Geometric transformations of plane to sphere?

Question

Geometry

There is a flat image - a geographical map of the Earth. With the help of what transformations and transformation matrices, you can visually give it volume in the form of a spherical shape. That is, to transform a two-dimensional image so that it is stretched over a sphere, or the sphere is behind the image and bulging out, gives the center of the plane a spherical shape.
What is the name of this type of projection/transformation, what can you read specialized on this topic?

Answer 1

You need to start with a clear understanding of what is primary and what is secondary.
The primary terrain is on a sphere (in fact, on an ellipsoid ). The map (flat) is secondary. To depict the area on the map, various map projections are used. They were invented a lot. Check out:
https://ru.wikipedia.org/wiki/List_cartographic...
To return a flat image to a spherical shape, you just need to apply the reverse transformations to those that were done when transferring to a plane. And for this you need to correctly determine in which projection your map is made. Beyond that, it's just math.