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Calculating the correct angle needed to bend a plane into a "cylinder shape".

I have a 5x5 diamond plane that when I bend it 396 degrees it becomes a "cylinder shape" 5x5

Another diamond grid 15x15 requires 372 degrees for it to close.

bend2 How can I calculate the angle (using a formula) I would need to bend other diamond planes into a "cylinder shape"

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  • $\begingroup$ related blender.stackexchange.com/questions/199064/… $\endgroup$
    – lemon
    Nov 13 '20 at 13:52
  • $\begingroup$ @lemon yes it is similar but I noticed if I change the diamond shapes the angle required is different I'll post a animation and add it to the question. $\endgroup$
    – Rick T
    Nov 13 '20 at 13:57
  • $\begingroup$ yes... just noticed this was your question... : ) $\endgroup$
    – lemon
    Nov 13 '20 at 13:58
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    $\begingroup$ Either it is a linear relationship and you can use linear regression by mapping the difference in shape (only one parameter must vary) and the resulting angle. Or it's another thing and you would need good old mathematics. Could you elaborate on what parameter changed between your 2 tests ? $\endgroup$
    – Gorgious
    Nov 13 '20 at 14:34
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    $\begingroup$ According to linear regression the formula is angle = -2.4*(number of rows) + 408 °. Can you test it out with another number of rows ? $\endgroup$
    – Gorgious
    Nov 13 '20 at 14:49
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It is just linear, it seems

enter image description here

If it is for N diamonds in the line above, then the angle is:

360 * (1 + 1 / (2 * N))

as we need to fill one half one diamond plus these N.

Or to say it another way, this is the ratio of the size considering the half diamond by the size without it x the angle.

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