Body: <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>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-15T14:22:09.660Z
Comments.Text: 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
Comments.UserDisplayName: tomh
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-11-15T14:47:46.740Z
Comments.Text: @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?
Comments.UserDisplayName: Lawton
Tags: <animation><software-recommendation>
Title: Is there a program similar to After Effects that lets you animate the points of a polygon according to a mathematical function?
UserDisplayName: Lawton
ThreadText: # 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?  
  
  ---
  
  ## 0 answers
  
  