Tutorial: Animate 3D paths around the world

I kept seeing this request on the forums and while it felt like it should be possible in After Effects, I couldn't see a way to do it without needing to spend additional money.

This method uses After Effect's native Advanced 3D renderer, Expressions and Shape layers to let you create and animate arcs from one point to another.

The expressions used look complicated, but really just boil down to school trigonometry. Using Cosine and Sine equations, I was able to create Latitude and Longitude that allow me to move a null object anywhere on the imported 3D model of the Earth. Then using parenting, 3D layers and the Length and LookAt functions, I can add a shape layer that has its anchor on one null and has its other end on the other. With that, it's a simple matter to add Trim Paths and extrude the geometry. And if that sounds complicated, don't worry because I cover how to do it all in just 10 minutes.

Once done, you will be able to create flight paths or travel lines for a world map (or should that be a world travel map ?), rocket launches or a novel way to depict connections between countries.