In which quadrant is a point?

Hi

I have a 'circle' with irregular perimeter. Somewhere within that circle is a point. The circle is divided into 4 quadrants by 2 lines 45 and 135 degrees to x- axis.I know the coordinates of the point. How can I find exactly in which quadrant it lies?

Thank you

Answer 1

[Torsten]

The four quadrants are characterized by the following conditions (if the center of the circle is at (0,0)):

I quadrant: y<=x, y>=-x
II quadrant: y>=x y>=-x 
III quadrant: y<=x, y>=-x 
IV quadrant: y<=x, y<=-x

Use an if-statement to determine which quadrant the point under consideration is in.

Best wishes

Torsten.

[Timur Navruzov]

Thank you

Answer 2

[Thorsten]

If cx, cy is the center of your circle, you first determine the angle between point px, py and relative to the center:

 alpha = atan2(py-cy, px-cx);

Ensure that the angle is in the range [0,2*pi]:

if alpha < 0, alpha = alpha + 2*pi; end

The 45deg slice (== pi/4) that holds your point has the number

Oc = floor(alpha/(pi/4));

Numbers range from 0 to 7 counter-clockwise and start with the octant 0 to the right of the center.