Keyframing and Rotation Interpolation in Animation, Study notes of Fundamentals of Design

Keyframing is a technique in animation that saves time for the animator by allowing explicit thought about timing and the use of intermediary frames. The differences between keyframing and straight-ahead animation, the role of inbetweeners and inkers, and the challenges of interpolating rotations using matrices and euler angles. It also introduces alternative methods like axis-angle representation and quaternions.

Typology: Study notes

Pre 2010

Uploaded on 08/05/2009

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Keyframing
based on hand animation techniques
save time for the animator
force explicit thought about timing
[vs. straightahead animation]
animator −> inbetweener −> inker
Snow White:
$100/week −> $35/week −> $25/week
simple interpolation !=
intelligence/judgment of inbetweener
pf3
pf4
pf5

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Keyframingbased on hand animation techniquessave time for the animatorforce explicit thought about timing

animator −> inbetweener −> inkerSnow White:$100/week −> $35/week −> $25/week[vs. straightahead animation] simple interpolation !=intelligence/judgment of inbetweener

Keyframing ugly motion (as Alan showed!)F/m = a = d

2 x(t)/dt

2 => C

2 continuous

x(t) position of ballSplines for interpolation

Rotation Interpolation3x3 rigid body rotation matrix hasrows and columns that are orthonormal(unit length and perpendicular)

Rotx(90) −>Rotx(−90)point in the middle is1 0 0 00 0 0 00 0 0 00 0 0 1

simple interpolation won’tpreserve that property: objectwon’t rotate rigidly

Rotation−−Euler Anglesfixed order rotation aboutx,y,z = (17,42,89)if axes become aligned thenrepresentation breaks down: gimbal lockx,y,z = (0,90,0)

incremental changes in either x or zhave the same effect on the system.A degree of freedom has been "lost."

z x y Rotx(0)

z yx Roty(90)

z yx Rotz(0) x,y,z = (90,90−

∆,90)

will allow rotationby^ ∆^

about vertical axis.

angle and axis (x,y,z)[sin(

θ/2)(x,y,z), cos(

θ/2)]

Axis/Angle or Quaternions