Question

edit

So based on the answers so far (thanks for taking your time) I’m getting the sense that I’m probably NOT looking for a Normal Distribution function. Perhaps I’ll try to re-describe what I’m looking to do.

Lets say I have an object that returns a number of 0 to 10. And that number controls ‘speed’. However instead of 10 being the top speed, I need 5 to be the top speed, and anything lower or higher would slow down accordingly. (with easing, thus the bell curve)

I hope that’s clearer ;/

-original question
These are the times I wish I remembered something from math class.

I’m trying to figure out how to write a function in obj-C where I define the boundries, ex (0 – 10) and then if x = foo y = ? …. where x runs something like 0,1,2,3,4,5,6,7,8,9,10 and y runs 0,1,2,3,4,5,4,3,2,1,0 but only on a curve

Something like the attached image.

I tried googling for Normal Distribution but its way over my head. I was hoping to find some site that lists some useful algorithms like these but wasn’t very successful.

So can anyone help me out here ? And if there is some good sites which shows useful mathematical functions, I’d love to check them out.

TIA!!!

-added
I’m not looking for a random number, I’m looking for.. ex: if x=0 y should be 0, if x=5 y should be 5, if x=10 y should be 0…. and all those other not so obvious in between numbers

alt text http://dizy.cc/slider.gif

Answer 1

Okay, your edit really clarifies things. You’re not looking for anything to do with the normal distribution, just a nice smooth little ramp function. The one Paul provides will do nicely, but is tricky to modify for other values. It can be made a little more flexible (my code examples are in Python, which should be very easy to translate to any other language):

def quarticRamp(x, b=10, peak=5):     if not 0 <= x <= b:         raise ValueError   #or return 0     return peak*x*x*(x-b)*(x-b)*16/(b*b*b*b) 

Parameter b is the upper bound for the region you want to have a slope on (10, in your example), and peak is how high you want it to go (5, in the example).

Personally I like a quadratic spline approach, which is marginally cheaper computationally and has a different curve to it (this curve is really nice to use in a couple of special applications that don’t happen to matter at all for you):

def quadraticSplineRamp(x, a=0, b=10, peak=5):     if not a <= x <= b:         raise ValueError   #or return 0     if x > (b+a)/2:         x = a + b - x     z = 2*(x-a)/b     if z > 0.5:         return peak * (1 - 2*(z-1)*(z-1))     else:         return peak * (2*z*z) 

This is similar to the other function, but takes a lower bound a (0 in your example). The logic is a little more complex because it’s a somewhat-optimized implementation of a piecewise function.

The two curves have slightly different shapes; you probably don’t care what the exact shape is, and so could pick either. There are an infinite number of ramp functions meeting your criteria; these are two simple ones, but they can get as baroque as you want.