How to wrap design elements around a sphere?

[ozonshak]

Hello.  I'm attempting to wrap some design elements around a sphere and I'm having a hard time with it.  I've done this on curved and angled surfaces before (typically using emboss or deboss), but those typically have even surface areas (i.e. cylinder, planar angled surface, etc).  A sphere has increasing angles as you move towards the poles and that is causing my design elements to warp pretty badly into a "U" or "smile" shape.  I'm trying to embed the following on a basic sphere:

1) Wrap a line or curvy/sine wave all the way around the bottom hemisphere

2) embed simple SVG graphics on either hemisphere (top half or bottom half) - just 1 side, not all the way around

3) embed text on either hemisphere (top half or bottom half) - just 1 side, not all the way around

Does anyone have a design file that demonstrates how to do 1 or more of these that I can please take a look at?  I've been Googling around, but can't seem to find anything helpful.

Thanks in advance!

[Warmingup1953]

Cartographers have been challenged by the subtle terror of a sphere since Eratosthenes (276–194 BCE) was in short pants.

Let's see your best shot at #1. Please share the Fusion file.

[davebYYPCU]

Fusion 360 - Embossed Text on Sphere

Might help...

[ozonshak]

Yes, spheres are definitely a challenge 🙂

I've attached 2 attempts.  The first one "Sphere - design wrap" was a very basic attempt with a simple rectangle.  Doing an emboss curves the edges way up on the sides approaching the center of the sphere.  I'm looking to keep the design horizontally level around the lower half of the sphere.

For the second one "Sphere - design wrap 2", I was following this link for an example:

https://www.youtube.com/watch?v=G-9GNVpYjk4

This is definitely better, although more manual.  This could be workable if I can find a curvy wave design that meets properly on the opposing side.  I just used an extrapolation from a coil to get a sine wave.  However, it does not meet perfectly on the back side, the curves are way too steep (looking for more shallow bumps), and I had to manually "spline" this together on the back side which looks like a hot mess.  If you have any advice how to get a better, symmetric wavy pattern that connects nicely all the way around, I could probably use this approach from that link above.  It would also be nice to deboss instead of emboss here, but I could not get that working with this approach.