681 Introduction to Computer Graphics

1
Interpolation and Basic Techniques
Interpolation
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) z h(u)
Parametric form P P(u) (x,y,z)
Space-curve
P P(u) 0.0 ltult1.0
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
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
t2
t1
time
12
Ease-in/ease-out
acceleration
t1
t2
time
13
Ease-in/ease-out
distance
Linear segment
(arclength)
time
Sinusoidal segments