Does the order of steps 1 and 2 matter?

It's easier to project the point into the plane of the triangle first since we're building off of the subroutines we figured out before (e.g. point in half-plane test to determine if a point is inside a triangle). We also know that the closest point on the triangle has to be in the plane of the triangle, so we can work in the easier 2D space as opposed to 3D.

@skim: Can't we still do the half-plane test without the projection?

@dannycho7: In the 3D space it would be a half-space test (where you're partitioning R^3 into 2 spaces). I think mathematically it prob wouldn't be too much more complicated though.