Problem 2218. Wayfinding 1 - crossing

Created by J-G van der Toorn

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":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId1","target":"/media/image1.JPEG"}],"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>This is the first part of a series of assignments about wayfinding. The final goal is to be able to calculate the fastest route through a terrain of areas with different properties. The assignments will build on top of each other, gradually increasing the complexity, but guiding you stepwise towards the final goal. You can re-use code from preceding assignments to save some work.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>How many times does AB cross another line?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The first assignment deals with the problem of finding the lines we cross while going from A to B. The answer will be the number of times the segment AB intersects with the other lines. The other lines are isolated (or intersecting) line segments of two nodes each.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The inputs of the function</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>WayfindingIntersections(AB,L)</w:t></w:r><w:r><w:t> are a matrix</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>AB</w:t></w:r><w:r><w:t> of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a 3-dimensional matrix</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>L</w:t></w:r><w:r><w:t> of columns with x- and y-coordinates, each column either the start or the end of a line, and with all individual lines concatenated in the 3rd dimension.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ AB = [\n xA xB\n yA yB\n ]\n\n L = cat(3,...\n [ x1_start x1_end\n y1_start y1_end ] ...\n ,...\n [ x2_start x2_end\n y2_start y2_end ] ...\n ,...\n [ x3_start x3_end\n y3_start y3_end ] ... % etc.\n )]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your output n will be the number of times the line AB intersects with any of the other lines. The lines will not 'just touch' AB with their begin or end.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>p.s. I noticed later on that there is another Cody problem</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect\"><w:r><w:t>1720</w:t></w:r></w:hyperlink><w:r><w:t> that is somewhat similar. But this was a logical start for the series.</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>"},{"partUri":"/media/image1.JPEG","contentType":"image/JPEG","content":"data:image/JPEG;base64,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"}]}

This is the first part of a series of assignments about wayfinding. The final goal is to be able to calculate the fastest route through a terrain of areas with different properties. The assignments will build on top of each other, gradually increasing the complexity, but guiding you stepwise towards the final goal. You can re-use code from preceding assignments to save some work.How many times does AB cross another line?<img src = "http://i60.tinypic.com/mk7us1.png">The first assignment deals with the problem of finding the lines we cross while going from A to B. The answer will be the number of times the segment AB intersects with the other lines. The other lines are isolated (or intersecting) line segments of two nodes each.The inputs of the function <tt>WayfindingIntersections(AB,L)</tt> are a matrix <tt>AB</tt> of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a 3-dimensional matrix <tt>L</tt> of columns with x- and y-coordinates, each column either the start or the end of a line, and with all individual lines concatenated in the 3rd dimension.<pre> AB = [
 xA xB
 yA yB
 ]</pre><pre> L = cat(3,...
 [ x1_start x1_end
 y1_start y1_end ] ...
 ,...
 [ x2_start x2_end
 y2_start y2_end ] ...
 ,...
 [ x3_start x3_end
 y3_start y3_end ] ... % etc.
 ) </pre>Your output n will be the number of times the line AB intersects with any of the other lines. The lines will not 'just touch' AB with their begin or end.p.s. I noticed later on that there is another Cody problem <a href = "http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect">1720</a> that is somewhat similar. But this was a logical start for the series.

This is the first part of a series of assignments about wayfinding. The final goal is to be able to calculate the fastest route through a terrain of areas with different properties. The assignments will build on top of each other, gradually increasing the complexity, but guiding you stepwise towards the final goal. You can re-use code from preceding assignments to save some work.

*How many times does AB cross another line?*

<<http://i60.tinypic.com/mk7us1.png>>

The first assignment deals with the problem of finding the lines we cross while going from A to B. The answer will be the number of times the segment AB intersects with the other lines. The other lines are isolated (or intersecting) line segments of two nodes each.

The inputs of the function |WayfindingIntersections(AB,L)| are a matrix |AB| of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a 3-dimensional matrix |L| of columns with x- and y-coordinates, each column either the start or the end of a line, and with all individual lines concatenated in the 3rd dimension.

AB = [
   xA xB
   yA yB
 ]

L = cat(3,...
  [ x1_start x1_end
    y1_start y1_end ] ...
   ,...
  [ x2_start x2_end
    y2_start y2_end ] ...
   ,...
  [ x3_start x3_end
    y3_start y3_end ] ... % etc.
  )

Your output n will be the number of times the line AB intersects with any of the other lines. The lines will not 'just touch' AB with their begin or end.

p.s. I noticed later on that there is another Cody problem <http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect 1720> that is somewhat similar. But this was a logical start for the series.

Solve

Solution Stats

52 Solutions
20 Solvers

Last Solution submitted on Apr 28, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 27 Jun 2020

The problem's figure is missing. We can use our solution for problem 1720 (https://nl.mathworks.com/matlabcentral/cody/problems/1720-do-the-lines-intersect). However, line matrices are transposed in this problem. And for the picture, we can imagine an instance of Buffon's needle problem without horizontal lines.

Problem Recent Solvers20

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 2218. Wayfinding 1 - crossing

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author31

Problem Tags

Community Treasure Hunt

Problem 2218. Wayfinding 1 - crossing

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author31

Problem Tags

Community Treasure Hunt

Players