How to figure out a graphs function

Question

I'm trying to figure out how to time an animation in CSS, and all I have to work with is this image with some graph-plots of the animation-speed.

I did have some calculus 10 years ago, but the knowledge of deducting a function from a graph (if I ever learned that), is long gone. Can someone help me along the way please?

Question

What I need is a function of x to calculate y, that I can use in all three examples (they are all the same, but condenced in the x-direction).

Even though the illustration starts with 1, I guess it would be easier to have 0 as the origo as it tends to be in graphs :)

Google material image-load animation (http://www.google.com/design/spec/patterns/imagery-treatment.html#imagery-treatment-image-load)

Would something like $\frac1N x(b-x)e^{-ax}$ suit? Example... — draks ..., Jul 11 '14 at 06:13
That would be perfect! Write it out as an answer, and I'll accept it. How did you do that? :) — Yngve B-Nilsen, Jul 11 '14 at 06:40
Your shapes could also be obtained as $ax(b-x)^n$ with $n\ge 2$. — Lutz Lehmann, Jul 11 '14 at 06:55

score 0 · Accepted Answer · answered Jul 11 '14 at 07:41

0

Your graph looks like something like $$ \frac1N x(b-x)e^{-ax} $$ would suit your needs, where $N$ is a normalization factor: $N=\frac{e^{-ab}(2+ab)+(ab-2)}{a^3}$

answered Jul 11 '14 at 07:41

draks ...

18,449

How to figure out a graphs function

1 Answers1