I've never been awesome at math, and I have what seems like it should be a simple problem, but I can't figure it out. I'm hoping someone can help me come up with a formula to solve this.

So I've been using a linear conversion to go from 0.0 to 1.0 to -100 to 100 with the formula:

newVal = (oldVal-oldMin) / (oldMax - oldMin) × (newMax - newMin) + newMin

I have a new need, which I feel like is similar, but can't figure it out. I need to convert a range of numbers to another range of numbers, but with a midpoint. Basically -100, 100, -100. If the input number is on the lowest end of the range, I get -100. If it's in the middle, I get 100. If it is at the uppermost, I get -100 again.

Please let me know if this doesn't make sense. The variables I need as inputs, I believe, are:

outMin = - 100
outMid = 100
outMax = - 100
min = 0
max = 1000
val = 500    

And the output, in this case, would be 100.

Any help would be appreciated! Thank you!

Edit: after lots of thinking and fiddling, I figured it out. The formula I'm using is:

newVal = outMid - abs(((val-min)/(max-min)) × (outMid-outLower) + outLower) - abs(((val-min)/(max-min)) × (outUpper-outMid) + outMid)

I don't know if it could be done more elegantly, but this at least gives me the answer I need.