{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2024-12-19T00:41:30.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2024-12-19T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2218,"title":"Wayfinding 1 - crossing","description":"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.\r\n\r\n*How many times does AB cross another line?*\r\n\r\n\u003c\u003chttp://i60.tinypic.com/mk7us1.png\u003e\u003e\r\n\r\nThe 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.  \r\n\r\nThe 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.\r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n L = cat(3,...\r\n  [ x1_start x1_end\r\n    y1_start y1_end ] ...\r\n   ,...\r\n  [ x2_start x2_end\r\n    y2_start y2_end ] ...\r\n   ,...\r\n  [ x3_start x3_end\r\n    y3_start y3_end ] ... % etc.\r\n  )  \r\n\r\nYour 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. \r\n\r\np.s. I noticed later on that there is another Cody problem \u003chttp://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect 1720\u003e that is somewhat similar. But this was a logical start for the series.","description_html":"\u003cp\u003eThis 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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eHow many times does AB cross another line?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i60.tinypic.com/mk7us1.png\"\u003e\u003cp\u003eThe 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.\u003c/p\u003e\u003cp\u003eThe inputs of the function \u003ctt\u003eWayfindingIntersections(AB,L)\u003c/tt\u003e are a matrix \u003ctt\u003eAB\u003c/tt\u003e 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 \u003ctt\u003eL\u003c/tt\u003e 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.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e L = cat(3,...\r\n  [ x1_start x1_end\r\n    y1_start y1_end ] ...\r\n   ,...\r\n  [ x2_start x2_end\r\n    y2_start y2_end ] ...\r\n   ,...\r\n  [ x3_start x3_end\r\n    y3_start y3_end ] ... % etc.\r\n  )  \u003c/pre\u003e\u003cp\u003eYour 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.\u003c/p\u003e\u003cp\u003ep.s. I noticed later on that there is another Cody problem \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect\"\u003e1720\u003c/a\u003e that is somewhat similar. But this was a logical start for the series.\u003c/p\u003e","function_template":"function n = WayfindingIntersections(AB,L)\r\n  n = randi(size(L,3)+1)-1;\r\nend","test_suite":"%%\r\nAB = [2 0;0 5];\r\nL = cat(3,...\r\n    [1 0;2 2],...\r\n    [-1 4;3 3],...\r\n    [-3 2;0 2],...\r\n    [2 3;4 2]...\r\n    );\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 2;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 6 -3 ; 5 2 ];\r\nL = cat(3,...\r\n[ 2 2 ; 2 -9 ],...\r\n[ -2 3 ; 8 8 ],...\r\n[ 7 -1 ; 4 6 ],...\r\n[ 7 -3 ; -6 1 ],...\r\n[ -6 -6 ; -1 2 ],...\r\n[ 5 -8 ; 3 4 ],...\r\n[ 3 5 ; -8 -9 ],...\r\n[ 8 -8 ; 4 -3 ],...\r\n[ -7 9 ; -5 9 ],...\r\n[ 6 3 ; 8 3 ],...\r\n[ 0 4 ; 9 -2 ],...\r\n[ -8 0 ; 4 0 ],...\r\n[ 6 8 ; 6 0 ],...\r\n[ -6 2 ; -6 9 ],...\r\n[ 8 -4 ; 1 -5 ],...\r\n[ 5 -1 ; -5 -3 ],...\r\n[ -2 -9 ; 6 -5 ],...\r\n[ 8 6 ; 6 -7 ],...\r\n[ -4 2 ; 5 2 ],...\r\n[ 8 6 ; 0 6 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ -3 -1 ; -3 7 ];\r\nL = cat(3,...\r\n[ 9 8 ; 1 6 ],...\r\n[ -4 -6 ; -3 9 ],...\r\n[ -2 8 ; 7 5 ],...\r\n[ -3 5 ; -8 2 ],...\r\n[ 1 2 ; 3 5 ],...\r\n[ 4 -5 ; -3 -5 ],...\r\n[ 8 5 ; -1 -2 ],...\r\n[ 4 8 ; 3 5 ],...\r\n[ -3 -4 ; 7 8 ],...\r\n[ 9 7 ; -1 -3 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 1;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 5 9 ; -9 0 ];\r\nL = cat(3,...\r\n[ 3 -1 ; 1 -2 ],...\r\n[ -5 3 ; -3 4 ],...\r\n[ -9 -2 ; -3 -7 ],...\r\n[ -6 -5 ; -1 -3 ],...\r\n[ 4 -3 ; 5 -9 ],...\r\n[ -6 -2 ; -4 -4 ],...\r\n[ -1 -7 ; -3 -4 ],...\r\n[ 0 9 ; 6 3 ],...\r\n[ -6 1 ; -7 -8 ],...\r\n[ 6 5 ; 6 5 ],...\r\n[ 5 6 ; -5 -1 ],...\r\n[ 7 9 ; -7 -7 ],...\r\n[ -9 -4 ; -2 -3 ],...\r\n[ 3 5 ; -2 5 ],...\r\n[ -3 -4 ; 5 -6 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 0;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 6 -3 ; 6 -7 ];\r\nL = cat(3,...\r\n[ -7 0 ; -3 0 ],...\r\n[ -1 5 ; -8 0 ],...\r\n[ 8 -5 ; 1 4 ],...\r\n[ -4 -4 ; 7 3 ],...\r\n[ 0 0 ; 4 -5 ],...\r\n[ -2 -3 ; -4 4 ],...\r\n[ 4 -8 ; 2 -5 ],...\r\n[ -7 6 ; 6 3 ],...\r\n[ -2 -7 ; -3 -8 ],...\r\n[ -6 5 ; 8 7 ],...\r\n[ 9 -9 ; 5 -9 ],...\r\n[ 6 8 ; 4 6 ],...\r\n[ 2 7 ; 5 -2 ],...\r\n[ -7 -5 ; -1 -7 ],...\r\n[ -8 -2 ; 0 -6 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 45 25 ; 23 101 ];\r\nL = cat(3,...\r\n[ 94 6 ; 2 71 ],...\r\n[ 40 -9 ; 51 84 ],...\r\n[ -8 97 ; 72 105 ],...\r\n[ 18 59 ; 36 88 ],...\r\n[ 95 56 ; 10 -6 ],...\r\n[ 61 48 ; 96 22 ],...\r\n[ 12 100 ; 94 16 ],...\r\n[ 103 90 ; 54 106 ],...\r\n[ 108 53 ; 34 68 ],...\r\n[ 9 20 ; 1 7 ],...\r\n[ 76 64 ; -8 106 ],...\r\n[ 60 9 ; 51 69 ],...\r\n[ 75 62 ; 60 -7 ],...\r\n[ 80 -8 ; 70 68 ],...\r\n[ 8 30 ; 68 67 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ -5 -6 ; -2 -6 ];\r\nL = cat(3,...\r\n[ -1 -7 ; -7 -1 ],...\r\n[ -4 -6 ; -6 -5 ],...\r\n[ -7 -2 ; -1 -5 ],...\r\n[ -9 -6 ; -4 -4 ],...\r\n[ -9 -3 ; -3 -2 ],...\r\n[ -2 -1 ; -3 -2 ],...\r\n[ -4 -5 ; -6 -9 ],...\r\n[ -8 -1 ; -4 -6 ],...\r\n[ -1 -5 ; -5 -1 ],...\r\n[ -4 -6 ; -2 -5 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 6;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 1 6 ; 6 7 ];\r\nL = cat(3,...\r\n[ 5 8 ; 2 8 ],...\r\n[ 6 5 ; 3 2 ],...\r\n[ 4 8 ; 6 1 ],...\r\n[ 7 2 ; 7 9 ],...\r\n[ 1 8 ; 1 2 ],...\r\n[ 1 6 ; 1 9 ],...\r\n[ 2 6 ; 1 2 ],...\r\n[ 3 9 ; 2 4 ],...\r\n[ 5 9 ; 2 8 ],...\r\n[ 2 8 ; 2 5 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 1;\r\nassert(isequal(n,n_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":26,"created_at":"2014-02-25T14:46:37.000Z","updated_at":"2017-05-05T15:03:02.000Z","published_at":"2014-02-25T14:59:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHow many times does AB cross another line?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWayfindingIntersections(AB,L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![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  )]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep.s. I noticed later on that there is another Cody problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1720\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that is somewhat similar. But this was a logical start for the series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"}]}"},{"id":2219,"title":"Wayfinding 2 - traversing","description":"This is the second 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. See \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing [1]\u003e.\r\n\r\n*How many times does AB cross the boundary of area F?*\r\n\r\n\u003c\u003chttp://i59.tinypic.com/219vz42.png\u003e\u003e\r\n\r\nFor this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.\r\n\r\nThe inputs of the function WayfindingBoundaryCrossing(AB,F) 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 matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.\r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n F = [\r\n  [ x1 x2 ... xn ;\r\n    y1 y2 ... yn ]\r\n\r\nYour output n will be the number of times the line AB crosses the boundary of F. Note that AB may cross the boundary of F at a corner node of F.\r\n","description_html":"\u003cp\u003eThis is the second 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. See \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\"\u003e[1]\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eHow many times does AB cross the boundary of area F?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i59.tinypic.com/219vz42.png\"\u003e\u003cp\u003eFor this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.\u003c/p\u003e\u003cp\u003eThe inputs of the function WayfindingBoundaryCrossing(AB,F) 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 matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e F = [\r\n  [ x1 x2 ... xn ;\r\n    y1 y2 ... yn ]\u003c/pre\u003e\u003cp\u003eYour output n will be the number of times the line AB crosses the boundary of F. Note that AB may cross the boundary of F at a corner node of F.\u003c/p\u003e","function_template":"function n = WayfindingBoundaryCrossing(AB,F)\r\n  n = randi(size(F,2))-1;\r\nend","test_suite":"%%\r\nAB = [ 0 0 ; 6 -8 ];\r\nF = [\r\n      -4    4    4   -4\r\n       2    2   -4   -4\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 2;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nAB = [ 0 0 ; 4 -6 ];\r\nF = [\r\n      -6    4    0\r\n      -0    2   -4\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 2;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nAB = [ 6 -6 ; 0 0 ];\r\nF = [\r\n      -8   -8    4\r\n       2   -4   -0\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 1;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nAB = [ 8 -6 ; 6 -8 ];\r\nF = [\r\n      -6    0   -3    7    9    4    6   -4   -7   -2   -7   -8\r\n      -9   -9    0   -4    1    7   -0    4   -1   -7   -5   -9\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nn_correct = randi(9)-1;\r\nAB = [ 0 0 ; n_correct*2-9 -10 ];\r\nF = [\r\n      -2   -2    2    2   -2   -2    2    2   -2   -2    2    2   -2   -2    4    4\r\n      -8   -6   -6   -4   -4   -2   -2   -0   -0    2    2    4    4    6    6   -8\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nassert(isequal(n,n_correct));","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2014-02-26T11:59:09.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-02-25T15:14:11.000Z","updated_at":"2017-05-05T15:03:15.000Z","published_at":"2014-02-26T11:59:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second 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. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHow many times does AB cross the boundary of area F?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function WayfindingBoundaryCrossing(AB,F) 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 matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ AB = [\\n   xA xB\\n   yA yB\\n ]\\n\\n F = [\\n  [ x1 x2 ... xn ;\\n    y1 y2 ... yn ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour output n will be the number of times the line AB crosses the boundary of F. 