Convert from one range to another - actionscript-3

Question

I have two sets of ranges that I need to be translated from one to the other.
The first range is -100 ↔ 100 with 0 being default.
The second range is 0.0 ↔ 10.0 with 1 being default.
I am working in AS3 with the first range and the second range is a python class and I need these numbers to line up.
I am adjusting brightness of a video in realtime with a slider. The video filter accepts values between -100 ↔ 100. I need to then take that value and pass it to a python script but it only accepts values from 0.0 ↔ 10.0
I tried this function I found on the net, but it doesn't translate the values correctly in this particular case.
private function convertRange(originalStart:Number,originalEnd:Number,newStart:Number,newEnd:Number,value:Number):Number
{
var originalRange:Number = originalEnd - originalStart;
var newRange:Number = newEnd - newStart;
var ratio:Number = newRange / originalRange;
var newValue:Number = value * ratio;
var finalValue:Number = newValue + newStart;
return finalValue;
}
Is this even possible? Hopefully my question is clear, please let me know if it needs clarification.
This is the python class I am referring to: https://github.com/dubhater/vapoursynth-adjust It uses the second range whereas AS3 uses the first range.

Answer 1

Why not trying something like this :
function from_AS_to_PY(as_value:Number): Number // as_value : -100 ----- 0 ----- 100
{
var py_value:Number = (as_value / 100);
py_value = (py_value <= 0 ? py_value : py_value * 9) + 1;
return py_value;
}
function from_PY_to_AS(py_value:Number): Number // py_value : 0 - 1 --------- 10
{
var as_value:Number = (py_value <= 1 ? py_value - 1 : ((py_value - 1) / 9)) * 100;
return as_value;
}
trace(from_AS_to_PY(-100)); // gives : 0
trace(from_AS_to_PY(-99)); // gives : 0.01
trace(from_AS_to_PY(-1)); // gives : 0.99
trace(from_AS_to_PY(0)); // gives : 1
trace(from_AS_to_PY(1)); // gives : 1.09
trace(from_AS_to_PY(99)); // gives : 9.91
trace(from_AS_to_PY(100)); // gives : 10
//---------------------------------------------------
trace(from_PY_to_AS(0)); // gives : -100
trace(from_PY_to_AS(0.01)); // gives : -99
trace(from_PY_to_AS(0.99)); // gives : -1
trace(from_PY_to_AS(1)); // gives : 0
trace(from_PY_to_AS(1.09)); // gives : 1
trace(from_PY_to_AS(9.91)); // gives : 99
trace(from_PY_to_AS(10)); // gives : 100
Hope that can help.

Answer 2

There is a fundamental difficulty with the problem. You are trying to fit three point of one range onto another range. If you were just interested in matching the two end points that would be easy you can use a linear interpolation y = 10 * (x+100) /200 or simply y = (x+100)/20 or equivalently y=x/20+5. The problem is it this does not match the default value and x=0 -> 5.
This might be the solution you want. However if it is important that he default values match you need to use a non-linear solution. There are many possible solutions. You can use a piecewise-linear solution like akmozo solution, which needs an if statement. if x<0 then y = x/100+1 else y = 1 + 9 x /100. The problem with this one is that you do not get a smooth response. Consider adjusting the slider from min to max, you see a very slow increase in brightness to start with and then it starts to increase much faster once you pass zero.
The big difference between the first half of the range and the second half suggests an exponential type solution. y = A exp(b x). Taking y = exp(x * ln(10)/100) matches the center point and the top end, the bottom end is just a little bit high at 0.1, rather than zero. This might be fine, if not you could find an exponential solution y = A exp(b x)-c which matches all three points.
Another possibility is using a power. An equation like y = A pow(x,n). A bit of calculation shows y=10 pow(x/200+0.5),3.321928095) matches all three points. The constant 3.321928095 = ln(0.1)/ln(0.5).
In the diagram the black curve is a simple linear solution. The red curve is the piecewise linear one, the green is the exponential one then the blue is the power.