Rick Parent - CIS681

Interpolation and Basic Techniques

Representing and interpolating orientations

Interpolation

Speed control along curve

Path following

Keyframing

Animation languages

Free form deformations

Global deformations

Rick Parent - CIS681

Curves

Explicit form: y = f(x)

Implicit form: 0 = f(x,y)

x = f(u)

y = g(u)Parametric form:

Good for testing points or good for generating points?

Rick Parent - CIS681

Curves

Space-curve P = P(u) 0.0 <=u<=1.0

u=1/3

u=2/3

u=0.0

u=1.0

Parametric form: P = P(u) = (x,y,z)x = f(u)y = g(u)z = h(u)

Rick Parent - CIS681

Curves

Local v. global control

Computational complexity

Continuity

Interpolation v. approximation Hermite

Bezier

Catmull-Rom

Blended parabolas

Expressiveness

B-splines, NURBS

Rick Parent - CIS681

Space-Time Curve

Given arclength* w, find u such that P = P(u)

where w = arclength(P(0.0), P(u))

w=0.3 w=0.6

w=0.0

w=1.0u=0.2 u=0.5

* relative arclength

Rick Parent - CIS681

Arc Length

**put in definition of arclengh**

Rick Parent - CIS681

Arc Length

**calculating arc length by over sampling**

Rick Parent - CIS681

Arc Length

**calculating arc length by Gaussian quadrature**

Rick Parent - CIS681

Controlling Motion Along a Curve

Rick Parent - CIS681

Ease-in/ease-out

distance

time

Rick Parent - CIS681

Ease-in/ease-out

velocity

timet1 t2

Rick Parent - CIS681

Ease-in/ease-out

acceleration

timet1 t2

Rick Parent - CIS681

Ease-in/ease-out

distance

time

Linear segment(arclength)

Sinusoidal segments