Problem 1720. Do the line-segments intersect?

Created by Ned Gulley

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You are given two line segments. Do they cross?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Examples</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ a = [0,0; 1,1];\n b = [0,1; 1,0];\n tf = true\n\n a = [0,0; 1,0];\n b = [0,1; 1,1];\n tf = false]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

341 Solutions
62 Solvers

Last Solution submitted on Jul 18, 2021

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

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!

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.

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 Solvers62

Problem Tags

geometry intersection

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1720. Do the line-segments intersect?

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers62

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 1720. Do the line-segments intersect?

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers62

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players