How to draw a globe in 2D?

Question

I want to draw such globe:

Let's say my input params are:

• center (x,y)
• radius
• number of meridians
• number of parallels.

I know such concepts as:

• 2D ellipse equation
• 4x4 projection matrix for 3D -> 2D perspective projection

I looked at Wikipedia's list of map projections, in many of them parallels are lines instead of curved lines.

Do you know which approach is the most simple for this problem? How to choose formula for each meridian/parallel?

Thanks in advance.

Answer 1

A relatively simple option (though doesn't seem to be exactly your case) is the stereographic projection. https://en.wikipedia.org/wiki/Stereographic_projection. It is a central projection onto a meridional plane, with the projection center on the sphere.

The meridians and parallels are all circular arcs (in fact Apollonius circles https://en.wikipedia.org/wiki/Circles_of_Apollonius#Circles_sharing_a_radical_axis). They keep meeting at right angles.