Now that we have a way to plot great circles on to equirectangular planes, how do we use that to detect the pitch and roll of the camera and consequently stabilise the video?

This post will be a bit mathematically involved. Bear with me. Projections Let’s jump right into the math. The formula for projecting any point in latitude, longtitude to its (x,y) equivalent on a rectangular plane is: x = λcos(φ1) y = φ λ is the longitude; φ is the latitude; φ1 are the standard parallels (north and south of the equator) where the scale of the projection is true; x is the horizontal position along the map; y is the vertical position along the map.

For an internal project at my company, I was asked to write code to draw great circles projected on to an equirectangular plane. Why this is useful I will discuss a little later, but first, what exactly are great circles? great circle on Earth A great circle is the largest circle that can be drawn on any given sphere. Every circle in Euclidean 3-space is a great circle of exactly one sphere.