Unrap a 3D curved object to a flat 2D object

[Ed McCauley]

photo below is a segment of a of 20-deg truncated cone segment. The diameter of the base of the full cone is 3.75". Can Photoshop accurately "unwrap" this into a flat 2D object?

Thanks to all who take the time to read my question...

 

[Rich54]

Unwrapping and flattening a truncated cone gives the general shape of the diagram below—specifically the arc portion shaded in gray. Photoshop has the ability to accurately draw this kind of shape, but it does not have the ability to calculate any of the required dimensions. Those calculations would need to be done externally.

• To draw this diagram in Photoshop, you first need two concentric circles with radius r1 and r2. Photoshop has a vector shape tool that will draw a perfect circle to an exact diameter that you specify.
• Once you've got concentric circles, you need to slice them at angle A. In Photoshop, draw a horizontal line through the center, representing the diameter of the outer circle. Then copy that line to a new layer and rotate it by the desired angle A.
• Using those lines as guides, you can mask away the unneeded portion of the concentric circles, leaving just the shape of the gray portion.

You will need to know the top and bottom diameters of the 3D cone, as well as the cone's height. From those inputs, you can calculate r1, r2 and angle A. These equations are shown at the bottom of the diagram and require knowledge of trigonometry and algebra. (I was a math major in college a very very long time ago, so even though I'm quite rusty, these equations are not too intimidating to me. But I can imagine most people running for the hills at the thought of calculating an Inverse Tangent.)

I got this diagram here, which also contains a more detailed mathematical derivation:

https://madebyjohn.blogspot.com/2012/01/making-cone.html