{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","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":"2026-05-26T00:00:00.000Z","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":44825,"title":"Relative points in 2D: problem 3","description":"The 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T.  A landmark point is observed by the robot, as a bearing angle relative to its x-axis (in degrees and increasing counter clockwise) and a range.  What is the coordinate of the landmark with respect to the world coordinate frame?","description_html":"\u003cp\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T.  A landmark point is observed by the robot, as a bearing angle relative to its x-axis (in degrees and increasing counter clockwise) and a range.  What is the coordinate of the landmark with respect to the world coordinate frame?\u003c/p\u003e","function_template":"function PB = user_function(T, bearing, range)\r\n  % Input:  T a 3x3 homogeneous transformation matrix\r\n  %         bearing a scalar angle\r\n  %         range a scalar distance\r\n  % Output: PB a 2x1 vector representing the coordinate of a point\r\n  P = ;\r\nend","test_suite":"th = 2*pi*rand;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nT = [R t; 0 0 1];\r\nPB = rand(2,1)*10-5;\r\nbearing = rand*360-180;\r\nrange = rand*20+5;\r\n\r\nP = user_function(T, bearing, range);\r\n%%\r\nassert(all(size(P) == [2 1]), 'The point should be described by a 2x1 vector')\r\n%%\r\nassert(isreal(P), 'The point should be described by a vector of real, not complex, numbers');\r\n%%\r\nPB = range*[cosd(bearing); sind(bearing)];\r\nPref = R'*PB - R' * t;\r\nassert( all(abs(P-Pref) \u003c 0.001), 'The relative coordinates are not correct')\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T01:23:18.000Z","updated_at":"2026-05-24T23:08:39.000Z","published_at":"2019-01-10T01:23:18.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\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\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. 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A landmark point is observed by the robot, as a bearing angle relative to its x-axis (in degrees and increasing counter clockwise) and a range.  What is the coordinate of the landmark with respect to the world coordinate frame?","description_html":"\u003cp\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T.  A landmark point is observed by the robot, as a bearing angle relative to its x-axis (in degrees and increasing counter clockwise) and a range.  What is the coordinate of the landmark with respect to the world coordinate frame?\u003c/p\u003e","function_template":"function PB = user_function(T, bearing, range)\r\n  % Input:  T a 3x3 homogeneous transformation matrix\r\n  %         bearing a scalar angle\r\n  %         range a scalar distance\r\n  % Output: PB a 2x1 vector representing the coordinate of a point\r\n  P = ;\r\nend","test_suite":"th = 2*pi*rand;\r\nt = rand(2,1)*20-10;\r\nR = [cos(th) -sin(th); sin(th) cos(th)];\r\nT = [R t; 0 0 1];\r\nPB = rand(2,1)*10-5;\r\nbearing = rand*360-180;\r\nrange = rand*20+5;\r\n\r\nP = user_function(T, bearing, range);\r\n%%\r\nassert(all(size(P) == [2 1]), 'The point should be described by a 2x1 vector')\r\n%%\r\nassert(isreal(P), 'The point should be described by a vector of real, not complex, numbers');\r\n%%\r\nPB = range*[cosd(bearing); sind(bearing)];\r\nPref = R'*PB - R' * t;\r\nassert( all(abs(P-Pref) \u003c 0.001), 'The relative coordinates are not correct')\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":61,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":77,"created_at":"2019-01-10T01:23:18.000Z","updated_at":"2026-05-24T23:08:39.000Z","published_at":"2019-01-10T01:23:18.000Z","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\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\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\u003eThe 2D pose of a robot, with respect to a world coordinate frame {O}, is described by a 3x3 homogenous transform matrix T. 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