Basic Examples (3) 

Determine if two segments intersect:

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Show a trapezoid:

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Determine if diagonal segments of a trapezoid intersect:

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Determine if the non-parallel segments of a trapezoid intersect:

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Determine if neighboring segments of a trapezoid intersect:

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Determine an edge-case degeneracy:

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Show it:

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Scope (5) 

SegmentIntersectionQ works in 3D:

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Show the lines:

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Various 2D intersections:

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Various 2D non-intersections:

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Various 3D intersections:

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Various 3D non-intersections:

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Properties and Relations (5) 

Find disjoint segment pairs from a set of twelve points:

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With timings, find all segment pairs that intersect:

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With timings, use RegionIntersection to find all segment pairs that intersect:

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Note the timing difference and compare the two results:

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Show the results:

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Possible Issues (2) 

Various bad inputs will not work:

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Degenerate overlaps are returned as intersections:

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Neat Examples (2) 

Of the 210 possible disjoint pairs of the 21 segments defined by 7 points, pick out those that intersect:

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Nine crossings happens to be the minimum for seven points. Show it:

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For 27 points, the minimal number of intersections is 6180. Set it up:

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Find the crossings:

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Show it:

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