April 9th, 2005

Composed Me

Graphing Functions

I tried all yesterday evening to make a graphing function that will make it easy to plot a curve that made upgrading a stat easy at first but then as it reaches peak it becomes harder until it maxes out.

Each stat starts at a base, can be upgraded a max number of times (steps), and up to a max number (starts at 10 and, after being upgraded 20 times, maxes out at 100). The most I can come up with is f(x)=sqrt(x/steps)*(max-base)+base, but that seems too steep at first and slows down too much later.

Below is a graph of the function I wrote, and below that is a picture of what I want the curve to be more like.

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The things I want to be able to control are the base, steps, peak, and max. So far, I've only gotten control of the base, max, and steps, but not the peak. Le suggested using a circle, but the curve is too sharp on a basic circle. (Increasing from 10 to 100 in 20 steps, the first step increases by 20 and the last five steps barely increase by one point)

Anyone have any suggestions?
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