Need "Is the point in the pie?" in SQL

Question

In my SQL Table pie_on_coords, I have following

  id  |  direction_angle  |  pie_angle  |  position_x  |  position_y  |  pie_radius

Entries correspond something like this:

I supposed to find entries, which cover given point (x,y)

But how?

Answer 1

Check is polar coordinates (r, phi) of point (x, y) - (position_x, position_y) in ([0,pie_radius], [direction_angle - pie_angle/2, direction_angle + pie_angle/2]).

px = x - position_x
py = y - position_y
r = sqrt( px^2 + py^2 )
phi = atan2(py/px)

Point is in if:

r <= pie_radius
direction_angle - pie_angle/2 <= phi <= direction_angle + pie_angle/2

Take a care if direction_angle - pie_angle/2 < -pi or direction_angle + pie_angle/2 > pi.