CAD tip # 8962:

The add-in application SphereProj can be downloaded - like the other CAD Studio's freeware tools - from Download. Load it with APPLOAD and the run the SphereProj command. After you enter the sphere radius, the command marks a rectangular area that will be projected to the sphere (at 0,0,0). Any curve drawn in this area can be be transferred (projected) to the sphere surface (the horizontal axis of the rectangle will become the "equator" on the sphere, its upper and lower edges will become the north a south "poles"). The 3D projection respects the color of the original 2D curve. You can specify the precision of the conversion - the number of segments that the original curve(s) will be divided to.