给定同一个圆的两个圆段：A = [a1，a2]和B = [b1，b2]，其中：

• a1，a2，b1，b2的值介于-inf和+ inf之间
• a1 <= a2; b1 <= b2
• a2-a1 <= 360；b2-b1 <= 360

如何确定这两个圆弧段是否重叠？（即，如果它们相交或接触至少一点）

例子：

A=[  -45°,    45°]; B=[   10°,   20°] ==> overlap
A=[  -45°,    45°]; B=[   90°,  180°] ==> no overlap
A=[  -45°,    45°]; B=[  180°,  360°] ==> overlap
A=[ -405°,  -315°]; B=[  180°,  360°] ==> overlap
A=[-3600°, -3601°]; B=[ 3601°, 3602°] ==> overlap (touching counts as overlap)
A=[ 3600°,  3601°]; B=[-3601°,-3602°] ==> overlap (touching counts as overlap)
A=[    -1°,    1°]; B=[ 3602°, 3603°] ==> no overlap

这看起来像是一个看似简单的问题，但是我无法解决这个问题。目前，我对解决方案有一个基本的想法，该方案涉及将每个线段在相交0°时分成两部分，但是我不确定是否能涵盖所有情况，并且我想知道是否有一个优雅的公式。