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Old 05-15-2023, 10:16 PM
Laurence Finston Laurence Finston is offline
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Originally Posted by Laurence Finston View Post
I hope someone will correct me if I'm wrong, but I've looked at these figures and can't see any mistake.
I made a mistake when I set the value `a' for setting the angle used for rotating p0 around p2. I found the circumference of the base first, but then didn't use it. The correct procedure is to take the circumference of the base, divide it into the number of sections desired, find the angle required to draw a portion of a circle of that length when rotating p0 around p2 and use that value. That is straightforward, so I'm not going to bother to update the source code or the images.

The number of sections must be >= 3, but otherwise may be freely chosen.

This will always result in a development with an angle of 180 at p2. It doesn't really matter what this angle is, because when folded together, it will always become 360. If the development is done some other way and it's less, everything else remaining the same, the cone will have a base with a smaller diameter and the angle of the lines from the points on the circumference of the base to the fulcrum (the slope) will be steeper. If it's greater, the cone will have a base with a larger diameter and the slope will be flatter.

Put another way, with a smaller angle, when folding the development together, it's pushed further into the vertical dimension and with a larger one, it's pushed less far into it. For the extreme cases, with an angle of 360, it won't be possible to fold it and it will remain flat and with an angle of 0, it will be a straight line.
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