curves x = f(u) y = g(u) Parametric form: P = P(u) = (x,y,z) z = h(u)
Space-curve
P = P(u) <=u<=1.0

4. Curves Hermite Interpolation v. approximation Bezier
Computational complexity
Catmull-Rom
Expressiveness
Blended parabolas
Local v. global control
B-splines, NURBS
Continuity

5. Space-Time Curve w=0.0 w=0.3 w=0.6 w=1.0 u=0.5 u=0.2
Given arclength* w, find u such that
P = P(u)
where w = arclength(P(0.0), P(u))
* relative arclength

6. Arc Length
**put in definition of arclengh**

7. Arc Length
**calculating arc length by over sampling**

8. Arc Length
**calculating arc length by Gaussian quadrature**

9. Controlling Motion Along a Curve

10. Ease-in/ease-out
distance
time

11. Ease-in/ease-out
velocity t1 t2
time

12. Ease-in/ease-out
acceleration t1 t2
time

13. Ease-in/ease-out distance Linear segment (arclength) time
Sinusoidal segments