<p>I have some irregular polygons defined by points whose coordinates depend on a variable <code>r</code>, for example:</p>
<pre><code>x = if(1 / sqrt(10) &lt;= r &lt; 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 &lt; 1 / sqrt(10)) { 
        (2 (5 - r²) + r sqrt(5 - r²)) / 5
    }

y = if(1 / sqrt(10) &lt;= r &lt; 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 &lt; 1 / sqrt(10)) {
        ((5 - r²) - 2 r sqrt(5 - r²)) / 5
    }
</code></pre>
<p>I want to create a high-quality rendered video of the polygons changing shape as <code>r</code> 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?</p>

CC BY-SA 4.0
2022-11-15T14:22:09.660Z
you can do this kind of thing in Blender: https://blender.stackexchange.com/questions/63697/how-can-i-generate-an-object-from-a-mathematical-function
tomh
CC BY-SA 4.0
2022-11-15T14:47:46.740Z
@tomh The linked question appears to be about creating a 3D surface according to an implicit function. It doesn't look like Blender allows defining individual vertex coordinates of a 2D shape with an animating function. Am I missing something?
Lawton
<animation><software-recommendation>
Is there a program similar to After Effects that lets you animate the points of a polygon according to a mathematical function?
Lawton
# Is there a program similar to After Effects that lets you animate the points of a polygon according to a mathematical function?

(Asked by: username_0 on 2022-11-15)

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?

**Tags:** animation, software-recommendation

> **Comments:**
> **username_1**: you can do this kind of thing in Blender: https://blender.stackexchange.com/questions/63697/how-can-i-generate-an-object-from-a-mathematical-function  
> **username_0**: @username_1 The linked question appears to be about creating a 3D surface according to an implicit function. It doesn't look like Blender allows defining individual vertex coordinates of a 2D shape with an animating function. Am I missing something?  

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## 0 answers

