Problem 1720. Do the lines intersect?

Created by Ned Gulley

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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

Solution Stats

303 Solutions
80 Solvers

Last Solution submitted on Jun 25, 2020

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Celestino on 11 Mar 2014

What about
a = [0,0; 2,2]; b = [1,1; 3,3];
?

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!

Solution Comments

Solution 659287

1 Comment

1 Comment

Andrew Newell on 14 May 2017

I like the conceptual clarity of this one.

Solution 416465

1 Comment

1 Comment

Celestino on 11 Mar 2014

For
a = [0,0; 2,2]; b = [1,1; 3,3];
a = [0,0; 2,2]; b = [2,2; 3,3];

Problem Recent Solvers80

Problem Tags

geometry intersection