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DDX0g++LUucf3VIZv0FAHy/Pcar8RvGE15eTfvZmZ2J5WGMdFHsOgrtrLw1oPh+H7RKsTFetxdMOvsDxXM/DWaMXd9Af9a8Ssv0B5/nVP4hR3MfiHdLIzQyIGhHYDoR+deZW562I9jzWX5nv4WNLDYNYrl5pX+40fF/i3T9Q0uTTrMyTEuCZTwvB7Z5Ndr8CGH9gawvcXMZ/NTWanwn0gfCS68VxajPfXj2QuYVVdkceCNykcklcMOval+A11/pGt2Rb70cUwH+6SD/6FXJnWGUMtnGHk/wAUcDxcsRiFUnue0UUUV+bHeFFFFABSNlV3N8q+rcCvOPiL8TV8Mu2k6Rsl1TH72VuVt89sd2/lXl9t4f8AHPjvdf8Al3l5Ex/19xLtT/gO4gflX0ODyGdWkq9eapxff+kck8Uk7QV2fSnnRf8APeL/AL+D/GnKyM21ZEZvRWBr5z/4U94y/wCfOD/wLj/xpr/CPxrbr5qWCuR0EVym78Pmrf8AsTBPbFL8P8yfrFT+U+kGVl+VuKK+ddB+IPifwXqP9n6utxcW0bbZbO8zvQf7DHlf5V75pWq2et6VBqWnyebbTrlT3U91Yeo715uY5RVwVpS96L2aNqVdT06l6iiivJNw71Wf/j7X8Ks1m6hci1guro9IInc/gpNb0I800kUup8wWupJpni9tQaNpI47lnKjgkZNekW+taB4mhW3donY/8sbhQG/D/wCsa5P4X+FrTxp43Gm6iJWtTBLNKY22sMDAIPP8RWq/xF8JWvgnxQdHs9Ra8AiWViY9jRluit6nGD/wKv1WrhI1UnezR5+EzGWHThypxfRmh4m8DQ2tpNfaYXAjG6SB+cL3IPtXpH7P/jW4vY7jwrfSNJ9nj86zdjyEBAZPwyCPxrn9JaSy8IQvqMjOUtmeQv12kEgH8OKx/gPDNN8UYHi+5DbTPJ/ukbf5stRgak5qUZu9uptm2Hp03CpTVuZXsfV1FFFdx5AUUUUAFFFFABUE33/wqeoZPvD6UASr92lpq/dFOoAKKKKACiiigAqKeGK5gkhmVXikUoyt0YHgipaKAPi/UbKbwF8RrizfdssrkqD/AH4W6H8UNdV4701dQ8Pm6i+Z7VvMBHdG4P8A7Ka6T9ovw1tfTfE0Kfe/0O5I9RlkP/oY/AV5W/jLUX0SDS4UVNsfkvJ95pB0A56ccVx16MpVI1Ibr8j1MHi6cKFSjV2e3qesfAvVo9d8Ka74Ku248p3iDf8APOQbXH4Mc/8AAq8/+Ft4+gfEuGzuvkaYyWUoPZj0/wDH1WsXT9A8YaeV1DTrLVLV1X5ZbdXjfH4YNZM97qKa01/dSy/2iJvOeWX7+/Odxz3zVV408TRnRTTumjz1GcGm0fXmaXrWV4c8Q2fijRYdTs5FO9QJo+8MmOVNaor8nq0p0puE1Zo9mMlJXQVR1fUBo+h3+pMu77LA8wHqQOB+dXqo6tp0es6Nd6XMzJHdRGNnTqM9xTocntI8/wAN1f0CV7Ox8+/DnQP+Ey8avNqm6eCLdd3W7/lqc8Kf95jzX0hGq/KiqqouFVVXAAHYCuL8B+AE8EfbZWv/ALXcXWE3LHtVUBz0yeSa7SvXzzHxxeItSleCWn6nPh6ThHVanjV/8dLiC/mitdCgaFHIUyyMGIHcgV3HgHxp/wAJrptzO9l9kmtnCMFYspDAkEE/TmtK78H+Gb64kubrQ7GWaRtzu0eCSe5xitHT9OsNKtfsun2kFpb7t3lxLgZPc0sVisunQ5KFJxnprf8A4IQhVU7t6HLfErwtb+I/Ct1cGNf7RsYjNBJ3KryyH2I/WuH+Bmsyi91HQ5GJikj+1RD0ZSA35g/+O17PLEk0MkD/ADJLGUf6EYNcN4L+GkHg/XZ9U/tBrtijRwr5e3ardS3Jya2wuYUv7Oq4au9fsinSftVOKO9ooor506wrhviTqg03wJqkm757rFsn/Azz/wCOhq7WZtsW1fvHgV4N8X/EkGoaha6NZzLJFZktOycjzTxt/AcV7mRYWWIxcXbRO7+RlXnyUm+rOj/Z7s4rFPEfia8/d21rbiPzPRRmST8gq15zHLP44+IM99dKf9LuTPKOuyMc7fwGFqrpaeK7/SG0zS/7TfTWYl4IN4iYnrux8p6d6igfXPCN/wCa1vLaysu0rLFw49Of6V+izmmnCLXMebQiozjOony3O1+IOp/ZdFSyRsPdNz7oOf54r0P9nrw19h8N3evzR/vdQk8uEn/nkhx+rZ/75rwy9u7zxr4ns4IIQk1y0dtDGGyAScfzOa+y9G0uDRdGstLthiC1hWFPcKMZP1qMLR9lSUXubZjivrFdyW2yNCiiiuk4QooooAKKKKACoZPvD6VNUMn3h9KAJF+6KdSL92loAKKKKACiiigAooooA8y+O19HZ/DC6iaNXN1cRQKT/Cc78j8EryD4UaDBMLnWriNZHifyYA38DYyW+vK4r13486fJe/DKeVBn7HcxTt9MlP8A2evL/hFfJJpF/p+797HKJgP9kjB/UV5mcSnHBzcDty+MJV1zno1YfiPwzp/iezaK6RUuQv7q5C/Mh9/Ue1bgoxXwtGtOjNTg7M+nqU4TTjJHifhDXb34f+M2tr0MluZPIvouxXPDj6dR/wDXr6U/3fmXsa+ePi3ZpFrdldqu154MP7lTjP5GvUvht4stvEnhi3t9wGo2MKQzxluWVRhZB6g9/Q16ueYf6zhqeOhHW3vHz9P91VlRbO1ooor5A6wooooAKKKKACiiigBKWiq9zOkMbMzKiqpZnZsBFHUk1UIuTsgOG+KPi1/D+grDaSbL69zHEy9UQfece/OBXnHw98Ex6qTq+qR77NWxDEf+WzDqT/sj9ay/iJ4nh8UeJfNtN32O2TyIS38YBJLY7ZJr2bRbNLDQbC0RdojgQfjjJP519vJSyzL4wgrTnuY4aCxGIbe0S4qrHGsaIqInARVwF+gFZOr6dbanbTWV1HvgmX/vg/3h7itiqN1IkcjSO21I13OzdgOTXh0JzVRSW57yjFxaa0PJvhk66H8XtJiuI0kZbt7U57MwZAR+Jr6/r4/+H0T+IPjFpc0S8G/N2R6KpMn9K+wK/SI3sr7nxU7cztsLRRRVEhRRRQAUUUUAFRyfe/CpKhk+8PpQBIv3RTqav3RTqACiiigAooooAKKKKAKWp6fb6rptzp92m+2uYmhkH+ywwa+Q9RsNX+FnjpoJFyYT+7Y8Jcwnv+P6Ee1fZArmvGHgvR/G2l/YtTh+dMmG4Th4ie4P8xUzipxcZK6ZUZOLTW55toPiLTPEdqsthMvm7f3luzfvEPuP6itZ8Rxs8reWi8l34AHuTXmevfArxfolyZdH8rU4AcpJBIIpR9VYj9CaxR8PPiTq0q2s2lao65/5eZcIPxZsV85V4cg53hOy+89eGbtQ95alTx1rQ8UeKILbTFaeKPFtBt6ysTyR9ScCp9e8NeJfhR4ktrpZcYwYL2Jf3cnHzIf5EGvZPhn8G4PCt2msa1JHd6qv+piQZjtz65P3m/l+tZfxp+JemxWtz4SsrW21C6b5bqSVd6W59F/6aD17fXp71KhThSVFL3UrHlVarnN1HuXfCvxK0TxHp7S3Vzb6beQrunhnkCr/ALyMeo9uorUPjzwmrbT4hsfwkJ/pXz5oPgPXfEEYuLe3WC0PS4uG2Kfp3P4CumX4NXePm1q1B/2Y2NeLLhCjVm5wuk+n/DkzzenS92clc9jtvGXhi6kVINf05nPQNMF/nitpRuVXHzIejLyD9DXz/c/BzVY491rqdnM/9xtyfqRisjT9c8WfDfUxBIJYY87mtJ/milHt2/Fa48XwfKEL0pO/n/mjWhm1Oq7J3PpjFFYXhLxVYeMNIF7ZfJImEnt2bLRMf5g9jXm3j34tSpPNpXhmUIqnZLfKcsx7iP0H+1+VfM4bKMViK7oJWa3v0PQnXhGHNc9a1DVdN0pd2paha2n/AF3mCn8jzWT/AMJ74S/6GGx/76P+FeGaZ8O/E/iH/Tbs/Z0l5869kO5/fHLGtj/hTV531u1/79tX11LguMo+/Jt+VkeXPOaUXbmR7APGfhmaNjDr+nPsUk/vgMAd8HFeNePPiLN4kkbR9GMqaczYZsHfdHPHHZfQfnUV98INat4y9neWd2R/AGMbfhuGP1rG8L6zd/DzxhHd3+jxTTQcSQXUeHQH+JD/AAt6Gu3CcOUcDU9o7t9L9BrMY4iPLTkP8U/D3WfCGiaVqWpx7Pt27fFjmBh0Vj6kc16h4J8Rwa/odvGJE+3W8Yjmh/iOBgOB3Br1NT4c+J/gz/n6068XkdHhcf8AoLqf8kV4H4j+B3izQrxp9EX+07UHckkDhJUHupI5/wB3NdOPwMMbT5JOzWxvhMU8PO6Wh6TO4t4md/lUd24H615T458bw3Fu+laXIJFk4nuB0Yf3V/qaqx/Dn4j606wzaXqJHreS7FH/AH2a9Q8CfAW10u4i1HxRLFfXCcpZR8wg/wC2T976dPrXFgskhh5+0m+ZnXiM1nVg4RVh/wABvAkukabL4m1KLZc3qbbVGXlIepb/AIFxj2HvXtdJ0pa9w8kKKKKACiiigAooooAKhk+8PpU1Ryfe/CgB6/dpaRfu0tABRRRQAUUUUAFFFFABRRRQAUUUUAcf8SfFB8I+Br7UomAu2xBbZ/56NwD+Ay3/AAGvm/4c+Fl8S6rPqepI01latucPz58jchSf1P8A9evT/wBpKd10PQrYfce5kcj3VQB/6FXIeBPF/hvQvCcNpeXvk3bSySSr5LN1OF5A9BW+HUXU996HJjp1I0X7NXb7Hpv91fuqvygLwFHoKK5b/hZPhL/oKt/4Dv8A/E0f8LJ8Jf8AQVb/AMB3/wDia9f2tPuj5r6rX/lf3HU1Q1rRbLxBpkmn3y5iPMcn8ULdmX/PNYv/AAsjwl/0FW/8B3/+Jo/4WP4S/wCgq3/gO/8A8TUynTlGzkio4fERkpRi015M8dafWfB2q6npsVw0Ezo9pcbOjofT69q7X4XeEobiP/hIb+NJFV9lpG/I3Dq5Ht2965r4iarpes+JlvtJn86J4EWR/LKfOMjv7Yr0Hw7458KaZ4Z0yxk1LypYbZVkTyJGw/Vug9TXm0KdJVm3Y9zF1K7wy5E7vc7pmZm3N8zUVy3/AAsnwl/0FW/8B3/+Jo/4WT4S/wCgq3/gO/8A8TXqe1p/zI8D6rX/AJX9x1NYXizwvB4q0hrdlUX0ak2s/cN/cJ/utVP/AIWT4S/6Crf+A7//ABNH/CyPCX/QXb/wGk/+JqZTpSjZtGtOjiaclOEXf0OW+B/ii48PeNhol0xW01JvJaNv4Jh9w/U/d/H2r6kr4v1PUrR/iV/amkyb7c38dxE+0rk7lY8Hn71faFeJJWk0fVQd4ptC0UUUigooooAKKKKACiiigAooooAKhk+8PpU1QTff/CgCVfuinUi/dpaACiiigAooooAKKKKACiiigAooooA8I/aV/wCQZ4e/67T/AMkrz/wv8MrfxD4dttUfVJYWmZ18tYAwGGx13Cvffih4I/4TnwsbW3dUv7aTzrVm6E4wUPsR+oFfNkZ8deDZJtNjj1Sx+bc0QjJXPqOCPxFaUpRi/fV0YYiFWULUpWZ1v/CmbT/oOy/+Aw/+Ko/4Uzaf9B2X/wABh/8AFVyf/CXePv8An71P/vwf/iaP+Eu8ff8AP3qf/fg//E10+1w/8pxewx3/AD8X9fI6z/hTNp/0HZf/AAGH/wAVR/wpq0/6Dcv/AIDD/wCKrk/+Eu8ff8/ep/8Afg//ABNH/CXePv8An71P/vwf/iaPa4f+UPYY7/n4v6+RT8aeF4/Cmrw2MV21yJIFl3tHs6kjGMn0rr9M+Ettf6RZXraxIjXMCTbPswONwzjO6sKz8E+OfHElzqn2C7uHVcme6/d+Zjoq7sZP0qvBq/jrQIxpsR1W1SBiogaFvk9hkVlCdLnba0OirSrypqMJWl1Ou/4Uzaf9B2X/AMBh/wDFUf8ACmbT/oOy/wDgMP8A4quT/wCEu8ff8/ep/wDfg/8AxNH/AAl3j7/n71P/AL8H/wCJrX2uH/lOf2GO/wCfi/r5HWf8KZtP+g7L/wCAw/8AiqP+FNWn/Qbl/wDAYf8AxVcn/wAJd4+/5+9T/wC/B/8Aiad/wl/j7/n81T/vx/8AWo9rh/5Q9hjv+fi/r5Gdq+jJ4f8AG50uOZphb3MYEhXBbO09OfWvtqvmL4afDDXPEHiWDXtftriCwimFwz3IIkuXByBg84z1Jr6dxiuSVrux6UU0km9RaKKKkoKKKKACiiigAooooAKKKKACoJvv/hU9QTff/CgCVfuinU1fuinUAFFFFABRRRQAUUUUAFFFFACUVFNNFbQSTSyLHFGpd2bgADkk15LdfEzxHrt1N/wiWm2w02Ftn2y9OPNPsMjH06/StKdGdT4TOrWhSV5M9forzbwx8Spbqx1tPEFolrqGjwmeWOD7sqDuuc859/4hXHw3fjDxbB/bNx4kl0iCZiba1tcgBc+2PzNRViqKbrPlRPto2TR7zRXl3w/8W6uPEFx4U8RzLcXiR+ba3Y4MyDsfXjkf8CzXqNEo2tZ6PU0hNTV0LRRRSKCiiigAooooASql/f22mafPe3koitoELyyN/Co6nirZNcQmmeJbbxderfTLq3hrVMo8LYDWeRgDb3U9Dj604pPcls6rStUs9Z0yDUbGbzbadd8b7SNw+h5q6a8stfHfhf4fWEPhiO5vdTksC6M9vEG2fOx2scgZGcHFdr4a8WaR4ssWudJuN4Q7ZI3Xa8ZPTctXKnJa20FGaelzfooorMsKKKKACiiigAooooAKKKKACoJvv/hU9QTff/CgCVfuinU1fuinUAFFFFABRRRQAUUUUAJUF3d29jbSXN1PHBBGu55JGCqo9yanryH4uyG68ReGtJvZGi0eZnkmO7AdwQBk+2f/AB6tKNP2k1Ezqz5IORD8Q/HeneI9Kh8OeG7/AO1XGoTrDM8aEBY/TJAzk+nbNTQWltp9lDawfJaWseA3sOWY/XrRBptjY7fsun2tvj7jJGMj6N1qw0CzRtE8fmo64dGXIYehr26NFUlZHzOMxTxDV9EjidFNrqa+JdUv7lLW0vYZYpJOphiAAQ4HPzOUAHfa1SeFfErLosNrcabfytbrsSa2gMiuvb8aW78L6dd+NrWwto/KtfK+030CN8oCngY7bq7u5u1s7Sa5lbZb28ZcpHwqhR0AH5V89nmJpKUcO48zevax6lD36aa0R5zbeJksfHket6lY3Vv5PlpFDt+dI8/MxBxkkbv++q9u8N+NND8VeYul3RaaMbnglUq6g98Ht9K8V0WB9WubjXdR/e3E8h8oSchcdxn06CluLi/0rxha3Whoiag9uUG1QRzkEkdK1jWoSq/VUrOMd76Kx6sMHVpYVYhvST266n0bXK+JPH/h/wALy/Z767Z7vAP2eBN8gB6Z7D8a8kfRtQcm7m1+/k1Ffn81Zmxu68c1u/D/AEuKfTZtdvF+0ahd3D5nm+ZsDjv6muLFY/C4fDyxClzqLSstNX/TNZYavGcac48vNqd94Y8eaJ4smlg0+WVLmNdzQzx7G2+o6g1e8ReK9G8LWqz6tdrFu/1cQG53/wB1Rya8015xo3xF8O6tF+683KTlV+8oOGz/AMBNN0C2i8W+ItU8V6in2hPtBhsI5eVRF6HHsNv47jVSxuHjgVmE01Brbre9rf10MIqftXQXxXOx0X4p+G9b1FLGOW4tppOIxdRbA59AQSPzqG9+L3hOzv2tftM8+xtrywQF4wfr3/CuP+J0cMml6bAkCNdyXG2LavOMYI+mStaVpodrp2kf2UkETp5ZSUso/eOR8zE/Wu3Kp0sfho4nlcU76X7fI4cdipYSp7PdnYaz4r8KXGjSQXXiG2ghvoCqvFP8+1hjcuOQayfDuhaRpXhTUrvwvrN7qchtpBG7XplAkCnGEGFBz7Vyun+C9F0+FVezS7m2/vJZ8nJ9l6AViawbvwNqTX+gN9nh1GBoJI1yQj9io9R1X0rveEtH3ZGFPMo1J8rRu/DOKzXwjHJaojXjyP8Aa36yZzwD3ximaLPFpnxpb+zdi281uI79I/u+YxAHTvuK/wDj1S6Z8PNOtbBPtc979vljzPNDcmP5jyQMenvXNaLqdl4M1PVo7ktdtZXWbOBUANzOAVRpG67UByB6tnrivl8qjQxGYV61Co5Ps1pq+9+nyPYxEpwoQjOKXmfRTukabnZVUdSTgUqsJFyrAg9CK8FutH1LxG39p+MtUlTfjy7GNvLjhB+6DngH26+pptrJP8OvEGm3Vhe3T6TdT+TdWcrbh9R7jORX0TwMuTmvqefHMacqnIe/0U1WV1VhyDyDTq4T0AooooAKKKKACiiigAqCb7/4VPUE33/woAlX7op1Iv3aWgAooooAKKKKACiiigBK5T4h6Tpmp+D759SVSlnG1xG/dWUHp9eldX3rj/iiksnw31tYfveSCf8AdDKW/TNXS/iR1Jn8DPN/A8P2fwtDLLu33Mhk+bnao+VcflWN441aZdVhsre5aJIYt7eWxXLN649q6fRJI5PD+mtD/q/syKPw4P61ynivwzqV9q7X9hD9pSZRlFYbkIGOh7V9FHe58nBxlWbeht/Di08vTb7UG+Z7iYRAt/EFGT+pq54+uzb+HFtk+/dTBP8AgK/Mf/Zao+BbkN4YWJG2vb3EiyD3Y5FU/Gc8smv6DbM3ybi/zepYD+lfEN8+cSlUXwtv7lp+h71KPNFU110Ni0thZ2lvbL/yxjCn69/1pyxwwztP92a4xEXb07ItU5b9oVkllZFRcsS1c3/bd3Nqun6nPH5WnvcPFb7mxkjhzj23Lk/hXFhcJWxcqlS9lq359bH3eNxFLBxp02rvRLy6XO42hvl/vVc+Hsi/8I9NZt/rbO6kRx9eRWL9t2/K0X/j1Q6PrC6L4wXeuy01VRE57JMPun8f/Zq4ZUniMHVw630kvWP/AALmea0Zp069tE7P5ml8T4D/AGbpt1Hu3xXDp8vX5h/9auo0HSxo+gWdh/HHHmT/AH25b9adfQW+oJClzGzLDcJcAf7SnIBrN8WeJk0HQ5rpf+PqX91br/tnv/wHrXmrF1cbg6GV01qpP8Xp+p431dUa08TLaxgzTr4g+JilfntNHjJHozr/APZn/wAdrppJEjjaWVtiIpd3bsByTXFeAP3Oj3N6ysz3MuwFv7qdf/HjWn4o+36loclnpsamWRh5gaQKSg5IBPFfrGGwkcPRhQh8MVb/AIP3nw+LquvXbl1JfDetvrsWozldkUc4SEd1Qrnn3p+tWSahd6HbP827UUf8FUs38qr+HbF9D0dbV9rXMkhkmKtkA9AoPfAqa2vPtnjm1tF2f6FaSzv7M+FX/wAdrLNanscHVqx6J2+4vBUva4uEVtc6/wC9Llu7V5l4X01NQ1zUvEdwu9RdyC1DdC+cl/8AgI6e9dvreoHTdD1C83bfJt3YfXGB+tc94eh+z+GtLiX/AJ9w592b5if1r5DgfDtqrV72X5tn0PElX2cIU0c5r2r2l74vhs9Qu3h0uxk3ybcnzJBz29TxVlp7jxfrVvdQWztYwSGKyibg3V0w447Kv3mPZV9TWVr/AIR1O41y4ubCFZobmTfnzAPLJ6hs1d0i1fwf440JrW4eafyna92/dKHOVUen9a+7rJ8jseHh/Zc0dT6Gs7f7JZW9tu3+TGqb26nAxmrNFFfPn0QUUUUAFFFFABRRRQAVDJ94fSpqgm+/+FAEq/dFOpq/dFOoAKKKKACiiigAooooAKguLeO6tpLeeNXhkUpIjdCpGCKnooA8Au9G1/wFqUtjawLqGkyuXtkkba+D/dJ7juP0qG/1LxBd2UiLpsWi27rskvtQnEYQHrtzyT/ugn0r326tbe8haC6gimibqkqBgfwNZ9t4Z0KyuVubXR7CG4XlZI7ZAw+hxxXfHHS5bNannzwFOU+ex4fJ4U1rwzaW+v6LbStYsoilhu1IeZR/y1dP4Ax+6P4flzyazvEOqLr1lCP7G1S31C3bdE0cZkU56jcO3pX0swVlwelYNz4L8P3UzSNp/lsevkSyRD8kYCuW9KdVVqkfeXVGrw/8rPBbbStZ1iW3tNWE8SSt+7s4kAurwjsqH7o9ZHwq9ea9WX4Z2174VuLLUVhS/nRBEYM7LMJykceedoydx6sWYmuw0vQNJ0RX/s3T7e2Z/wDWOi/M/wDvN1P41qdqcqiWlJcqOhqc9aruz5m1mHXfB223vpbeT+GNJVIkI9V/vKPUGtfSfCGo66sd34jle1s/vx2cPySP7t/d/n9KvxT2+rfFLX7zW7mJZtOl8mygnYBUVTgMAePf/gWa0tU8caRp8nkW8raneu21Le0/eFj/ALw/+vXgZria6r/V8DS9/rJLv26erO7D1JTpXr1HyLpc3Lu7trCykurqVYraFfnd+eBx+JryjxFqX9t29xrt+sqW5jMOj2fdhnDTv/sj9W4HQ1tpput+MtYWLUoFmlhbdHo8MhENvn+K6lH3f90ZkPota/xL8OroHgyxYym4lk1GI31xtCbwFYIqqPuxr0VBwPrzXXkWTQwE1Uqu9R/h/Xf7jmx2LdaDUF7qHaRZf2fotjZ/xRwjf/vN8x/nWQ3i20s/EV7p2oP5UMcgEUu3IU4G5Wx7966OWWKNZLh2T7Oi+aX7bMZz+VYnw80FfErX0t7uSK9aS6YqqncobYgYMCMZ83/vmvr6tRU4XZ8nhaHt5y5iG78X2e5bXSFbVb+TiKCCIkZ9+5/Csuwi1jw1q6680T6qs2+3vzbcqsrcmNGGd5XC5K8Z+XtXrNn8N7KFGimvZzbPxJbWsUdqko9HMah2HtuxXVHSbBtOXTvscC2arsWBYwEAHTAHTFeZisRTr03SmrxejPawuD9g+aD1PC9e16bxXp/9n2dpdadpoYS6hfXsZSOFF7cdee3UnaBVbT9bufDUC6X4h0+6gWDAin8v7qn5lVx2PNe1w+DtCgvIbr7K8skDb4fPnkmWJv7yh2IB96s6r4e0/V9r3ETLMFws8TlXX8R1/GsMD7DAQVKhG0TXF4d4rWq7s8Wk8baXI6xabFdaldvxHBFGfmP6n8hWh4N8O3+reJpLrUNj3hdftoTmOziUhhBkceYxC5X+FN2eXr0NPAViPkl1DVJIG+9CLgRK/s3lqpP510djp9npdnHaWFtFbW0fCxxKFUfgK6a+N5laJlh8DCk7luiiivPPQCiiigAooooAKKKKACoJvv8A4VPUE33/AMKAJV+6KdTV+6KdQAUUVT1O7ex06e6itJbp41yIIvvP7CgC5RXn2l/EyTVNbk0qLwrq63EMiJc7lX9xuPBbnpUnhX4naTrmiwXmqXFlpVxPK8cdtJcglguBnkD1oA72iuZtPFUL6xrtre/ZLS10ry83LXaHIYZJdf4OfWtPStf0nXY5H0vULa8WNtr+TIG2/WgDTorlNN8Z2U76h/aUllYJbX7WULm9STziOnT7rH+71q4fGvhlbQ3Ta7YfZ1l8kyeeMb+uKAN+isbUPFGg6SsBv9Ws7cXC74vMmA3qf4h7e9PvvEmi6Yls99qllbpdf6lpJgBJ7j296ANaislfEmimyuL0apZ/ZrZ/Lnl84bY2/uk+tT6XrGna1a/adMvoLuHOC8EgcA+hxQBforlNL8aWFzol1qWqTWWnwW95Ja7jepIrbenzD+Ig/d61uWGradqlh9usb6C5tOf30MgZOOvI9KAOU8XfDew8T366hiBLraEkMsZYSAdM7WU8VW0j4XW1iuLi+8uFhhoNNg+yhx6PJuaUj/gYrpYvGHhqe4t7eLXbB5bn/Uok6nfzt4/EYqS98VaBpt+the6xZW92cfuZZgrc9M+lae2nblvoZ+yje9i7p2mWWk2aWmn2kVrbp92OJQo/SoNc0W01/RbnS72PfbzptPHIPZh7g81l+NPFp8IadY3gshd/ar2O02eZs27gx3Zwf7tXr3xVoOm362F7rFlb3bY/cyzBW56Z9Ki7vfqXy9DyCf4aa1a/8S6WTWbvT93yW9q0WyTH/TRnGwfVfzr1Twl4fbQ9OYzrEt3Pt3pDnZCijbHEmeSqjuepLHvVu/8AFOhaXPLBe6tZ280KB5I5JgGVSQAcfjSz+KdCtdOt9RuNWs4rK54gnaYbJPoa1qV5zVmZwowhsjZorKi8Q6NNBeTxapZvDZnbcyLMu2Ej+8c8VBF4s8P3GmTalFrNk1nCwSSfzhtQnoGPbNYmpuUVn2GrafqkM01heQXEUMhikeJwwRgASCfbNVLLxX4f1CeWCz1mxuJYULyJFOrFVXqeOwoA26KyU8RaM1raXS6naNBeSeVbSCUbZnzjap7nIpkXinQJ9V/suHWLJ7/cV8hZgXyOox60AbNFedf8LLKS6XG2lwSNfawdLzDerIIwCoDnap5w/wB3iusbxRoI1f8Ask6xZjUN+z7N5437v7uPX2oA2aK4bSfiRptzqOt22ry2mlrp9+9nE8twP320sN3IGOlaKeLhJ4/bwwtmuwWH237X5/BGQMbce/XNAHUUVkab4l0TWLqS107VrO7njGXjhmDkD14rXoAKKKKACoJvv/hU9QTff/CgCVfuinU1fuiqV9q+naZLaxXt3FbvdSeVAJGxvf8Auj35oAv0Vj6h4j0nS7iS2vL6OO4SA3Jh5L+UASW2jn+FquadqFtqum29/ZyeZbXEYljfaRuU8jg80AcV4R06+tfiZ4zup7S4it7loPJmkjKrLgHO1iMHHtXnlt4Ou/8AhR18j+Hbj+3GvQ6I1kftGNyDIG3djbur3B9e06LXBoz3G2++zG72Mpx5QOC27G39atWd/Z6laLdWN3BdW752zQSCRDjrhhxQB4tN4avbqXxut/omry29wtm0f2aLEkpUcmPcMPg9RXSfDhNZHiPVZby2eexaJBHqVzposp5WGMIVwNwA71302r2MFtJcPcqYo22sU+ba3TBxmrwYMM02mt0SpwbsmeAXfhrV7iO6hfRL94pPF3nMjWjEPAd2X6fc9+lbl34SLat8R2j0BtklpH9gZbTh28sk+V8vJ3f3e9ezZFJkeopFXPBYrLxCtpaWEuh3lqv9hiGKe20tZpp22/NFK8inyxntT9J0vUNI1TwhqOo6Be6lCmlNaGyWAGa3l8x/mMbkYGD1Ne23l9BZRq87bA7hAdpPJ6dKzda8LaH4j8ltVsUnkhz5cgdo5Ez1AdSG/WnZ2uTzRu1c8P0vRL/UPBt49hYy+XZeKPOmtbZRKyRqoHyIcq5XPSvSvh/pjR6xrer7dXxdmMNLqFslt5xUfeWJVGMeuOa7TS9K0/RbFLLTLSK2tU6Rxrgc96vZB70ijwKw8O3sXhKR73Ttctbi38QS3EMttab3hBSMCQwsMunHau4+H0Wr/wDCMa3/AGjpqQNNNKYZlshbS3YIP7x4hjBNei5HrRkeooC54AvhK+h+FXhvyvD90msJrAkuCtownWPMnzN8u7HCdfarmq6XfWH/AAmek3fh2/1LUNZuvNsbuG28yMqxyuZP4dle6ZBrFtfFGj32u3Gi2t55t/bKTLGsbYTBwQXxtz7ZoA4Tx5oerN8PPCunLBcX97Z3tp9o8iIyn5YnDMcZ4z3rA1bS76w/4TPSbvw7f6lqGs3Xm2N3DbeZGVY5XMn8OyvdKKAPHdE8JXi/EKZNb01ryCHw7HB9plhMkTzgRqQrkYLfe965nQdG1bR4vBmo6joV/dw2b3KS6cIP36lidriNsHHOfT5a+iKx9a8M6N4jSJdWslufJJMT7mRkJ67WUhh09aAPC7TRL/V/D/i+DS9PliWDxAk0ljEqM3lqZMxqvKnbleP9mr2u6DfapofiK/sLTxDdTTw28OLmwWDzisqH5Yo0DEqA3OK9s0fRNN0Ky+yaXZxWsGclU7n1JPJP1rSoA5mbTjpfgS4tdI0uBrj7EQlp5YCyvsxhhxnPevMfD9hq934w8HXU+l6jHbwxzpcI2li2gtiYyCg2qDjnq34d690rM0nXNP1tLp7CYyrbTvbS/IV2yL94cgUAeT+GvDWrweL7PRJ9NuF0nw/c3l5ayvGRFcbtvlAOeCQTmsZLDxDevoPnaJf201trkctxa22kiK3gAb74kC72yOpzj9K97u7u30+zmu7qRYbeFS8kjdFA6mqui63p3iDT1v8AS5zPbMxAfy2TJHswBoA8O0nw7rkZ0IPo1+hi8XPcSBraQbIf3P7w8cLw3PSn6nY+ItSt5kk0K9tbpNZSaSzstLUQhc/63zQu9z7g19A0UAeAT6fe2a/EGO58JajdS6rfzJY3CWhfku5UjIzt53Ajr+VXYPCfiJdWksvslwkreERZCfYfK87A/deZ93PbrXuVFAHivg7SLltW8OvPaa8t1o9u6yJLYRW8MJ27WTeFBl3duT6+ter6Jqc2saTDez6fdafJJnNvcrh0wccj3pJtd0uCPUGa/gY6fH5t2iSBnhAGfmUZI4FWNO1C21XTbe/s5PMtriMSxvtI3KeRweaALlFFFABUE33/AMKnqCb7/wCFAEq/dFcJ8WtJfUPAdxd23/H3pkiXsTr1XZ94/wDfJY13a/dFRyxRzxNFKivG4IZWXIYHqCKAPFbS+fxLF458bQM6LHpn2OykXKlCIg0mPQg7azbu71SbTNFuX1KW/t49FSSSxj1Y2k8bd5+fv/r9K9yg0XSrbT5NPt9Ns4bKXPmW8cCrG+euVAwc1WuvC+gX0NvFdaLp08VsuyBJLZCIx6KMcD2oA8n0/UpfEXiq1gXUtUayufDLt++kKSswZl3HGBnjrjmug+CMVr/wgP7m9eW4eRxND52fJ+ZtuF/hyOfevQ00nTYbtLyOwtUuUi8lJlhUSKn9wNjOPalstM0/TzM1lZWtq0zb5TBGE3n1bAGaAZ56pFrouqmK6lE6XOzb5nO3I+bH9a0p1murvXS15dILaJXjWOQgA7Sa7CTTbGUyGS1hcyfeJjB3fWl+w2oMx+zxfvhiT5B846YPrXfLGJ3dtf8Ahv8AI8WGVzTS5tP+H/zRx8ep3NhHpWpzzyvFNbNHIpYkbwCVOPU1CHuIX0OK7vriMTq7zN5hGc9ATXSap4ei1I20Bm8myhOTbxxgAn69utWLvRbe71C1uX+7bqyCPAKsCMc01iKX5/rb8yJYHEaq+itb8L/l+Zxct7cJbvDDdStbR6giRy+YckYbIz6dKtmcXB1K5vtVms7mC42RBWJ2qDxhM85rsRpliIFhFpD5StuCeWMA+uPWll06ymuFuHtIHmHSRkBP50pYqD6f1oXHLasdXK/l9/5X0MjxBqrR6NdrZTZu4lXft4ZA3fHasw3CWMd0dO1WWeX7H5hibLgH+/u6A+1dd9lg3O3kx5kGHO0fMPf1pltYWlpu+z20UO7rsUDP5VjGtGMbWOirhKtSfNzdLddPQ4m2uXguNKa2vZ53uoWNyrTFsHbnOO2Of++aitjdmw0i7+33fmXFwYX/AHnG0tjv3ruoNMsbZmeG0gjZuGKoBkUDT7NUjQWsISI7kHljCH1HpWv1uPRf1r/mc6y2p1l+fl/k/vMPw4ZYNX1WxaaWWKIoU81txGc968i02K88P6X8RdS0i8vGvLK9e2QtMW+QykNIw7yBR96vfY7aCKWSZIY0kk++yqAW+pqGDStPtWujb2NtE10xe4McKr5zHqXwPmPPeuWrPnlzWPTw1GVGnyt31Z4pe376NcwweHfEF7qEN74fuZ77ddmXy2WF2WUHPyNurvfhZYynwjZ6xd6lf3l3fQr5n2mcuqBWYKFB6e/rXS2nhjQdPiuIrPRrC3S4UpMsdsgEinqrYHI9q0LW0t7G1jt7OCK3gjGEjiUKqj2A4rM3PnjS59YbwRoOujxFq630uuixBa5LqEYHPynOTx3rR1rUta8Kal450vStU1KaG2gtnjkuJzLJHv8AL3sGPT77c17Unh7RY7SO0j0mwW2im86OFbZAiSD+MLjAb3qX+ydNF1cXX2C1Fxcrsnm8ld0q4xtdsZIx60AeJalqEuh6lcWXhzXb2/s7nw/Nc3TNdmXyXEbFZQ2flJO3p/eqa8bVNJ+HOgahFq2oyy65PapfTz3pUJGA2FWTB8oHPLV6/aeGNBsIbiCz0awghuBtmSO3UCQejDHIq0dKsG07+zmsbU2O3Z9m8oeXt9NuMUAcT8PDqMWsa3Zz30EtlG0bwWq6g149qSPmUuwBw3UV5vFqmrT3tparrN/D5/i6S2Lx3JyEJjGBnI4z06V79p2lafpFt9n06xgtICcmOCMIM+vFVx4e0RZFddGsFdLj7SrLbJlZv+eg4+9x160AeNXttPbw/EXw+2qajPY2FvFPAJ7ku6nG4gk9jnmnaeDHJ4I0K+1a9tNDvdON5JJ9rMfmTlT+738bVXC4H+1XtD6NpbvdO+m2bPeLsuWaFSZgOgfj5vxpl1oGj32nxWF1pdlNZw48qCSBTGmOm1cYH4UAeG/21rN1oem2ceuX/wBmHiY2NtfRznzJYDjHzfxYz3rf1DSZ3+Id14bi1vV4tPg0IyjZdncWDZBJr1T+xNJ+z2tudLs/ItWD28fkLthYdCgxwfpUraZYNetfGxtTdvH5JnMQ8xk/ulsZx7UAeGafd6tDofgTxKdd1GW8vdSFnOjz5iaISsmNv+6vJqOXxPPPf6Zrml32oL9q1pIfOudUDO8Z+9H9mA2qn3ea9wXQdHW3tbYaTYLBaSeZbx/Z12wtnO5BjCnPpUf/AAi+gee039iab5ryCZn+ypkuOjdOoz1oA8a8i303xV8R2j1S6ivYLR3tka5IaTdGzMcdW29vSn6RfPrWraLpviHW7yw0yPw+lzE63Zi86YkZYtn5iPm/75r2i50TSb24a5utMs553jMTSywKzMhHKkkZx7VFdeGdDvbW3tbrR7Ce3t+IY5LZWWMeijHFAHimj6rr2vr4Ctb3VtSgF3JdwyTRTlJJo1xgk9z1GT/Oup8Da3F4c1bxhp2razL/AGXpt7FFbTX85Ypv8wbdx/3R/OvSjpGmNJayHT7TzLQYtn8lcwg8fIcfL+FRtoWkM1w7aXZlrl1kmP2dcyspyrNxyQemaANOoZPvD6VNUE33/wAKAJV+6KdVVZ22rwP1p/nN7UAT0VB5ze1HnN7UAT0VD5h9BSpIW64oAloqEykdAKd5h9qAJKKh8w+gp28+goAkoqPzD7U7JoAdRTcmjJoAdRUfmH2p2TQA6iofMPoKd5h9qAJKKbk0ZNADqKbk0ZNADqKbk0ZNADqKbk0ZNADqKbk0ZNADqKj3n0FHmH2oAkoqHzD6CpMmgB1FNyab5h9qAJKKh8w+gp3mH2oAkqCb7/4U/efQU0uc9B+VAH//2Q==\"}]}"},{"id":2220,"title":"Wayfinding 3 - passed areas","description":"This is the third part of a series of assignments about wayfinding. The final goal of this series 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. See \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing [1]\u003e\r\n\u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing [2]\u003e . \r\n\r\n*Which areas are traversed?*\r\n\r\n\u003c\u003chttp://i58.tinypic.com/263wzdt.png\u003e\u003e\r\n\r\nFor this third assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments.\r\n\r\nIn this assignments, the areas do not overlap. If an area is crossed twice, it is listed twice in the returned vector. And if |AB| crosses first for example area |F2|, then |F3|, and then |F2| again, the output vector should contain |[ ... 2 3 2 ... ]|. Simple.\r\n\r\nThe inputs of the function |WayfindingPassed(AB,F)| 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 cell array |F| of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F. \r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\r\n\r\n\r\nYour output |v| will contain the indices in |F| of the crossed areas, in the correct order. In the example above, the correct answer is |[ 3 4 4 1 1]|. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'. If you pass the same area multiple times, and leave it in between, each event is listed.\r\n","description_html":"\u003cp\u003eThis is the third part of a series of assignments about wayfinding. The final goal of this series 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. See \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\"\u003e[1]\u003c/a\u003e \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\"\u003e[2]\u003c/a\u003e .\u003c/p\u003e\u003cp\u003e\u003cb\u003eWhich areas are traversed?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i58.tinypic.com/263wzdt.png\"\u003e\u003cp\u003eFor this third assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments.\u003c/p\u003e\u003cp\u003eIn this assignments, the areas do not overlap. If an area is crossed twice, it is listed twice in the returned vector. And if \u003ctt\u003eAB\u003c/tt\u003e crosses first for example area \u003ctt\u003eF2\u003c/tt\u003e, then \u003ctt\u003eF3\u003c/tt\u003e, and then \u003ctt\u003eF2\u003c/tt\u003e again, the output vector should contain \u003ctt\u003e[ ... 2 3 2 ... ]\u003c/tt\u003e. Simple.\u003c/p\u003e\u003cp\u003eThe inputs of the function \u003ctt\u003eWayfindingPassed(AB,F)\u003c/tt\u003e are a matrix \u003ctt\u003eAB\u003c/tt\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array \u003ctt\u003eF\u003c/tt\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\u003c/pre\u003e\u003cp\u003eYour output \u003ctt\u003ev\u003c/tt\u003e will contain the indices in \u003ctt\u003eF\u003c/tt\u003e of the crossed areas, in the correct order. In the example above, the correct answer is \u003ctt\u003e[ 3 4 4 1 1]\u003c/tt\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'. If you pass the same area multiple times, and leave it in between, each event is listed.\u003c/p\u003e","function_template":"function f = WayfindingPassed(AB,F)\r\n  f = 1:length(F);\r\nend","test_suite":"    %%\r\n\r\n    AB = [ 2 -2 ; 8 -6 ];\r\n    F{1} = [\r\n        -4   -4    4    4\r\n        -4   -0   -0   -4\r\n        ];\r\n    F{2} = [\r\n        -4   -4    4    4\r\n        2    6    6    2\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [2 1];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ 8 -4 ; 8 -8 ];\r\n    F{1} = [\r\n        -6    2    2   -4   -4    8    8   -6\r\n        -6   -6   -4   -4    2    2    4    4\r\n        ];\r\n    F{2} = [\r\n        -2   -2    4    4\r\n        -0   -2   -2   -0\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 1 2 1 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ -8 8 ; 8 -8 ];\r\n    F{1} = [\r\n        -2   -2    0    0\r\n        -0    2    2   -0\r\n        ];\r\n    F{2} = [\r\n        2    4    4   -6   -6   -4    2    4    4    2    2   -4   -4    2\r\n        -0   -0   -6   -6    4    6    6    4    2    2    4    4   -4   -4\r\n        ];\r\n    F{3} = [\r\n        -3   -3    1    0\r\n        -1   -3   -3   -1\r\n        ];\r\n    F{4} = [\r\n        5    9    9    5\r\n        -3   -3   -9   -9\r\n        ];\r\n    F{5} = [\r\n        -9  -10  -10   -9\r\n        9    9   10   10\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 2 1 2 4 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    AB = [ 0 0 ; -8 8 ];\r\n    F{1} = [\r\n        -4   -2   -2   -4\r\n        8    8    4    4\r\n        ];\r\n    F{2} = [\r\n        2    4    4    2\r\n        -0   -0   -6   -6\r\n        ];\r\n    F{3} = [\r\n        -4   -2   -2   -6   -6\r\n        -4   -4   -6   -6   -4\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    assert(isempty(f));\r\n    \r\n    %%\r\n\r\n    AB = [ 7 -8 ; 0 0 ];\r\n    F{1} = [\r\n        8    9    9    8\r\n        3    3   -2   -2\r\n        ];\r\n    F{2} = [\r\n        -9   -7   -7   -4   -4   -3   -3    0    0    1    1    4    4    5    5   -2   -8   -9\r\n        -2   -2    2    2   -2   -2    2    2   -2   -2    2    2   -2   -2    3    4    3    2\r\n        ];\r\n    F{3} = [\r\n        -2   -1   -1   -2\r\n        1    1   -4   -4\r\n        ];\r\n    F{4} = [\r\n        -6   -5   -5   -3    1    2    2    3    3    1   -4   -6\r\n        1    1   -3   -5   -5   -4    1    1   -5   -8   -7   -4\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 2 4 2 3 2 4 2 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ 0 -2 ; 0 -4 ];\r\n    F{1} = [\r\n        -3    3    3    2    2   -2   -2    2    2   -3\r\n        -5   -5    3    3   -3   -3    2    2    3    3\r\n        ];\r\n    F{2} = [\r\n        -1    1    1   -1\r\n        1    1   -1   -1\r\n        ];\r\n    F{3} = [\r\n        -4    4    4    5    5   -5   -5   -4\r\n        4    4   -7   -7    5    5   -1   -1\r\n        ];\r\n    F{4} = [\r\n        -5   -4   -4    4    4   -5\r\n        -1   -1   -6   -6   -7   -7\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 2 1 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ -2 0 ; 6 -6 ];\r\n    F{1} = [\r\n        2   -4   -4    2    2   -2    0   -2    2\r\n        -4   -4    4    4    2    2   -0   -2   -2\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 1 1 1 ];\r\n    assert(isequal(f,f_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2014-03-03T12:10:50.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-02-25T23:45:22.000Z","updated_at":"2017-05-05T15:03:27.000Z","published_at":"2014-03-03T09:46:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the third part of a series of assignments about wayfinding. The final goal of this series 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. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWhich areas are traversed?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this third assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this assignments, the areas do not overlap. If an area is crossed twice, it is listed twice in the returned vector. And if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crosses first for example area\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e again, the output vector should contain\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ ... 