Is it possible to determine if two segments intersect by looking at their domain and range?
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Is it possible to determine if two segments intersect by looking at their domain and range?
I’m assuming you’re talking about domain and range as intervals of the x and y axis on a 2d plane. In that case, the domain and range of the segment only define rectangular regions of the plane. For the same rectangular regions, the segments will sometimes intersect and sometimes not, depending on their orientation:
So this is a counter-example to your assertion. There is however something useful that you can do with the bounding boxes (domain and range) of the segments. You can “trivially reject” them as not possibly intersecting if their bounding boxes don’t intersect.