These animation accelleration questions have also intrigued/perplexed me
recently. I'm just now coming in at the tail-end of the discussion here, and I
see some good suggestions and explanations, better than what I've come up with
on my own.

Although not specifically what you're asking for, I did come up with a simple
way of starting off an animation's CAMERA motion at slow-to-zero speed, ramping
up to 'full speed' by the mid-point of the animation, then ramping back down to
slow-to-zero at the end:

#if(clock <= .5)
#declare my_clock = 1/2*pow(2*clock,2);
#else
#declare my_clock = 1 - 1/2*pow(2*(1 - clock),2);
#end

then just plug my_clock into your camera motions, with some appropriate
multiplier(s). This could be used for an object's motion instead. The exponent
in the pow() equations can be varied, and things will still come out right-- as
far as I've been able to determine, anyway. However, with this simple scheme,
there is never a point when the camera is moving at a constant speed; it's
always ramping either up or down.

As-is, though, it adds a bit of 'movie realism' to a moving (or panning/tilting)
camera.

Ken W.

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