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I'm considering the planar BSP problem, where we are required to partition a set of disjoint line segments in the plane, such that every region in the partition contains at most one line segment or a portion of one line segment.

My question is: is there a way of partition these line segments such that no line segment is split into more than one region?

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The answer is "No". Please see a counterexample below: 3Segments

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