2 3 2 ... ]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Simple.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWayfindingPassed(AB,F)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ AB = [\\n   xA xB\\n   yA yB\\n ]\\n\\n F = {\\n  [ x11 x12 ... x1n ;\\n    y11 y12 ... y1n ]\\n  [ x21 x22 ... x2n ;\\n    y21 y22 ... y2n ]\\n }]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour output\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will contain the indices in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the crossed areas, in the correct order. In the example above, the correct answer is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ 3 4 4 1 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'. If you pass the same area multiple times, and leave it in between, each event is listed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"}]}"},{"id":2226,"title":"Wayfinding 4 - Crossing, level 2","description":"This is the fourth part of a series of assignments about wayfinding. The final goal of this series 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. See \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing [1]\u003e\r\n\u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing [2]\u003e \u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas [3]\u003e. \r\n\r\n*Which areas are traversed?*\r\n\r\n\u003c\u003chttp://i62.tinypic.com/358qa1w.png\u003e\u003e\r\n\r\nFor this fourth assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments. Quite similar to \u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas assignment 3\u003e.\r\n\r\nHowever, now the areas may overlap. If case of traversing overlapping areas, the area with the highest index in |F| is the one listed.\r\nIf an area is crossed twice, it is listed twice in the returned vector. And if |AB| crosses first for example area |F2|, then |F3|, and then |F2| again, the output vector should contain |[ ... 2 3 2 ... ]|. That would also be the case when |F3| is contained in |F2|. But when |F2| is contained in |F3|, then |F2| is never crossed, as it has a lower index in F than |F3|. Consider the areas non-transparent and stacked on top of each other.\r\n\r\nThe inputs of the function |WayfindingPassed(AB,F)| 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 cell array |F| of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F. \r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\r\n\r\n\r\nYour output |f| will contain the indices in |F| of the crossed areas, in the correct order. In the example above, the correct answer is |[ 3 1 4 1 4 1]|. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'.","description_html":"\u003cp\u003eThis is the fourth part of a series of assignments about wayfinding. The final goal of this series 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. See \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\"\u003e[1]\u003c/a\u003e \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\"\u003e[2]\u003c/a\u003e \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\"\u003e[3]\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eWhich areas are traversed?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i62.tinypic.com/358qa1w.png\"\u003e\u003cp\u003eFor this fourth assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments. Quite similar to \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\"\u003eassignment 3\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eHowever, now the areas may overlap. If case of traversing overlapping areas, the area with the highest index in \u003ctt\u003eF\u003c/tt\u003e is the one listed.\r\nIf an area is crossed twice, it is listed twice in the returned vector. And if \u003ctt\u003eAB\u003c/tt\u003e crosses first for example area \u003ctt\u003eF2\u003c/tt\u003e, then \u003ctt\u003eF3\u003c/tt\u003e, and then \u003ctt\u003eF2\u003c/tt\u003e again, the output vector should contain \u003ctt\u003e[ ... 2 3 2 ... ]\u003c/tt\u003e. That would also be the case when \u003ctt\u003eF3\u003c/tt\u003e is contained in \u003ctt\u003eF2\u003c/tt\u003e. But when \u003ctt\u003eF2\u003c/tt\u003e is contained in \u003ctt\u003eF3\u003c/tt\u003e, then \u003ctt\u003eF2\u003c/tt\u003e is never crossed, as it has a lower index in F than \u003ctt\u003eF3\u003c/tt\u003e. Consider the areas non-transparent and stacked on top of each other.\u003c/p\u003e\u003cp\u003eThe inputs of the function \u003ctt\u003eWayfindingPassed(AB,F)\u003c/tt\u003e are a matrix \u003ctt\u003eAB\u003c/tt\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array \u003ctt\u003eF\u003c/tt\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\u003c/pre\u003e\u003cp\u003eYour output \u003ctt\u003ef\u003c/tt\u003e will contain the indices in \u003ctt\u003eF\u003c/tt\u003e of the crossed areas, in the correct order. In the example above, the correct answer is \u003ctt\u003e[ 3 1 4 1 4 1]\u003c/tt\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'.\u003c/p\u003e","function_template":"function f = WayfindingPassed(AB,F)\r\n  f = 1:length(F);\r\nend","test_suite":"%%\r\nAB = [ -10 10 ; -10 10 ];\r\nF{1} = [\r\n    -5    5   -8    0\r\n    -6    2    7    1\r\n    ];\r\nF{2} = [\r\n    4   -2    4    6\r\n    6   -7   -3   -2\r\n    ];\r\nF{3} = [\r\n    -5    6    3   -1\r\n    -6   -8    4   -2\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 3 2 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 21 ; 0 0 ];\r\nf_correct = randperm(20);\r\nF = arrayfun(@(n)[n+[0 1 1 0];-1 -1 1 1],f_correct,'uni',0);\r\nf = WayfindingPassed(AB,F);\r\nassert(isequal(f(f_correct),f_correct(f)));\r\n\r\n%%\r\nAB = [ -10 10 ; -10 10 ];\r\nF{1} = [\r\n    -5    9    0   -4    5\r\n    2    8   -1   -9   -8\r\n    ];\r\nF{2} = [\r\n    -2  -10   -4    0\r\n    8    7   -5    5\r\n    ];\r\nF{3} = [\r\n    -6    2   10\r\n    10   -4    8\r\n    ];\r\nF{4} = [\r\n    -10    8  -10\r\n    4   -8    2\r\n    ];\r\nF{5} = [\r\n    0    4    8   -3    1\r\n    -10    9   -8   -5    2\r\n    ];\r\nF{6} = [\r\n    6    6   -9   10\r\n    6   -3    4   -7\r\n    ];\r\nF{7} = [\r\n    9    7   -7\r\n    0    7   -5\r\n    ];\r\nF{8} = [\r\n    2    0   10\r\n    6  -10    0\r\n    ];\r\nF{9} = [\r\n    -7    2   -7   -7\r\n    3    5   -3    7\r\n    ];\r\nF{10} = [\r\n    -5    6    1    5\r\n    -10    0    8    4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 7 8 10 7 3 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\nAB = [ -10 10 ; -10 10 ];\r\nF{1} = [\r\n    2    5    8    5\r\n    2   -2    9   -5\r\n    ];\r\nF{2} = [\r\n    -8    2   -2    8   -8   -2\r\n    0    4    5   -9    8   -2\r\n    ];\r\nF{3} = [\r\n    5   -6   -2    1    0   10\r\n    10   -8    0   10   -2   -5\r\n    ];\r\nF{4} = [\r\n    10   -4  -10   -2    9\r\n    4    1    8   -4   -1\r\n    ];\r\nF{5} = [\r\n    -9   -7    2   -3\r\n    2   -9   -4    5\r\n    ];\r\nF{6} = [\r\n    -3   10    6    9    4   -2\r\n    10   -6    2    2    5   -5\r\n    ];\r\nF{7} = [\r\n    -1   -5   -5\r\n    3    0   -4\r\n    ];\r\nF{8} = [\r\n    8   -6    8   10   -7\r\n    8   -2   -5    3    7\r\n    ];\r\nF{9} = [\r\n    1  -10   -3   10    5\r\n    -5   -6    3   -6    8\r\n    ];\r\nF{10} = [\r\n    -7    0    8   -8\r\n    7   -8    3    9\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 5 9 10 9 3 1 8 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 4 -6 ; 0 0 ];\r\nF{1} = [\r\n    -4   -4    2    2   -2   -3   -3   -2    2    2   -4\r\n    2   -4   -4   -2    2    2   -2   -2    2    4    4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 0 ; 15 -8 ];\r\nF{1} = [\r\n    -4    4    4   -4\r\n    6    2    6    2\r\n    ];\r\nF{2} = [\r\n    -2   -2    6    6   -2\r\n    -0   -4   -0   -4   -0\r\n    ];\r\nF{3} = [\r\n    -1   -1    2    2\r\n    -6   -4   -6   -4\r\n    ];\r\nF{4} = [\r\n    -1    1   -1    1\r\n    -7   -7   -9   -9\r\n    ];\r\nF{5} = [\r\n    -2     2    -1     2    -1     1\r\n    14    10     6     6    10    14\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 5 5 1 2 3 4 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 0 ; -6 6 ];\r\nF{1} = [\r\n    -5    7    7   -5\r\n    -9   -9    9    9\r\n    ];\r\nF{2} = [\r\n    -1    1    1   -1\r\n    -7   -7   -5   -5\r\n    ];\r\nF{3} = [\r\n    -2   -2    2    2\r\n    4    2    2    4\r\n    ];\r\nF{4} = [\r\n    2    2   -2   -2\r\n    4    2    2    4\r\n    ];\r\nF{5} = [\r\n    -1    1    1   -1\r\n    2    2   -2   -2\r\n    ];\r\nF{6} = [\r\n    -2    0   -2\r\n    -2   -3   -4\r\n    ];\r\nF{7} = [\r\n    0    2    2\r\n    -3   -4   -2\r\n    ];\r\nF{8} = [\r\n    -1    0    1\r\n    -8   -6   -8\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [8 2 1 7 1 5 4 1];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 2 -2 ; 8 -6 ];\r\nF{1} = [\r\n    -4   -4    4    4\r\n    -4   -0   -0   -4\r\n    ];\r\nF{2} = [\r\n    -4   -4    4    4\r\n    2    6    6    2\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [2 1];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 8 -4 ; 8 -8 ];\r\nF{1} = [\r\n    -6    2    2   -4   -4    8    8   -6\r\n    -6   -6   -4   -4    2    2    4    4\r\n    ];\r\nF{2} = [\r\n    -2   -2    4    4\r\n    -0   -2   -2   -0\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 2 1 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ -8 8 ; 8 -8 ];\r\nF{1} = [\r\n    -2   -2    0    0\r\n    -0    2    2   -0\r\n    ];\r\nF{2} = [\r\n    2    4    4   -6   -6   -4    2    4    4    2    2   -4   -4    2\r\n    -0   -0   -6   -6    4    6    6    4    2    2    4    4   -4   -4\r\n    ];\r\nF{3} = [\r\n    -3   -3    1    0\r\n    -1   -3   -3   -1\r\n    ];\r\nF{4} = [\r\n    5    9    9    5\r\n    -3   -3   -9   -9\r\n    ];\r\nF{5} = [\r\n    -9  -10  -10   -9\r\n    9    9   10   10\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 1 2 4 ];\r\nassert(isequal(f,f_correct));\r\n\r\nAB = [ 0 0 ; -8 8 ];\r\nF{1} = [\r\n    -4   -2   -2   -4\r\n    8    8    4    4\r\n    ];\r\nF{2} = [\r\n    2    4    4    2\r\n    -0   -0   -6   -6\r\n    ];\r\nF{3} = [\r\n    -4   -2   -2   -6   -6\r\n    -4   -4   -6   -6   -4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nassert(isempty(f));\r\n\r\n%%\r\n\r\nAB = [ 7 -8 ; 0 0 ];\r\nF{1} = [\r\n    8    9    9    8\r\n    3    3   -2   -2\r\n    ];\r\nF{2} = [\r\n    -9   -7   -7   -4   -4   -3   -3    0    0    1    1    4    4    5    5   -2   -8   -9\r\n    -2   -2    2    2   -2   -2    2    2   -2   -2    2    2   -2   -2    3    4    3    2\r\n    ];\r\nF{3} = [\r\n    -2   -1   -1   -2\r\n    1    1   -4   -4\r\n    ];\r\nF{4} = [\r\n    -6   -5   -5   -3    1    2    2    3    3    1   -4   -6\r\n    1    1   -3   -5   -5   -4    1    1   -5   -8   -7   -4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 4 2 3 2 4 2 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 -2 ; 0 -4 ];\r\nF{1} = [\r\n    -3    3    3    2    2   -2   -2    2    2   -3\r\n    -5   -5    3    3   -3   -3    2    2    3    3\r\n    ];\r\nF{2} = [\r\n    -1    1    1   -1\r\n    1    1   -1   -1\r\n    ];\r\nF{3} = [\r\n    -4    4    4    5    5   -5   -5   -4\r\n    4    4   -7   -7    5    5   -1   -1\r\n    ];\r\nF{4} = [\r\n    -5   -4   -4    4    4   -5\r\n    -1   -1   -6   -6   -7   -7\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 1 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ -2 0 ; 6 -6 ];\r\nF{1} = [\r\n    2   -4   -4    2    2   -2    0   -2    2\r\n    -4   -4    4    4    2    2   -0   -2   -2\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 1 1 ];\r\nassert(isequal(f,f_correct));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-01T22:33:13.000Z","updated_at":"2014-03-06T07:49:23.000Z","published_at":"2014-03-06T07:49:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the fourth part of a series of assignments about wayfinding. The final goal of this series 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. