Projecting Sphere to Rectangle/Square using Mercerator Projection

Question

I am learning some projection technique where we can project a 3d object like globe to a 2d. I have the 3d coordinates of points on the surface of sphere same as globe. Here is a reference where a globe can be projected on a plane using Stereo-graphic projection (https://en.wikipedia.org/wiki/Stereographic_projection) but this projection project the globe to a circle but i am trying to project sphere to a rectangle the same way as the globe is projected on a small paper (https://en.wikipedia.org/wiki/Mercator_projection).

Answer 1

Both Stereographic and Mercator projections map the globe to unbounded regions. However, the Lambert cylindrical equal area projection does map the entire globe to a rectangle.