Problem 567. Crossing to Kissing - Untangle the Lines

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>Turn lines that cross into lines that kiss.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You will be given two lines that cross at some point. Your job is to untangle them in the following way. Imagine two line segments, L1 and L2. L1 goes from (0,0) to (2,2). L2 goes from (0,1) to (2,1). We can specify them like so.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ L1 = [0 0; \n 2 2]\n\n L2 = [0 1; \n 2 1]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>We want to transform these into two non-crossing segmented lines that look the same when plotted. To do this, we need to introduce a new point in each line. Both lines share this point, so now they \"kiss\" instead of crossing.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ L3 = [0 0; \n 1 1;\n 2 1]\n\n L4 = [0 1;\n 1 1;\n 2 2]\n\n * L1 * L4\n / /\n / /\n L2 *--/--* L2 L4 *--*--* L3\n / /\n / /\n L1 * L3 *]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your function should take the form</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ [L3,L4] = cross2kiss(L1,L2)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The lines L3 and L4 should be ordered by the y coordinate of their first point. So in the case above, the first point in L3 is [0 0], so it comes first.</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>"}]}

Turn lines that cross into lines that kiss.You will be given two lines that cross at some point. Your job is to untangle them in the following way. Imagine two line segments, L1 and L2. L1 goes from (0,0) to (2,2). L2 goes from (0,1) to (2,1). We can specify them like so.<pre> L1 = [0 0; 
 2 2]</pre><pre> L2 = [0 1; 
 2 1]</pre>We want to transform these into two non-crossing segmented lines that look the same when plotted. To do this, we need to introduce a new point in each line. Both lines share this point, so now they "kiss" instead of crossing.<pre> L3 = [0 0; 
 1 1;
 2 1]</pre><pre> L4 = [0 1;
 1 1;
 2 2]</pre><pre> * L1 * L4
 / /
 / /
 L2 *--/--* L2 L4 *--*--* L3
 / /
 / /
 L1 * L3 *</pre>Your function should take the form<pre> [L3,L4] = cross2kiss(L1,L2)</pre>The lines L3 and L4 should be ordered by the y coordinate of their first point. So in the case above, the first point in L3 is [0 0], so it comes first.

Turn lines that cross into lines that kiss.

You will be given two lines that cross at some point. Your job is to untangle them in the following way. Imagine two line segments, L1 and L2. L1 goes from (0,0) to (2,2). L2 goes from (0,1) to (2,1). We can specify them like so.

L1 = [0 0; 
       2 2]

L2 = [0 1; 
       2 1]

We want to transform these into two non-crossing segmented lines that look the same when plotted. To do this, we need to introduce a new point in each line. Both lines share this point, so now they "kiss" instead of crossing.

L3 = [0 0; 
       1 1;
       2 1]

L4 = [0 1;
       1 1;
       2 2]

* L1               * L4
           /                  /
          /                  /
   L2 *--/--* L2      L4 *--*--* L3
        /                  /
       /                  /
   L1 *               L3 *

Your function should take the form

[L3,L4] = cross2kiss(L1,L2)

The lines L3 and L4 should be ordered by the y coordinate of their first point. So in the case above, the first point in L3 is [0 0], so it comes first.

Solve

Solution Stats

89 Solutions
28 Solvers

Last Solution submitted on Jan 02, 2022

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 24 Jun 2020

Technically, L1 & L2 are line segments, and L3 & L4 are polylines.

Problem Recent Solvers28

Problem Tags

geometry

Community Treasure Hunt

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

Start Hunting!

Problem 567. Crossing to Kissing - Untangle the Lines

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers28

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 567. Crossing to Kissing - Untangle the Lines

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers28

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players