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWhich areas are traversed?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this fourth assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments. Quite similar to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eassignment 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, now the areas may overlap. If case of traversing overlapping areas, the area with the highest index in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the one listed. If an area is crossed twice, it is listed twice in the returned vector. And if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crosses first for example area\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e again, the output vector should contain\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ ... 2 3 2 ... ]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. That would also be the case when\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is contained in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. But when\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is contained in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is never crossed, as it has a lower index in F than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Consider the areas non-transparent and stacked on top of each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWayfindingPassed(AB,F)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ AB = [\\n   xA xB\\n   yA yB\\n ]\\n\\n F = {\\n  [ x11 x12 ... x1n ;\\n    y11 y12 ... y1n ]\\n  [ x21 x22 ... x2n ;\\n    y21 y22 ... y2n ]\\n }]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour output\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will contain the indices in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the crossed areas, in the correct order. In the example above, the correct answer is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ 3 1 4 1 4 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"}]}"},{"id":2242,"title":"Wayfinding 5 - Travel contour","description":"This is the fifth part of a series of assignments about wayfinding. The final goal of this series 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. See \r\n\u003chttp://www.mathworks.nl/matlabcentral/cody/?term=tag%3Awayfinding search:tag=wayfinding\u003e for the other assignments.\r\n\r\nThis time, you will travel around a polygon, over its contour. You get the nodes of the polygon, in the correct order, as a |2xn| array |F|. The last node of |F| is connected to the first node.\r\n\r\n|a| is the index in |F| of the starting node, and |b| is the goal. \r\n\r\n\u003c\u003chttp://i61.tinypic.com/iq8p69.png\u003e\u003e\r\n\r\nCalculate the shortest distance from |a| to |b| over the contour of the polygon. \r\n\r\nThe distance is measured as the Euclidean distance between points. You can not enter the internal area of the polygon. The contour of the polygon does not self-intersect.","description_html":"\u003cp\u003eThis is the fifth part of a series of assignments about wayfinding. The final goal of this series 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. See  \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/?term=tag%3Awayfinding\"\u003esearch:tag=wayfinding\u003c/a\u003e for the other assignments.\u003c/p\u003e\u003cp\u003eThis time, you will travel around a polygon, over its contour. You get the nodes of the polygon, in the correct order, as a \u003ctt\u003e2xn\u003c/tt\u003e array \u003ctt\u003eF\u003c/tt\u003e. The last node of \u003ctt\u003eF\u003c/tt\u003e is connected to the first node.\u003c/p\u003e\u003cp\u003e\u003ctt\u003ea\u003c/tt\u003e is the index in \u003ctt\u003eF\u003c/tt\u003e of the starting node, and \u003ctt\u003eb\u003c/tt\u003e is the goal.\u003c/p\u003e\u003cimg src = \"http://i61.tinypic.com/iq8p69.png\"\u003e\u003cp\u003eCalculate the shortest distance from \u003ctt\u003ea\u003c/tt\u003e to \u003ctt\u003eb\u003c/tt\u003e over the contour of the polygon.\u003c/p\u003e\u003cp\u003eThe distance is measured as the Euclidean distance between points. You can not enter the internal area of the polygon. The contour of the polygon does not self-intersect.\u003c/p\u003e","function_template":"function d = polygon_distance(F,a,b)\r\n  d = 0;\r\nend","test_suite":"%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 1;\r\nb = 3;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 2;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 1;\r\nb = 2;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 1;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 4;\r\nb = 1;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 1;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 3;\r\nb = 3;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 0;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [zeros(1,101) ones(1,101);0:100 100:-1:0];\r\na = 1;\r\nfor b = randi(size(F,2)/2,1,100)\r\n  d = polygon_distance(F,a,b);\r\n  d_correct = b-1;\r\n  assert(isequal(d,d_correct));\r\nend\r\n\r\n%%\r\nF = [zeros(1,101) ones(1,101);0:100 100:-1:0];\r\na = 1;\r\nfor b = randi(size(F,2)/2,1,100)+size(F,2)/2\r\n  s = rand(1)+1;\r\n  d = polygon_distance(F*s,a,b);\r\n  d_correct = (size(F,2)-b+1)*s;\r\n  assert(abs(d-d_correct)\u003c1e-10);\r\nend\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2014-03-10T14:22:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-10T09:32:11.000Z","updated_at":"2014-03-10T14:22:52.000Z","published_at":"2014-03-10T13:43:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the fifth part of a series of assignments about wayfinding. The final goal of this series 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. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/?term=tag%3Awayfinding\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esearch:tag=wayfinding\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for the other assignments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis time, you will travel around a polygon, over its contour. You get the nodes of the polygon, in the correct order, as a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2xn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The last node of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is connected to the first node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the index in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the starting node, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the goal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the shortest distance from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the contour of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe distance is measured as the Euclidean distance between points. You can not enter the internal area of the polygon. 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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2218,"title":"Wayfinding 1 - crossing","description":"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.\r\n\r\n*How many times does AB cross another line?*\r\n\r\n\u003c\u003chttp://i60.tinypic.com/mk7us1.png\u003e\u003e\r\n\r\nThe 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.  \r\n\r\nThe 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.\r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n L = cat(3,...\r\n  [ x1_start x1_end\r\n    y1_start y1_end ] ...\r\n   ,...\r\n  [ x2_start x2_end\r\n    y2_start y2_end ] ...\r\n   ,...\r\n  [ x3_start x3_end\r\n    y3_start y3_end ] ... % etc.\r\n  )  \r\n\r\nYour 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. \r\n\r\np.s. I noticed later on that there is another Cody problem \u003chttp://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect 1720\u003e that is somewhat similar. But this was a logical start for the series.","description_html":"\u003cp\u003eThis 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.\u003c/p\u003e\u003cp\u003e\u003cb\u003eHow many times does AB cross another line?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i60.tinypic.com/mk7us1.png\"\u003e\u003cp\u003eThe 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.\u003c/p\u003e\u003cp\u003eThe inputs of the function \u003ctt\u003eWayfindingIntersections(AB,L)\u003c/tt\u003e are a matrix \u003ctt\u003eAB\u003c/tt\u003e 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 \u003ctt\u003eL\u003c/tt\u003e 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.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e L = cat(3,...\r\n  [ x1_start x1_end\r\n    y1_start y1_end ] ...\r\n   ,...\r\n  [ x2_start x2_end\r\n    y2_start y2_end ] ...\r\n   ,...\r\n  [ x3_start x3_end\r\n    y3_start y3_end ] ... % etc.\r\n  )  \u003c/pre\u003e\u003cp\u003eYour 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.\u003c/p\u003e\u003cp\u003ep.s. I noticed later on that there is another Cody problem \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect\"\u003e1720\u003c/a\u003e that is somewhat similar. But this was a logical start for the series.\u003c/p\u003e","function_template":"function n = WayfindingIntersections(AB,L)\r\n  n = randi(size(L,3)+1)-1;\r\nend","test_suite":"%%\r\nAB = [2 0;0 5];\r\nL = cat(3,...\r\n    [1 0;2 2],...\r\n    [-1 4;3 3],...\r\n    [-3 2;0 2],...\r\n    [2 3;4 2]...\r\n    );\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 2;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 6 -3 ; 5 2 ];\r\nL = cat(3,...\r\n[ 2 2 ; 2 -9 ],...\r\n[ -2 3 ; 8 8 ],...\r\n[ 7 -1 ; 4 6 ],...\r\n[ 7 -3 ; -6 1 ],...\r\n[ -6 -6 ; -1 2 ],...\r\n[ 5 -8 ; 3 4 ],...\r\n[ 3 5 ; -8 -9 ],...\r\n[ 8 -8 ; 4 -3 ],...\r\n[ -7 9 ; -5 9 ],...\r\n[ 6 3 ; 8 3 ],...\r\n[ 0 4 ; 9 -2 ],...\r\n[ -8 0 ; 4 0 ],...\r\n[ 6 8 ; 6 0 ],...\r\n[ -6 2 ; -6 9 ],...\r\n[ 8 -4 ; 1 -5 ],...\r\n[ 5 -1 ; -5 -3 ],...\r\n[ -2 -9 ; 6 -5 ],...\r\n[ 8 6 ; 6 -7 ],...\r\n[ -4 2 ; 5 2 ],...\r\n[ 8 6 ; 0 6 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ -3 -1 ; -3 7 ];\r\nL = cat(3,...\r\n[ 9 8 ; 1 6 ],...\r\n[ -4 -6 ; -3 9 ],...\r\n[ -2 8 ; 7 5 ],...\r\n[ -3 5 ; -8 2 ],...\r\n[ 1 2 ; 3 5 ],...\r\n[ 4 -5 ; -3 -5 ],...\r\n[ 8 5 ; -1 -2 ],...\r\n[ 4 8 ; 3 5 ],...\r\n[ -3 -4 ; 7 8 ],...\r\n[ 9 7 ; -1 -3 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 1;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 5 9 ; -9 0 ];\r\nL = cat(3,...\r\n[ 3 -1 ; 1 -2 ],...\r\n[ -5 3 ; -3 4 ],...\r\n[ -9 -2 ; -3 -7 ],...\r\n[ -6 -5 ; -1 -3 ],...\r\n[ 4 -3 ; 5 -9 ],...\r\n[ -6 -2 ; -4 -4 ],...\r\n[ -1 -7 ; -3 -4 ],...\r\n[ 0 9 ; 6 3 ],...\r\n[ -6 1 ; -7 -8 ],...\r\n[ 6 5 ; 6 5 ],...\r\n[ 5 6 ; -5 -1 ],...\r\n[ 7 9 ; -7 -7 ],...\r\n[ -9 -4 ; -2 -3 ],...\r\n[ 3 5 ; -2 5 ],...\r\n[ -3 -4 ; 5 -6 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 0;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 6 -3 ; 6 -7 ];\r\nL = cat(3,...\r\n[ -7 0 ; -3 0 ],...\r\n[ -1 5 ; -8 0 ],...\r\n[ 8 -5 ; 1 4 ],...\r\n[ -4 -4 ; 7 3 ],...\r\n[ 0 0 ; 4 -5 ],...\r\n[ -2 -3 ; -4 4 ],...\r\n[ 4 -8 ; 2 -5 ],...\r\n[ -7 6 ; 6 3 ],...\r\n[ -2 -7 ; -3 -8 ],...\r\n[ -6 5 ; 8 7 ],...\r\n[ 9 -9 ; 5 -9 ],...