Little planets effect (小行星特效)

I got a task to implement this effect recently.
Before it's assigned to me, there was a fragment shader in the codebase to handle this effect.
But the view angle can not be rotated.

So I try to "google" whether there is any information about it.

Then I found this page .

It's a way to project a sphere to a plane.

It's called "stereographic projection";

Φ = asin( cos(c) sin(Φ₀) + (y sin(c) cos(Φ₀) / r )

λ = λ₀ + atan( x sin(c) / (r cos(Φ₀) cos(c) - y sin(Φ₀) sin(c) )

I can use the above equation to calculate the position correspond to the x,y coordinate on the plane. 

After I adjust the fragment shader by the equation, the user can watch this planet at any angle.

It's quite interesting to try the OpenGL shader, I can generate such amazing results by a few lines of code.

By the way, if you would like to try such kind of effect by your self, you can download  Insta360Player.

If I didn't find a way to implement the little planets effect, I will try to decompile it's apk.