Ellipsoids are spheres that have been stretched about one or more axes.
The Kabsch Algorithm finds the optimal translation and rotation that minimizes the distance between two sets of matched points.
A rotation matrix is really just an orthonormal basis (a set of three orthogonal, unit vectors representing the x, y, and z bases of your rotation).
One of my favorite functions projects points onto line segments.
Orthogonal Regression is the process of finding the line that best fits a set of points by minimizing their squared orthogonal distances to it.