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
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