How do 3D transforms of iOS views work under the hood?

When it comes to transforming a view, one can think of it as applying a calculation to each individual point of the view’s layer, such that for every (x, y, z), we obtain a new (x', y', z'). That calculation is actually a multiplication of the coordinates (x, y, z) by a matrix (good ol' linear algebra). How we construct our matrix is through the use of various types of CATransform3Ds, which we’ll now dive into.