How create a Geodesic line on the surface of a cylinder?

AZΘRÆN

ⵊ am making a decorative bead and am using a Onshape document to give a clear picture of what the disign should be. It will be a jade bead with a silver inlay. 

A GEODESIC is a term that ⵊ know from physics. It is the shortest path between 2 points on a curved surface. Think of the line that an airplanes path taces on the surface of the earth as it flies long distance. 

I'm sure that im missing a super easy way to do this, but this is new ground for me. 

Thanks for the help in advance ::D

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This is the pattern that will be engraved and inlayed



And it looks great from the front 



But when viewed off axis the fact that is a (Euclidean) projection becomes clear 





The warping of the lines is what ⵊ would like to normalize and "average" out. 

S1mon

I don't know of a super simple universal way to solve this, but in the case of a cylinder, I think you could just use the Wrap feature. The unwrapped curve would be a diagonal line for most of what you're sketching out. I'm not convinced that these would be true geodesic curves (they're actually helixes), but it might actually be what you want.
https://cad.onshape.com/help/Content/wrap.htm

EvanReese

I'd also reach for the Wrap tool for this first.

I have another thought that isn't exactly what you're asking for, but is relevant enough that it could be helpful. Freeform Spline supports faces as references, so you can create a curve that's pretty close to following a surface, which you can follow up with a Projected Curve in "Curve-to-face" mode to pull the Freeform Spline to the face. The result is a pretty interactive way to draw a curve directly on any face. Here's an example part studio. In the gif below I check "Final" to edit the spline while still seeing the resulting projected curve. I think if you use this method with a 2-point spline (i.e. line) it should end up pretty close to a geodesic.

S1mon

I don't know of a super simple universal way to solve this, but in the case of a cylinder, I think you could just use the Wrap feature. The unwrapped curve would be a diagonal line for most of what you're sketching out. I'm not convinced that these would be true geodesic curves (they're actually helixes), but it might actually be what you want.
https://cad.onshape.com/help/Content/wrap.htm

EvanReese

I'd also reach for the Wrap tool for this first.

I have another thought that isn't exactly what you're asking for, but is relevant enough that it could be helpful. Freeform Spline supports faces as references, so you can create a curve that's pretty close to following a surface, which you can follow up with a Projected Curve in "Curve-to-face" mode to pull the Freeform Spline to the face. The result is a pretty interactive way to draw a curve directly on any face. Here's an example part studio. In the gif below I check "Final" to edit the spline while still seeing the resulting projected curve. I think if you use this method with a 2-point spline (i.e. line) it should end up pretty close to a geodesic.