\r\n[ 6 8 ; 4 6 ],...\r\n[ 2 7 ; 5 -2 ],...\r\n[ -7 -5 ; -1 -7 ],...\r\n[ -8 -2 ; 0 -6 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 45 25 ; 23 101 ];\r\nL = cat(3,...\r\n[ 94 6 ; 2 71 ],...\r\n[ 40 -9 ; 51 84 ],...\r\n[ -8 97 ; 72 105 ],...\r\n[ 18 59 ; 36 88 ],...\r\n[ 95 56 ; 10 -6 ],...\r\n[ 61 48 ; 96 22 ],...\r\n[ 12 100 ; 94 16 ],...\r\n[ 103 90 ; 54 106 ],...\r\n[ 108 53 ; 34 68 ],...\r\n[ 9 20 ; 1 7 ],...\r\n[ 76 64 ; -8 106 ],...\r\n[ 60 9 ; 51 69 ],...\r\n[ 75 62 ; 60 -7 ],...\r\n[ 80 -8 ; 70 68 ],...\r\n[ 8 30 ; 68 67 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ -5 -6 ; -2 -6 ];\r\nL = cat(3,...\r\n[ -1 -7 ; -7 -1 ],...\r\n[ -4 -6 ; -6 -5 ],...\r\n[ -7 -2 ; -1 -5 ],...\r\n[ -9 -6 ; -4 -4 ],...\r\n[ -9 -3 ; -3 -2 ],...\r\n[ -2 -1 ; -3 -2 ],...\r\n[ -4 -5 ; -6 -9 ],...\r\n[ -8 -1 ; -4 -6 ],...\r\n[ -1 -5 ; -5 -1 ],...\r\n[ -4 -6 ; -2 -5 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 6;\r\nassert(isequal(n,n_correct));\r\n\r\n%\r\nAB = [ 1 6 ; 6 7 ];\r\nL = cat(3,...\r\n[ 5 8 ; 2 8 ],...\r\n[ 6 5 ; 3 2 ],...\r\n[ 4 8 ; 6 1 ],...\r\n[ 7 2 ; 7 9 ],...\r\n[ 1 8 ; 1 2 ],...\r\n[ 1 6 ; 1 9 ],...\r\n[ 2 6 ; 1 2 ],...\r\n[ 3 9 ; 2 4 ],...\r\n[ 5 9 ; 2 8 ],...\r\n[ 2 8 ; 2 5 ]...\r\n);\r\nn = WayfindingIntersections(AB,L)\r\nn_correct = 1;\r\nassert(isequal(n,n_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":26,"created_at":"2014-02-25T14:46:37.000Z","updated_at":"2017-05-05T15:03:02.000Z","published_at":"2014-02-25T14:59:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHow many times does AB cross another line?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWayfindingIntersections(AB,L)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![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  )]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep.s. I noticed later on that there is another Cody problem\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/1720-do-the-lines-intersect\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e1720\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e that is somewhat similar. But this was a logical start for the series.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"}]}"},{"id":2219,"title":"Wayfinding 2 - traversing","description":"This is the second 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. See \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing [1]\u003e.\r\n\r\n*How many times does AB cross the boundary of area F?*\r\n\r\n\u003c\u003chttp://i59.tinypic.com/219vz42.png\u003e\u003e\r\n\r\nFor this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.\r\n\r\nThe inputs of the function WayfindingBoundaryCrossing(AB,F) 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 matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.\r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n F = [\r\n  [ x1 x2 ... xn ;\r\n    y1 y2 ... yn ]\r\n\r\nYour output n will be the number of times the line AB crosses the boundary of F. Note that AB may cross the boundary of F at a corner node of F.\r\n","description_html":"\u003cp\u003eThis is the second 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. See \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\"\u003e[1]\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eHow many times does AB cross the boundary of area F?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i59.tinypic.com/219vz42.png\"\u003e\u003cp\u003eFor this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.\u003c/p\u003e\u003cp\u003eThe inputs of the function WayfindingBoundaryCrossing(AB,F) 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 matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e F = [\r\n  [ x1 x2 ... xn ;\r\n    y1 y2 ... yn ]\u003c/pre\u003e\u003cp\u003eYour output n will be the number of times the line AB crosses the boundary of F. Note that AB may cross the boundary of F at a corner node of F.\u003c/p\u003e","function_template":"function n = WayfindingBoundaryCrossing(AB,F)\r\n  n = randi(size(F,2))-1;\r\nend","test_suite":"%%\r\nAB = [ 0 0 ; 6 -8 ];\r\nF = [\r\n      -4    4    4   -4\r\n       2    2   -4   -4\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 2;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nAB = [ 0 0 ; 4 -6 ];\r\nF = [\r\n      -6    4    0\r\n      -0    2   -4\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 2;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nAB = [ 6 -6 ; 0 0 ];\r\nF = [\r\n      -8   -8    4\r\n       2   -4   -0\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 1;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nAB = [ 8 -6 ; 6 -8 ];\r\nF = [\r\n      -6    0   -3    7    9    4    6   -4   -7   -2   -7   -8\r\n      -9   -9    0   -4    1    7   -0    4   -1   -7   -5   -9\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nn_correct = 7;\r\nassert(isequal(n,n_correct));\r\n\r\n%%\r\nn_correct = randi(9)-1;\r\nAB = [ 0 0 ; n_correct*2-9 -10 ];\r\nF = [\r\n      -2   -2    2    2   -2   -2    2    2   -2   -2    2    2   -2   -2    4    4\r\n      -8   -6   -6   -4   -4   -2   -2   -0   -0    2    2    4    4    6    6   -8\r\n  ];\r\nn = WayfindingBoundaryCrossing(AB,F);\r\nassert(isequal(n,n_correct));","published":true,"deleted":false,"likes_count":3,"comments_count":4,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":"2014-02-26T11:59:09.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-02-25T15:14:11.000Z","updated_at":"2017-05-05T15:03:15.000Z","published_at":"2014-02-26T11:59:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the second 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. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eHow many times does AB cross the boundary of area F?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this second assignment in this series you have to calculate how many times we cross the boundary of a single area while going from A to B. Our path from A to B is a straight line. And the area boundary is a closed polygon consisting of a finite number of straight segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function WayfindingBoundaryCrossing(AB,F) 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 matrix F of columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is connected to the first.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ AB = [\\n   xA xB\\n   yA yB\\n ]\\n\\n F = [\\n  [ x1 x2 ... xn ;\\n    y1 y2 ... yn ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour output n will be the number of times the line AB crosses the boundary of F. 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\"}]}"},{"id":2220,"title":"Wayfinding 3 - passed areas","description":"This is the third part of a series of assignments about wayfinding. The final goal of this series 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. See \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing [1]\u003e\r\n\u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing [2]\u003e . \r\n\r\n*Which areas are traversed?*\r\n\r\n\u003c\u003chttp://i58.tinypic.com/263wzdt.png\u003e\u003e\r\n\r\nFor this third assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments.\r\n\r\nIn this assignments, the areas do not overlap. If an area is crossed twice, it is listed twice in the returned vector. And if |AB| crosses first for example area |F2|, then |F3|, and then |F2| again, the output vector should contain |[ ... 2 3 2 ... ]|. Simple.\r\n\r\nThe inputs of the function |WayfindingPassed(AB,F)| 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 cell array |F| of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F. \r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\r\n\r\n\r\nYour output |v| will contain the indices in |F| of the crossed areas, in the correct order. In the example above, the correct answer is |[ 3 4 4 1 1]|. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'. If you pass the same area multiple times, and leave it in between, each event is listed.\r\n","description_html":"\u003cp\u003eThis is the third part of a series of assignments about wayfinding. The final goal of this series 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. See \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\"\u003e[1]\u003c/a\u003e \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\"\u003e[2]\u003c/a\u003e .\u003c/p\u003e\u003cp\u003e\u003cb\u003eWhich areas are traversed?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i58.tinypic.com/263wzdt.png\"\u003e\u003cp\u003eFor this third assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments.\u003c/p\u003e\u003cp\u003eIn this assignments, the areas do not overlap. If an area is crossed twice, it is listed twice in the returned vector. And if \u003ctt\u003eAB\u003c/tt\u003e crosses first for example area \u003ctt\u003eF2\u003c/tt\u003e, then \u003ctt\u003eF3\u003c/tt\u003e, and then \u003ctt\u003eF2\u003c/tt\u003e again, the output vector should contain \u003ctt\u003e[ ... 2 3 2 ... ]\u003c/tt\u003e. Simple.\u003c/p\u003e\u003cp\u003eThe inputs of the function \u003ctt\u003eWayfindingPassed(AB,F)\u003c/tt\u003e are a matrix \u003ctt\u003eAB\u003c/tt\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array \u003ctt\u003eF\u003c/tt\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\u003c/pre\u003e\u003cp\u003eYour output \u003ctt\u003ev\u003c/tt\u003e will contain the indices in \u003ctt\u003eF\u003c/tt\u003e of the crossed areas, in the correct order. In the example above, the correct answer is \u003ctt\u003e[ 3 4 4 1 1]\u003c/tt\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'. If you pass the same area multiple times, and leave it in between, each event is listed.\u003c/p\u003e","function_template":"function f = WayfindingPassed(AB,F)\r\n  f = 1:length(F);\r\nend","test_suite":"    %%\r\n\r\n    AB = [ 2 -2 ; 8 -6 ];\r\n    F{1} = [\r\n        -4   -4    4    4\r\n        -4   -0   -0   -4\r\n        ];\r\n    F{2} = [\r\n        -4   -4    4    4\r\n        2    6    6    2\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [2 1];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ 8 -4 ; 8 -8 ];\r\n    F{1} = [\r\n        -6    2    2   -4   -4    8    8   -6\r\n        -6   -6   -4   -4    2    2    4    4\r\n        ];\r\n    F{2} = [\r\n        -2   -2    4    4\r\n        -0   -2   -2   -0\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 1 2 1 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ -8 8 ; 8 -8 ];\r\n    F{1} = [\r\n        -2   -2    0    0\r\n        -0    2    2   -0\r\n        ];\r\n    F{2} = [\r\n        2    4    4   -6   -6   -4    2    4    4    2    2   -4   -4    2\r\n        -0   -0   -6   -6    4    6    6    4    2    2    4    4   -4   -4\r\n        ];\r\n    F{3} = [\r\n        -3   -3    1    0\r\n        -1   -3   -3   -1\r\n        ];\r\n    F{4} = [\r\n        5    9    9    5\r\n        -3   -3   -9   -9\r\n        ];\r\n    F{5} = [\r\n        -9  -10  -10   -9\r\n        9    9   10   10\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 2 1 2 4 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    AB = [ 0 0 ; -8 8 ];\r\n    F{1} = [\r\n        -4   -2   -2   -4\r\n        8    8    4    4\r\n        ];\r\n    F{2} = [\r\n        2    4    4    2\r\n        -0   -0   -6   -6\r\n        ];\r\n    F{3} = [\r\n        -4   -2   -2   -6   -6\r\n        -4   -4   -6   -6   -4\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    assert(isempty(f));\r\n    \r\n    %%\r\n\r\n    AB = [ 7 -8 ; 0 0 ];\r\n    F{1} = [\r\n        8    9    9    8\r\n        3    3   -2   -2\r\n        ];\r\n    F{2} = [\r\n        -9   -7   -7   -4   -4   -3   -3    0    0    1    1    4    4    5    5   -2   -8   -9\r\n        -2   -2    2    2   -2   -2    2    2   -2   -2    2    2   -2   -2    3    4    3    2\r\n        ];\r\n    F{3} = [\r\n        -2   -1   -1   -2\r\n        1    1   -4   -4\r\n        ];\r\n    F{4} = [\r\n        -6   -5   -5   -3    1    2    2    3    3    1   -4   -6\r\n        1    1   -3   -5   -5   -4    1    1   -5   -8   -7   -4\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 2 4 2 3 2 4 2 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ 0 -2 ; 0 -4 ];\r\n    F{1} = [\r\n        -3    3    3    2    2   -2   -2    2    2   -3\r\n        -5   -5    3    3   -3   -3    2    2    3    3\r\n        ];\r\n    F{2} = [\r\n        -1    1    1   -1\r\n        1    1   -1   -1\r\n        ];\r\n    F{3} = [\r\n        -4    4    4    5    5   -5   -5   -4\r\n        4    4   -7   -7    5    5   -1   -1\r\n        ];\r\n    F{4} = [\r\n        -5   -4   -4    4    4   -5\r\n        -1   -1   -6   -6   -7   -7\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 2 1 ];\r\n    assert(isequal(f,f_correct));\r\n    \r\n    %%\r\n\r\n    AB = [ -2 0 ; 6 -6 ];\r\n    F{1} = [\r\n        2   -4   -4    2    2   -2    0   -2    2\r\n        -4   -4    4    4    2    2   -0   -2   -2\r\n        ];\r\n    f = WayfindingPassed(AB,F);\r\n    f_correct = [ 1 1 1 ];\r\n    assert(isequal(f,f_correct));","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":13,"test_suite_updated_at":"2014-03-03T12:10:50.000Z","rescore_all_solutions":false,"group_id":26,"created_at":"2014-02-25T23:45:22.000Z","updated_at":"2017-05-05T15:03:27.000Z","published_at":"2014-03-03T09:46:27.