How to convert spherical coordinates to equirectangular projection coordinates?

Question

Simplified question

How do you convert a spherical coordinate (θ, φ) into a position (x, y) on an equirectangular projection (also called \'geographic projection\')

Answer 1

hmm, i think maybe you should go one step back. Consider your camera angle (70mm ? or so). but your background image is a 360 degree in horizontal (but also vertical). Consider the perspective distortions on both type of pictures. For the background pict, in a vertical sense only the horizon is not vertically distorted. Sadly its only a thin line. As the distortion increases the more you get to the top or bottom.

Its not constant as in barrel distortion, but it depends on vertical distance of horizon.

I think the best way to realize the difference is to take a side view of both type of camera's and the target they supposed to project upon, from there its trigonometry, math.

Note that for the 70mm picture you need to know the angle it was shot. (or estimate it)