[leowbattle]

> Almost everything can be done better ... use the stereographic projection

I was just learning about stereographic projection earlier. Isn't it odd how when you know something you notice it appearing in places.

Can you give an example of an operation that could be performed better using stereographic projection rather than angles?

[jacobolus]

Generally you can just stick to storing 2-coordinate vectors and using vector operations.

The places where you might want to convert to a 1-number representation are when you have a lot of numbers you want to store or transmit somewhere. Using the stereographic projection (half-angle tangent) instead of angle measure works better with the floating point number format and uses only rational arithmetic instead of transcendental functions.