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Interpolation and Basic Techniques

This article explores various interpolation and keyframing techniques for animation, including speed control along curves, representing and interpolating orientations, free form deformations, global deformations, and path following. It also discusses different forms of curves, such as parametric, explicit, and implicit forms, and their usefulness in testing and generating points.

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Interpolation and Basic Techniques

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  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. u=0.0 u=2/3 u=1.0 u=1/3 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 <=u<=1.0

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

  5. w=0.0 w=0.3 w=0.6 w=1.0 u=0.5 u=0.2 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

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