Problem 1720. Do the line-segments intersect?

Created by Ned Gulley
Appears in Computational Geometry III

Difficulty:Rate

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You are given two line segments. Do they cross?
Consider one segment as (x1,y1) to (x2,y2), the other segment as (x3,y3) to (x4,y4). You are given a = [x1 y1; x2 y2]; b = [x3 y3; x4 y4]. Return tf=true if a and b intersect or tf=false if a and b do not touch.
When lines do intersect they will do so cleanly at exactly one non-endpoint. That is, they will not nest, overlap, or "kiss" at the endpoints.
Examples
 a = [0,0; 1,1];
 b = [0,1; 1,0];
 tf = true
 a = [0,0; 1,0];
 b = [0,1; 1,1];
 tf = false

Solve

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Last Solution submitted on Oct 27, 2024

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Ned Gulley on 12 Mar 2014

Hi Celestino. I added a little bit more clarifying text to the problem statement. That's an interesting test case, but not one I will use for this problem. You could make your own extension to this problem, though!

Doddy Kastanya on 26 Dec 2020

Test Case 4 should be "true" since these lines intersect.

For Test Case 3, the two lines are on top of each other, so they will technically intersect infinite times :).

Dyuman Joshi on 20 Feb 2021

@Doddy
The question asks if the "line segments" intersect or not, not the whole line. For lines touching, it is clearly stated in the problem statement, that the line segments should not be overlapping and should intersect only at a single point.

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Problem 1720. Do the line-segments intersect?

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Problem 1720. Do the line-segments intersect?

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