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the third part of a series of assignments about wayfinding. The final goal of this series 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. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e .\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWhich areas are traversed?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this third assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this assignments, the areas do not overlap. If an area is crossed twice, it is listed twice in the returned vector. And if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crosses first for example area\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e again, the output vector should contain\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ ... 2 3 2 ... ]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Simple.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWayfindingPassed(AB,F)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ AB = [\\n   xA xB\\n   yA yB\\n ]\\n\\n F = {\\n  [ x11 x12 ... x1n ;\\n    y11 y12 ... y1n ]\\n  [ x21 x22 ... x2n ;\\n    y21 y22 ... y2n ]\\n }]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour output\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will contain the indices in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the crossed areas, in the correct order. In the example above, the correct answer is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ 3 4 4 1 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'. If you pass the same area multiple times, and leave it in between, each event is listed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"}]}"},{"id":2226,"title":"Wayfinding 4 - Crossing, level 2","description":"This is the fourth part of a series of assignments about wayfinding. The final goal of this series 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. See \u003chttp://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing [1]\u003e\r\n\u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing [2]\u003e \u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas [3]\u003e. \r\n\r\n*Which areas are traversed?*\r\n\r\n\u003c\u003chttp://i62.tinypic.com/358qa1w.png\u003e\u003e\r\n\r\nFor this fourth assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments. Quite similar to \u003chttp://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas assignment 3\u003e.\r\n\r\nHowever, now the areas may overlap. If case of traversing overlapping areas, the area with the highest index in |F| is the one listed.\r\nIf an area is crossed twice, it is listed twice in the returned vector. And if |AB| crosses first for example area |F2|, then |F3|, and then |F2| again, the output vector should contain |[ ... 2 3 2 ... ]|. That would also be the case when |F3| is contained in |F2|. But when |F2| is contained in |F3|, then |F2| is never crossed, as it has a lower index in F than |F3|. Consider the areas non-transparent and stacked on top of each other.\r\n\r\nThe inputs of the function |WayfindingPassed(AB,F)| 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 cell array |F| of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F. \r\n\r\n AB = [\r\n   xA xB\r\n   yA yB\r\n ]\r\n\r\n F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\r\n\r\n\r\nYour output |f| will contain the indices in |F| of the crossed areas, in the correct order. In the example above, the correct answer is |[ 3 1 4 1 4 1]|. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'.","description_html":"\u003cp\u003eThis is the fourth part of a series of assignments about wayfinding. The final goal of this series 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. See \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\"\u003e[1]\u003c/a\u003e \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\"\u003e[2]\u003c/a\u003e \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\"\u003e[3]\u003c/a\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eWhich areas are traversed?\u003c/b\u003e\u003c/p\u003e\u003cimg src = \"http://i62.tinypic.com/358qa1w.png\"\u003e\u003cp\u003eFor this fourth assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments. Quite similar to \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\"\u003eassignment 3\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eHowever, now the areas may overlap. If case of traversing overlapping areas, the area with the highest index in \u003ctt\u003eF\u003c/tt\u003e is the one listed.\r\nIf an area is crossed twice, it is listed twice in the returned vector. And if \u003ctt\u003eAB\u003c/tt\u003e crosses first for example area \u003ctt\u003eF2\u003c/tt\u003e, then \u003ctt\u003eF3\u003c/tt\u003e, and then \u003ctt\u003eF2\u003c/tt\u003e again, the output vector should contain \u003ctt\u003e[ ... 2 3 2 ... ]\u003c/tt\u003e. That would also be the case when \u003ctt\u003eF3\u003c/tt\u003e is contained in \u003ctt\u003eF2\u003c/tt\u003e. But when \u003ctt\u003eF2\u003c/tt\u003e is contained in \u003ctt\u003eF3\u003c/tt\u003e, then \u003ctt\u003eF2\u003c/tt\u003e is never crossed, as it has a lower index in F than \u003ctt\u003eF3\u003c/tt\u003e. Consider the areas non-transparent and stacked on top of each other.\u003c/p\u003e\u003cp\u003eThe inputs of the function \u003ctt\u003eWayfindingPassed(AB,F)\u003c/tt\u003e are a matrix \u003ctt\u003eAB\u003c/tt\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array \u003ctt\u003eF\u003c/tt\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/p\u003e\u003cpre\u003e AB = [\r\n   xA xB\r\n   yA yB\r\n ]\u003c/pre\u003e\u003cpre\u003e F = {\r\n  [ x11 x12 ... x1n ;\r\n    y11 y12 ... y1n ]\r\n  [ x21 x22 ... x2n ;\r\n    y21 y22 ... y2n ]\r\n }\u003c/pre\u003e\u003cp\u003eYour output \u003ctt\u003ef\u003c/tt\u003e will contain the indices in \u003ctt\u003eF\u003c/tt\u003e of the crossed areas, in the correct order. In the example above, the correct answer is \u003ctt\u003e[ 3 1 4 1 4 1]\u003c/tt\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'.\u003c/p\u003e","function_template":"function f = WayfindingPassed(AB,F)\r\n  f = 1:length(F);\r\nend","test_suite":"%%\r\nAB = [ -10 10 ; -10 10 ];\r\nF{1} = [\r\n    -5    5   -8    0\r\n    -6    2    7    1\r\n    ];\r\nF{2} = [\r\n    4   -2    4    6\r\n    6   -7   -3   -2\r\n    ];\r\nF{3} = [\r\n    -5    6    3   -1\r\n    -6   -8    4   -2\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 3 2 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 21 ; 0 0 ];\r\nf_correct = randperm(20);\r\nF = arrayfun(@(n)[n+[0 1 1 0];-1 -1 1 1],f_correct,'uni',0);\r\nf = WayfindingPassed(AB,F);\r\nassert(isequal(f(f_correct),f_correct(f)));\r\n\r\n%%\r\nAB = [ -10 10 ; -10 10 ];\r\nF{1} = [\r\n    -5    9    0   -4    5\r\n    2    8   -1   -9   -8\r\n    ];\r\nF{2} = [\r\n    -2  -10   -4    0\r\n    8    7   -5    5\r\n    ];\r\nF{3} = [\r\n    -6    2   10\r\n    10   -4    8\r\n    ];\r\nF{4} = [\r\n    -10    8  -10\r\n    4   -8    2\r\n    ];\r\nF{5} = [\r\n    0    4    8   -3    1\r\n    -10    9   -8   -5    2\r\n    ];\r\nF{6} = [\r\n    6    6   -9   10\r\n    6   -3    4   -7\r\n    ];\r\nF{7} = [\r\n    9    7   -7\r\n    0    7   -5\r\n    ];\r\nF{8} = [\r\n    2    0   10\r\n    6  -10    0\r\n    ];\r\nF{9} = [\r\n    -7    2   -7   -7\r\n    3    5   -3    7\r\n    ];\r\nF{10} = [\r\n    -5    6    1    5\r\n    -10    0    8    4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 7 8 10 7 3 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\nAB = [ -10 10 ; -10 10 ];\r\nF{1} = [\r\n    2    5    8    5\r\n    2   -2    9   -5\r\n    ];\r\nF{2} = [\r\n    -8    2   -2    8   -8   -2\r\n    0    4    5   -9    8   -2\r\n    ];\r\nF{3} = [\r\n    5   -6   -2    1    0   10\r\n    10   -8    0   10   -2   -5\r\n    ];\r\nF{4} = [\r\n    10   -4  -10   -2    9\r\n    4    1    8   -4   -1\r\n    ];\r\nF{5} = [\r\n    -9   -7    2   -3\r\n    2   -9   -4    5\r\n    ];\r\nF{6} = [\r\n    -3   10    6    9    4   -2\r\n    10   -6    2    2    5   -5\r\n    ];\r\nF{7} = [\r\n    -1   -5   -5\r\n    3    0   -4\r\n    ];\r\nF{8} = [\r\n    8   -6    8   10   -7\r\n    8   -2   -5    3    7\r\n    ];\r\nF{9} = [\r\n    1  -10   -3   10    5\r\n    -5   -6    3   -6    8\r\n    ];\r\nF{10} = [\r\n    -7    0    8   -8\r\n    7   -8    3    9\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 5 9 10 9 3 1 8 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 4 -6 ; 0 0 ];\r\nF{1} = [\r\n    -4   -4    2    2   -2   -3   -3   -2    2    2   -4\r\n    2   -4   -4   -2    2    2   -2   -2    2    4    4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 0 ; 15 -8 ];\r\nF{1} = [\r\n    -4    4    4   -4\r\n    6    2    6    2\r\n    ];\r\nF{2} = [\r\n    -2   -2    6    6   -2\r\n    -0   -4   -0   -4   -0\r\n    ];\r\nF{3} = [\r\n    -1   -1    2    2\r\n    -6   -4   -6   -4\r\n    ];\r\nF{4} = [\r\n    -1    1   -1    1\r\n    -7   -7   -9   -9\r\n    ];\r\nF{5} = [\r\n    -2     2    -1     2    -1     1\r\n    14    10     6     6    10    14\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 5 5 1 2 3 4 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 0 ; -6 6 ];\r\nF{1} = [\r\n    -5    7    7   -5\r\n    -9   -9    9    9\r\n    ];\r\nF{2} = [\r\n    -1    1    1   -1\r\n    -7   -7   -5   -5\r\n    ];\r\nF{3} = [\r\n    -2   -2    2    2\r\n    4    2    2    4\r\n    ];\r\nF{4} = [\r\n    2    2   -2   -2\r\n    4    2    2    4\r\n    ];\r\nF{5} = [\r\n    -1    1    1   -1\r\n    2    2   -2   -2\r\n    ];\r\nF{6} = [\r\n    -2    0   -2\r\n    -2   -3   -4\r\n    ];\r\nF{7} = [\r\n    0    2    2\r\n    -3   -4   -2\r\n    ];\r\nF{8} = [\r\n    -1    0    1\r\n    -8   -6   -8\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [8 2 1 7 1 5 4 1];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 2 -2 ; 8 -6 ];\r\nF{1} = [\r\n    -4   -4    4    4\r\n    -4   -0   -0   -4\r\n    ];\r\nF{2} = [\r\n    -4   -4    4    4\r\n    2    6    6    2\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [2 1];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 8 -4 ; 8 -8 ];\r\nF{1} = [\r\n    -6    2    2   -4   -4    8    8   -6\r\n    -6   -6   -4   -4    2    2    4    4\r\n    ];\r\nF{2} = [\r\n    -2   -2    4    4\r\n    -0   -2   -2   -0\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 2 1 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ -8 8 ; 8 -8 ];\r\nF{1} = [\r\n    -2   -2    0    0\r\n    -0    2    2   -0\r\n    ];\r\nF{2} = [\r\n    2    4    4   -6   -6   -4    2    4    4    2    2   -4   -4    2\r\n    -0   -0   -6   -6    4    6    6    4    2    2    4    4   -4   -4\r\n    ];\r\nF{3} = [\r\n    -3   -3    1    0\r\n    -1   -3   -3   -1\r\n    ];\r\nF{4} = [\r\n    5    9    9    5\r\n    -3   -3   -9   -9\r\n    ];\r\nF{5} = [\r\n    -9  -10  -10   -9\r\n    9    9   10   10\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 1 2 4 ];\r\nassert(isequal(f,f_correct));\r\n\r\nAB = [ 0 0 ; -8 8 ];\r\nF{1} = [\r\n    -4   -2   -2   -4\r\n    8    8    4    4\r\n    ];\r\nF{2} = [\r\n    2    4    4    2\r\n    -0   -0   -6   -6\r\n    ];\r\nF{3} = [\r\n    -4   -2   -2   -6   -6\r\n    -4   -4   -6   -6   -4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nassert(isempty(f));\r\n\r\n%%\r\n\r\nAB = [ 7 -8 ; 0 0 ];\r\nF{1} = [\r\n    8    9    9    8\r\n    3    3   -2   -2\r\n    ];\r\nF{2} = [\r\n    -9   -7   -7   -4   -4   -3   -3    0    0    1    1    4    4    5    5   -2   -8   -9\r\n    -2   -2    2    2   -2   -2    2    2   -2   -2    2    2   -2   -2    3    4    3    2\r\n    ];\r\nF{3} = [\r\n    -2   -1   -1   -2\r\n    1    1   -4   -4\r\n    ];\r\nF{4} = [\r\n    -6   -5   -5   -3    1    2    2    3    3    1   -4   -6\r\n    1    1   -3   -5   -5   -4    1    1   -5   -8   -7   -4\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 4 2 3 2 4 2 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ 0 -2 ; 0 -4 ];\r\nF{1} = [\r\n    -3    3    3    2    2   -2   -2    2    2   -3\r\n    -5   -5    3    3   -3   -3    2    2    3    3\r\n    ];\r\nF{2} = [\r\n    -1    1    1   -1\r\n    1    1   -1   -1\r\n    ];\r\nF{3} = [\r\n    -4    4    4    5    5   -5   -5   -4\r\n    4    4   -7   -7    5    5   -1   -1\r\n    ];\r\nF{4} = [\r\n    -5   -4   -4    4    4   -5\r\n    -1   -1   -6   -6   -7   -7\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 2 1 ];\r\nassert(isequal(f,f_correct));\r\n\r\n%%\r\n\r\nAB = [ -2 0 ; 6 -6 ];\r\nF{1} = [\r\n    2   -4   -4    2    2   -2    0   -2    2\r\n    -4   -4    4    4    2    2   -0   -2   -2\r\n    ];\r\nf = WayfindingPassed(AB,F);\r\nf_correct = [ 1 1 1 ];\r\nassert(isequal(f,f_correct));","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-01T22:33:13.000Z","updated_at":"2014-03-06T07:49:23.000Z","published_at":"2014-03-06T07:49:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the fourth part of a series of assignments about wayfinding. The final goal of this series 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. See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/2218-wayfinding-1-crossing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2219-wayfinding-2-traversing\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e[3]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWhich areas are traversed?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this fourth assignment in this series you have to calculate which areas are traversed and in which order, while going from A to B. Our path from A to B is a straight line. And the area boundaries are closed polygons consisting of a finite number of straight segments. Quite similar to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/problems/2220-wayfinding-3-passed-areas\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eassignment 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHowever, now the areas may overlap. If case of traversing overlapping areas, the area with the highest index in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the one listed. If an area is crossed twice, it is listed twice in the returned vector. And if\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e crosses first for example area\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e again, the output vector should contain\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ ... 2 3 2 ... ]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. That would also be the case when\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is contained in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. But when\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is contained in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is never crossed, as it has a lower index in F than\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Consider the areas non-transparent and stacked on top of each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs of the function\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWayfindingPassed(AB,F)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e are a matrix\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eAB\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of two columns, each with x-y coordinates, of our straight path from A (1st column) to B (2nd column), and a cell array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of 2-D matrices with columns with x- and y-coordinates, each column a subsequent node of the polygon boundary of the area. The last node is implicitly connected to the first. The index of each area, to be referred to in the output vector, is equal to its position in the cell array F.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ AB = [\\n   xA xB\\n   yA yB\\n ]\\n\\n F = {\\n  [ x11 x12 ... x1n ;\\n    y11 y12 ... y1n ]\\n  [ x21 x22 ... x2n ;\\n    y21 y22 ... y2n ]\\n }]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour output\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will contain the indices in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the crossed areas, in the correct order. In the example above, the correct answer is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[ 3 1 4 1 4 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Crossing means 'being present in that area', so if A, the start, is in area 3, it is considered as 'crossed'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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\"}]}"},{"id":2242,"title":"Wayfinding 5 - Travel contour","description":"This is the fifth part of a series of assignments about wayfinding. The final goal of this series 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. See \r\n\u003chttp://www.mathworks.nl/matlabcentral/cody/?term=tag%3Awayfinding search:tag=wayfinding\u003e for the other assignments.\r\n\r\nThis time, you will travel around a polygon, over its contour. You get the nodes of the polygon, in the correct order, as a |2xn| array |F|. The last node of |F| is connected to the first node.\r\n\r\n|a| is the index in |F| of the starting node, and |b| is the goal. \r\n\r\n\u003c\u003chttp://i61.tinypic.com/iq8p69.png\u003e\u003e\r\n\r\nCalculate the shortest distance from |a| to |b| over the contour of the polygon. \r\n\r\nThe distance is measured as the Euclidean distance between points. You can not enter the internal area of the polygon. The contour of the polygon does not self-intersect.","description_html":"\u003cp\u003eThis is the fifth part of a series of assignments about wayfinding. The final goal of this series 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. See  \u003ca href = \"http://www.mathworks.nl/matlabcentral/cody/?term=tag%3Awayfinding\"\u003esearch:tag=wayfinding\u003c/a\u003e for the other assignments.\u003c/p\u003e\u003cp\u003eThis time, you will travel around a polygon, over its contour. You get the nodes of the polygon, in the correct order, as a \u003ctt\u003e2xn\u003c/tt\u003e array \u003ctt\u003eF\u003c/tt\u003e. The last node of \u003ctt\u003eF\u003c/tt\u003e is connected to the first node.\u003c/p\u003e\u003cp\u003e\u003ctt\u003ea\u003c/tt\u003e is the index in \u003ctt\u003eF\u003c/tt\u003e of the starting node, and \u003ctt\u003eb\u003c/tt\u003e is the goal.\u003c/p\u003e\u003cimg src = \"http://i61.tinypic.com/iq8p69.png\"\u003e\u003cp\u003eCalculate the shortest distance from \u003ctt\u003ea\u003c/tt\u003e to \u003ctt\u003eb\u003c/tt\u003e over the contour of the polygon.\u003c/p\u003e\u003cp\u003eThe distance is measured as the Euclidean distance between points. You can not enter the internal area of the polygon. The contour of the polygon does not self-intersect.\u003c/p\u003e","function_template":"function d = polygon_distance(F,a,b)\r\n  d = 0;\r\nend","test_suite":"%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 1;\r\nb = 3;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 2;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 1;\r\nb = 2;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 1;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 4;\r\nb = 1;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 1;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [0 0 1 1;0 1 1 0];\r\na = 3;\r\nb = 3;\r\nd = polygon_distance(F,a,b);\r\nd_correct = 0;\r\nassert(isequal(d,d_correct))\r\n\r\n%%\r\nF = [zeros(1,101) ones(1,101);0:100 100:-1:0];\r\na = 1;\r\nfor b = randi(size(F,2)/2,1,100)\r\n  d = polygon_distance(F,a,b);\r\n  d_correct = b-1;\r\n  assert(isequal(d,d_correct));\r\nend\r\n\r\n%%\r\nF = [zeros(1,101) ones(1,101);0:100 100:-1:0];\r\na = 1;\r\nfor b = randi(size(F,2)/2,1,100)+size(F,2)/2\r\n  s = rand(1)+1;\r\n  d = polygon_distance(F*s,a,b);\r\n  d_correct = (size(F,2)-b+1)*s;\r\n  assert(abs(d-d_correct)\u003c1e-10);\r\nend\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":6556,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2014-03-10T14:22:52.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-03-10T09:32:11.000Z","updated_at":"2014-03-10T14:22:52.000Z","published_at":"2014-03-10T13:43:07.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is the fifth part of a series of assignments about wayfinding. The final goal of this series 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. See \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.nl/matlabcentral/cody/?term=tag%3Awayfinding\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esearch:tag=wayfinding\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for the other assignments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis time, you will travel around a polygon, over its contour. You get the nodes of the polygon, in the correct order, as a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2xn\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. The last node of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is connected to the first node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the index in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of the starting node, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the goal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the shortest distance from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e over the contour of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe distance is measured as the Euclidean distance between points. You can not enter the internal area of the polygon. 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