Algorithms are given for calculating the inclinations at which total eclipses become partial eclipses and partial eclipses become grazing eclipses. It is shown that the larger star in a contact or nearly contact system is so distorted in shape that it becomes self-eclipsing, as a shallow concavity develops near the point of contact. Algorithms are also given for calculating critical values of the Roche equipotential and for calculating the coordinates of some of the Lagrangian points.