04-16-2007, 07:34 AM
...time passes...
Ok, I've got all the measurements done and the function fit. The data aren't entirely linear, but pretty close. It makes me wonder if I might be off in my measurements by 1/60th of a second on some of them. Oh well.
The function that provides the best fit is a third-order polynomial. THIS IS VALID FOR SPEEDS 1-20 ONLY! Fortunately, there aren't any other possible speeds. ;D
The function is accurate to +/- 0.5 tps (or 8 px per second). That should be good enough for most applications. Those that require more precision can use the lookup table.
Here it is:
y = ax^3 + bx^2 + cx + d
a = 0.000397348
b = -0.006289512
c = 1.808243877
d = 0.041327132
With y being the speed of the object in tps, and x being the speed of the object in MM speed numbers.
I haven't tested this yet, but given the method employed I feel confident that it worked.
Ok, I've got all the measurements done and the function fit. The data aren't entirely linear, but pretty close. It makes me wonder if I might be off in my measurements by 1/60th of a second on some of them. Oh well.
The function that provides the best fit is a third-order polynomial. THIS IS VALID FOR SPEEDS 1-20 ONLY! Fortunately, there aren't any other possible speeds. ;D
The function is accurate to +/- 0.5 tps (or 8 px per second). That should be good enough for most applications. Those that require more precision can use the lookup table.
Here it is:
y = ax^3 + bx^2 + cx + d
a = 0.000397348
b = -0.006289512
c = 1.808243877
d = 0.041327132
With y being the speed of the object in tps, and x being the speed of the object in MM speed numbers.
I haven't tested this yet, but given the method employed I feel confident that it worked.