Line following help with acute and right angles
If you use analog processing of the photodiodes, you can get away with just two photodiodes with slightly overlapping areas so you know exactly how misaligned you are before losing sight of the line completely. But you still might want a pair of outermost sensors to catch the line if the center pair loses track. With four analog sensors in a 2x2 grid (a nearly minimal ring) and slightly overlapping fields I dont think you would ever lose track of the line

A full blown method is to use a ring of photodiodes and search where the line enters the circle and where it leaves, and remember those positions 200ms in the past so you can track which ones are which so you know if a crossover suddenly appeared or which direction is forward at sharp angles. Though if your ring has enough elements you could use phototransistors and get by without analog processing, relying on the number of elements for resolution.

The key here is not to check whether the sensors read black or white. It is to check how dark it is relative to the opposite sensor so you know exactly how much you are veering off by and to be able to do it on more than one axis.