I need to sort a set of vectors in circular order. The simplest approach would be to use the angle between the vectors and a fixed axis. To get the angle, one would have to normalize the vectors which includes performing an expensive square root calculation.
As I want to avoid the costs and I don't need the particular angle - just some value that gives me the same order - I was wondering if there is a way to calculate a value for each vector that does not require the vector to be normalized and yields a similar value like the angle (i.e. if angle(x) > angle(y) then f(x) > f(y)
).