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What is exactly the definition of "Straddle"?

Can you please explain what do they mean exactly or a sketch? A segment P1P2 Straddles a line if point P1 lies on the one side of the line and point P2 lies on the other side. A boundary case of P1 or P2 lies directly on the line. (Taken from Introduction to algorithms 3rd)

After a couple of answers: enter image description here

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  • $\begingroup$ The sentence you give actually is a definition. $\endgroup$ – AlexE Oct 24 '13 at 9:44
  • $\begingroup$ Well I didn't Understand the definition that's why I am asking. I mean it's obvious that I didn't understand it $\endgroup$ – Hani Gotc Oct 24 '13 at 13:10
  • $\begingroup$ What isn't so obvious is where your understanding breaks down. A line (let's call it L) divides the plane into two parts (half-planes is a term we use). A line segment has two endpoint, say P1 and P2. If the two endpoints are neither of them on the line, and instead the two endpoints are in different parts of the plane as divided by L (different half-planes), then we say the line segment P1P2 "straddles" line L. If you've ever straddled a bicycle, you know about having your two feet on opposite sides of the bicycle. $\endgroup$ – hardmath Oct 24 '13 at 15:45
  • $\begingroup$ ohhh now I get it!! ok ok I understand, let me plot it. Thank you @hardmath, can you add your answer as solution? $\endgroup$ – Hani Gotc Oct 24 '13 at 15:50
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A line L separates the plane into two half-planes. That is, removing L leaves two (unbounded) regions on either side of L.

We may use the word straddle to describe a line segment that connects these two half-planes by having an endpoint P1 or P2 in each of the two separated regions. Visually we see that line segment P1P2 crosses line L and defines a point of intersection strictly between the two endpoints P1 and P2.

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