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=1.0 u=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 time t1 t2

Rick Parent - CIS681 Ease-in/ease-out acceleration time t1 t2

Rick Parent - CIS681 Ease-in/ease-out distance time Linear segment (arclength) Sinusoidal segments