"RusHHouR" <gee### [at] mailnu> wrote in message 
news:web.445cc6ee24781bb447d3ae5e0@news.povray.org...
> Hmmmm.... Chris! Would you mind helping me a bit more? please...?
>
> http://download.yousendit.com/75D992413B17076C
>
> If i blink in a constant rythm, it looks ok! ;)
>
> Seriously though, what needs to be added to make it move a bit smoother in
> both directions? I dont understand this code (which of course bothers me)
> so Im a bit afraid of trying to tweak it out of control...
>
> Used:
>

Hi,
Ah yes. My apologies. I was in a bit of a hurry at the time and should have 
tested it with a range of values. By coincidence it worked with the first 
values I tried and I just assumed I'd therefore got my maths right (an 
incorrect assumption as it turned out). Also now I've got a bit more time 
I'll try and explain what's going on a little better. (I like your animation 
by the way). The following code should work and is explained below.

// +kfi0 +kff50    Use 320*240,No AA
camera {location  <3.2,4.5,0> look_at <0.2,3.9,0>}
light_source {<30, 10, -300> color rgb 2}
#include "math.inc"

#declare MyClock = clock*5;
#declare SecondsPerCycle = 1; // One complete flap every 1 second
#declare skylt = cylinder {0,-y,0.05 pigment {color rgb <1,1,0>}}

// Calculate a number that varies linearly between -1 and +1 over the cycle
#declare CyclePosition = mod(MyClock,SecondsPerCycle)*2/SecondsPerCycle-1;

// Apply a sine function to give a value that stays out at the extremes
// for longer
#declare CycleFactor = sind(180*CyclePosition);

object {skylt
  rotate x*(CycleFactor*7.5-2.5)
  translate <0.2,3.9,0>
}

Step 1.
The clock variable changes from 0 to 1 in a linear way as POV-Ray renders 
each of the frames you tell it to render. If you use the command line 
options shown at the top of the example above, then POV-Ray will render 51 
frames and the clock passes from 0 to 1 in steps of 0.02.
MyClock is set to clock*5 to represent 5 seconds  for the animation which 
would represent about 10 frames per second.  The value of MyClock therefore 
passes from 0 to 5.

Step 2.
Using mod() gives the remainder after an integer division, so, the result 
passes from 0 to SecondsPerCycle, then starts again at 0 and repeats this 
'MyClock/SecondsPerCycle' times (in this case 5 times).
My first mistake was in forgetting to divide this value by SecondsPerCycle, 
which is needed to give a number that cycles from 0 to 1 and does so 5 times 
during the animation sequence.
Multiplying by 2 and subtracting 1 gives a number that cycles from -1 to 1 
in a linear way.
You could use this value to swing your sign back and forth, but it would 
give abrupt changes at the extremes of the swing, whereas a freely swinging 
pendulum slows down at the top ends of its swing.

Step 3.
A standard representation of a sine wave passes from 0 to -1 up to 1 and 
back down to 0 in the 'y' axis as the 'x' value changes from -180 to +180 
degrees (This was my second mistake where I originally had 90 degrees which 
compensated for the first mistake, but only when the value of SecondPerCycle 
was set to 2).
With a sine wave, for a given linear step in the 'x' direction, the step in 
the 'y' direction varies in a sinusoidal manner taking smaller steps as 'y' 
approaches the extremes (-1 and 1) and larger steps as 'y' passes through 
y=0. This is what you want to use for rotating your sign so that the sign 
moves less between each frame as it nears the extremes of its swing and more 
between each frame as it passes through the middle of the swing.

Step 4.
Multiplying by 7.5 makes the value pass from -7.5 to +7.5 and subtracting 
2.5 gives -10 to +5.

Hope this helps and I hope I didn't make any mistakes this time.
Any questions?  :-)

Regards,
Chris B.

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