Requesting Help: Smooth Keyframe Interpolation Alg

I use parametric animations.
That is: normalize start and end situations (start = 0, end = 1) e.g. (millisecs() - startTime) / float(duration)

and then use the parameter to animate.
Then you can bias the parameter to ease-in or out the animation.
I hope this is what you mean.

example:

SuperStrict

Graphics 800, 600, 0

'In this example I will use elapsed time as a parameter.
'The tween will take fDuration milliseconds
Local fDuration# = 3000.0	'3000 millisecond
Local iStart% = MilliSecs()

Local fp#				'fp is the animation parameter
Local fStartX# = 50		'start at 50,550
Local fStartY# = 550
Local fTargetX# = 750	'move to 750,50
Local fTargetY# = 50


While Not KeyHit(KEY_ESCAPE) 	'press Esc to quit
	Cls
	'use elapsed time to calculate parameter
	'you can use whatever you like: number of frames, MouseX(), the hue of a color, the number of characters typed in a string, etc.
	fp = (MilliSecs() - iStart) / fDuration
	
	If fp >= 1 Then		'restart animation
		fp = 1
		iStart = MilliSecs() 
	End If
	
	'select one of the bias functions
'	fp = BiasIn(fp) 	'accelerate
'	fp = BiasOut(fp)	'decelerate	
'	fp = BiasBoth(fp)	'well.. accelerate and decelerate
	
	'use parameter to find the 'inbetween' positions
	Local fx# = fp * (fTargetX - fStartX) + fStartX
	Local fy# = fp * (fTargetY - fStartY) + fStartY
	
	'draw an oval at calculated x,y position
	DrawOval(fx-20, fy-20, 40, 40)
	Flip
Wend
	
End

'there are a lot of bias functions suitable. I've chosen these...
Function BiasIn#(fp#) 
	Return Sin((fp - 1) * 90) + 1
End Function

Function BiasOut#(fp#) 
	Return Sin(fp * 90)
End Function

Function BiasBoth#(fp#) 
	Return (- Cos(fp * 180) + 1) / 2.0
End Function