Does the problem of rotating a sprite depending on the coordinate axes of movement have a solution?

Question

Mathematics

I want to write a universal function for the dependence of the rotation of the character sprite on the value of the control axes.
Namely:
We have two axes:
X (horizontal) and Y (vertical), respectively,
The angle of rotation of the sprite depends on the coordinates (see figure)
According to these data, I picked up a functional dependence, but it works only in 50% of cases (at zero points)

The resulting function in EXEL looks like:
=ABS(((A2+2)*-90)*A2)+ABS(((B2*90)-90)*-1*B2
) the only function will be in transform.rotate(0,0,FUN) (Unity code)
Is there a solution to this problem? Or you have to register the change in the angle of the sprite when you press the keys ...

Answer 1

It's not very clear (in particular: a pair of x and y can only take 8 values?), but it seems that you need the atan2 function. Just keep in mind that it, as expected, assumes that zero degrees is in the positive direction of the x-axis.

Answer 2

45*y*(2*x^2+x-2)+90*(x^2+x+1)