# Is there a program similar to After Effects that lets you animate the points of a polygon according to a mathematical function?

I have some irregular polygons defined by points whose coordinates depend on a variable `r`, for example:

``````x = if(1 / sqrt(10) <= r < 1 / sqrt(5)) {
-2 r² + r sqrt(1 - r²) - sqrt(2 r⁴ - r² + 2 r sqrt(1 - r²) (2 - 2 r²) - 1) + 2
} else if(r < 1 / sqrt(10)) {
(2 (5 - r²) + r sqrt(5 - r²)) / 5
}

y = if(1 / sqrt(10) <= r < 1 / sqrt(5)) {
(r sqrt(1 - r²)) / (1 - r²) (-2 r² + r sqrt(1 - r²) - sqrt(2 r⁴ - r² + 2 r sqrt(1 - r²) (2 - 2 r²) - 1) + 2)
} else if(r < 1 / sqrt(10)) {
((5 - r²) - 2 r sqrt(5 - r²)) / 5
}
``````

I want to create a high-quality rendered video of the polygons changing shape as `r` varies, but After Effects, my normal go-to for animations, does not allow the user to control the exact positions of the points of shape layers with expressions in the way that I want. Is there an alternative animation program that supports this kind of thing?

• this is probably not on topic here you should go to vide production se. But sure animation software that can do this exist. Ones that come to mind are Maya, 3DS max, Blender etc etc. But also lots of other software too like Mathematica, Python+Matplotlib etc. although im pretty sure you can do this in after effects too but in a bit comvoluted manner. Commented Nov 15, 2022 at 20:58
• @joojaa I looked at software like Blender, but it doesn't seem like it allows you to define vertex location with functions attached to a variable slider or the like, unless I'm missing something. Commented Nov 15, 2022 at 21:27
• definitely missing the entire core of the node system. I have done this both in maya and blender no problem. Commented Nov 15, 2022 at 21:55
• Video editing and video editing software questions are generally off-topic here. Ask on Video Production Stack Exchange instead. Commented Nov 16, 2022 at 11:12