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I'm new to geometry nodes and I want to do graph animation. I want to graph rises rapidly, the nearer gets to the middle high point and gets slowly down on both sides in the same way. This is what I want to get:
And this is what I've done so far:
This is what I got with it.
And I know that I won't get the middle point with this function, but I don’t care now. I tried to find an answer on the Internet, but I couldn’t find anything. How can I do it?
TL;DNR: There's a blend file at the end with a node tree that creates a mirrored sigmoid function that accomplishes what you want.
You can accomplish roughly this with this node group:
It generates this curve:
Set keyframes on the amplitude value to change the height of the curve. That's your "certain number".
The upper framed nodes create a mesh line whose range runs from 0 to whatever maximum X value you set in the range input node.
The lower framed nodes create the function you want to plot. In this case it's merely $A*sin(f*x)$ over the range set in the top part; where $A$ is the amplitude value and $f$ is the frequencey value.
By changing the Math nodes between the separateXYZ and combineXYZ nodes you can change the overall shape of the curve to the one you want.
If you want it centered on the origin, you can simply use a Transform node on the end to move it back, or do a bit of arithmetic on the x value of the coordinates to move it in the Set Postion node. I've done the later.
You're looking for a symmetric variation of the sigmoid function $$ e^x / (e^x + 1) $$
You want the negative values to be in the range of around -4 to around 4 and the positive values to be in the reverse of that range. Multiply the result by your "certain number" to get a curve that looks like your drawing.
Here's a node group that gives you the negative half of the curve. Note that I've added the nodes to move the curve back so it ends on the origin.
Note that if you replace $e$ with multiples of $e$ you can make the curve more pronounced: Here I've replaced $e$ with $3e$:
Finally, by doing the curve twice, once with the x range fed to the function reversed you get this mess of nodes:
and this result:
It's designed to be symmetric and you can control the two points on the X axis using the Range input that's in the upper framed area. If you don't want symmetry you will have to do a bit of extra work.
Here's a blend file containing the final node group.
or you choose the simple way, with this very easy to understand and very easy to handle setup:
so...what you see is what you get... ;)
