This question arises out of what I thought would be the simple task of modeling a nameplate bent around a conic surface (example) in CAD. To visualize, grab a business card and wrap it around any conic shape such as a pint glass.
How do I calculate the equation of the line formed by bending the nameplate relative to the nameplate's own coordinate system (x,y). The way the CAD package works, I have to bend the nameplate before attaching it to the surface and can use an equation to define the curve.
(assume the center of the name plate is centered between r1 and r2)
Thank you for your time!
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$\begingroup$Each of the four edges of nameplate is a geodesic and has zero geodesic curvature even after bending.
The edges need to be isometrically mapped from plane to cone lateral surface.
Lengths, angles and zero lateral curvature all get carried through.
In order to appreciate these draw a larger rectangle on a sheet of paper and roll it into a cone by hand.
The easiest way is generate coordinates on flat or plane cone development and map them onto cone by a suitable transformation/mapping plane to cone.This is to be done for four lines containing the four edges.
Each of the four nameplate edges should be Geodesics on a cone
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