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Keyframes
Define parameter values manually at selected points in time (keyframes); let the software interpolate the values for all remaining frames (“inbetweening”, “tweening”)
Use: translation, rotation, scaling, object parameters, light parameters, material parameters, ...
Function curves
Control of ease-in/ease-out through linear interpolation (“lerp”) or spline-like curves
Demo: function curve editors of Cinema 4D and Maya
Rotations cannot be interpolated easily
Translations and scalings can easily be interpolated between keyframes, but rotations cannot, at least if one uses HPB rotation angles (one type of “Euler angles”) to do the blending: Due to the non-commutativity of rotations, the object does not rotate smoothly. (Demo in Cinema 4D). On top of that, objects may get stuck due to gimbal lock.
These problems can be overcome with other descriptions of rotations:
Rotation vectors: vectors parallel to the rotation axis and with the length corresponding to the angle
Unit quaternions
Procedural animation
Use a straight formula for a simple motion such as the rotation of a planet around the sun.
Physics-based: Compute the motion (more or less) according to the laws of physics
Particle systems: mostly “dumb”, point-like and collision-ignorant
More or less complex collision handling: rigid-body dynamics, soft-body dynamics (demo in Cinema 4D), in particular for hair/fur and cloth rendering (another demo); Physics Engines such as Nvidia/AGEIA PhysX (example 1, 2) or Intel/Havok
Behavioral animation
Let quasi-autonomous entities be controlled by scripts
Crowd, flock and herd behavior, demo
Thinking Particles, demo