How to correctly compare ranges of angles?

Question

Algorithms

Two sectors are given: from angle A1 radians to angle A2 radians, and from angle B1 radians. up to B2 rad.
It is necessary to determine whether they have intersections.

How to solve it correctly-beautifully?

Something stalled with uncertainties when the angle can be set both as 7 * PI / 4, and it is also as -PI / 4.

illustration

The angles from the X-axis to the rays OA, OB, OC and OD are given.
Interested in whether the AOB and COD ranges intersect.

For unambiguity, each range can be considered a given angle of its bisector and half-width.

How to "correctly" normalize values?

Answer 1

One of the solutions. Let the sector A be described by an ordered pair {A1,A2}, i.e., A sector is the area obtained by going around the circle in a clockwise direction from point A1 to point A2.
1. Bring the values ​​of all angles to the range from [0, 2pi).
2. If A1 > A2, then split the sector into two: S1 = [A1, 2pi) U [0, A2].
3. Using the set algebra and the algorithm of intersection of ordinary segments, one can find the intersection:
[A1, A2] ∩ [B1, B2] - the usual algorithm
( [A1, 2pi) U [0, A2] ) ∩ [B1, B2] = ( [B1, B2] ∩ [A1, 2pi) ) U ( [B1, B2] ∩ [0, A2] ) - for each of the intersections, the usual algorithm
( [A1, 2pi) U [0, A2] ) ∩ ( [B1 , 2pi) U [0, B2] ) - it is obvious that they intersect at least at the point 0

Answer 2

Something stalled with uncertainties, when the angle can be set both as 7 * PI / 4, and it is also as -PI / 4

The easiest way to avoid slipping with uncertainties is to normalize the input values ​​and continue to work with pure arithmetic