Interpolation and Basic Techniques Interpolation Speed control along

Interpolation and Basic Techniques Interpolation Speed control along curve Representing and interpolating orientations Path following Keyframing Animation languages Free form deformations Global deformations Rick Parent - CIS 681

Curves Explicit form: y = f(x) Implicit form: 0 = f(x, y) Parametric form: x = f(u) y = g(u) Good for testing points or good for generating points? Rick Parent - CIS 681

Curves Parametric form: P = P(u) = (x, y, z) x = f(u) y = g(u) z = h(u) u=0. 0 u=2/3 u=1. 0 u=1/3 Space-curve P = P(u) 0. 0 <=u<=1. 0 Rick Parent - CIS 681

Curves Interpolation v. approximation Hermite Computational complexity Bezier Expressiveness Catmull-Rom Local v. global control Blended parabolas Continuity B-splines, NURBS Rick Parent - CIS 681

Space-Time Curve w=0. 0 w=0. 3 u=0. 2 w=0. 6 u=0. 5 w=1. 0 Given arclength* w, find u such that P = P(u) where w = arclength(P(0. 0), P(u)) * relative arclength Rick Parent - CIS 681

Arc Length **put in definition of arclengh** Rick Parent - CIS 681

Arc Length **calculating arc length by over sampling** Rick Parent - CIS 681

Arc Length **calculating arc length by Gaussian quadrature** Rick Parent - CIS 681

Controlling Motion Along a Curve Rick Parent - CIS 681

Ease-in/ease-out distance time Rick Parent - CIS 681

Ease-in/ease-out velocity t 1 t 2 time Rick Parent - CIS 681

Ease-in/ease-out acceleration t 1 t 2 time Rick Parent - CIS 681

Ease-in/ease-out distance Linear segment (arclength) time Sinusoidal segments Rick Parent - CIS 681