Question

I have a rather simple question for you..
I feel like I should have found the answer a long time ago but somehow I can’t wrap my head around this trivial problem.

Given a vector v = (x,y) , I would like to know it’s ‘general’ orientation. That is either ‘Up’, ‘Down’, ‘Left’ or ‘Right’

A vector’s general orientation is ‘Up’ if a Vector’s orientation is between 45 and 135 degrees. ‘Left’ is between 135 and 225 degrees. ‘Down’ is between 225 and 315 degrees. ‘Right’ is between 315 and 45 degrees.

I don’t really care for the cases where the angle is exactly 45, 135, 225 or 315 degrees.

The catch is, I don’t want to use trigonometry. I’m pretty sure there’s a simple solution.

I think a solution could split the whole circle in eight. Here’s what I have so far.

if(x > 0 && y > x)
    return Up
if(x > 0 && y > 0 && y < x )
    return Right

... etc ...

Basically, I know I could find a solution. I’m more interested in your own approach to this problem.

Thanks !

EDIT : The vector used is not normalized. You can represent any vector using a pair of points. Simply pretend the origin of the vector is (0,0).

Answer 1

There is a way, indeed. All you have to realize is that if abs(y) > abs(x), then the direction is vertical, otherwise the direction is horizontal. If vertical, the sign on y will indicate up/down, otherwise, the sign on x will indicate left/right. So:

if (abs(y) > abs(x)) {
  if (y > 0) up else down
} else {
  if (x > 0) right else left
}

The 45ish angles will always go left or right.