{"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":2375,"title":"Obscured by Earth","description":"Given two points in \u003chttp://en.wikipedia.org/wiki/Earth-centered_inertial ECI\u003e reference frame, check wheather they are in line-of-sight, i.e, they are not obscured by Earth.\r\nNote that the Earth is assumed as a sphere with  6,378,137.0 m radius (equatorial radius according to \u003chttp://en.wikipedia.org/wiki/WGS84 WGS-84\u003e).\r\n\r\nInputs:\r\n\r\n* x1: [x y z]    ECI coordinates of the first reference point\r\n* x2: [x y z]    ECI coordinates of the second reference point\r\n\r\nOutputs:\r\n\r\n* inLOS:    true if the line-of-sight is not obscured by Earth","description_html":"\u003cp\u003eGiven two points in \u003ca href = \"http://en.wikipedia.org/wiki/Earth-centered_inertial\"\u003eECI\u003c/a\u003e reference frame, check wheather they are in line-of-sight, i.e, they are not obscured by Earth.\r\nNote that the Earth is assumed as a sphere with  6,378,137.0 m radius (equatorial radius according to \u003ca href = \"http://en.wikipedia.org/wiki/WGS84\"\u003eWGS-84\u003c/a\u003e).\u003c/p\u003e\u003cp\u003eInputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003ex1: [x y z]    ECI coordinates of the first reference point\u003c/li\u003e\u003cli\u003ex2: [x y z]    ECI coordinates of the second reference point\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003einLOS:    true if the line-of-sight is not obscured by Earth\u003c/li\u003e\u003c/ul\u003e","function_template":"function inLOS = in_los(x1, x2)\r\n  inLOS = false;\r\nend","test_suite":"\r\n%%\r\nx1 = [10e6 10e6 10e6];\r\nx2 = x1.*[-1 -1 1];\r\nassert(isequal(in_los(x1, x2), true))\r\n%%\r\nx1 = [10e6 10e6 10e6];\r\nx2 = 2*x1;\r\nassert(isequal(in_los(x1, x2), true))\r\n%%\r\nx1 = [10e6 10e6 10e6];\r\nx2 = -x1;\r\nassert(isequal(in_los(x1, x2), false))\r\n%%\r\nx1 = 2*(6378137+1e-3)/sqrt(3)*[1 1 0]/sqrt(2);\r\nx2 = 2*(6378137+1e-3)/sqrt(3)*[1 0 1]/sqrt(2);\r\nassert(isequal(in_los(x1, x2), true))\r\n%%\r\nx1 = 2*(6378137-1e-3)/sqrt(3)*[1 1 0]/sqrt(2);\r\nx2 = 2*(6378137-1e-3)/sqrt(3)*[1 0 1]/sqrt(2);\r\nassert(isequal(in_los(x1, x2), false))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":20319,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T14:29:37.000Z","updated_at":"2026-05-28T02:36:33.000Z","published_at":"2014-06-18T14:30:50.000Z","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\":[],\"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\u003eGiven two points in\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://en.wikipedia.org/wiki/Earth-centered_inertial\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eECI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e reference frame, check wheather they are in line-of-sight, i.e, they are not obscured by Earth. Note that the Earth is assumed as a sphere with 6,378,137.0 m radius (equatorial radius according 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://en.wikipedia.org/wiki/WGS84\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWGS-84\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\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex1: [x y z] ECI coordinates of the first reference point\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex2: [x y z] ECI coordinates of the second reference point\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\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einLOS: true if the line-of-sight is not obscured by Earth\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 type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":2375,"title":"Obscured by Earth","description":"Given two points in \u003chttp://en.wikipedia.org/wiki/Earth-centered_inertial ECI\u003e reference frame, check wheather they are in line-of-sight, i.e, they are not obscured by Earth.\r\nNote that the Earth is assumed as a sphere with  6,378,137.0 m radius (equatorial radius according to \u003chttp://en.wikipedia.org/wiki/WGS84 WGS-84\u003e).\r\n\r\nInputs:\r\n\r\n* x1: [x y z]    ECI coordinates of the first reference point\r\n* x2: [x y z]    ECI coordinates of the second reference point\r\n\r\nOutputs:\r\n\r\n* inLOS:    true if the line-of-sight is not obscured by Earth","description_html":"\u003cp\u003eGiven two points in \u003ca href = \"http://en.wikipedia.org/wiki/Earth-centered_inertial\"\u003eECI\u003c/a\u003e reference frame, check wheather they are in line-of-sight, i.e, they are not obscured by Earth.\r\nNote that the Earth is assumed as a sphere with  6,378,137.0 m radius (equatorial radius according to \u003ca href = \"http://en.wikipedia.org/wiki/WGS84\"\u003eWGS-84\u003c/a\u003e).\u003c/p\u003e\u003cp\u003eInputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003ex1: [x y z]    ECI coordinates of the first reference point\u003c/li\u003e\u003cli\u003ex2: [x y z]    ECI coordinates of the second reference point\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003einLOS:    true if the line-of-sight is not obscured by Earth\u003c/li\u003e\u003c/ul\u003e","function_template":"function inLOS = in_los(x1, x2)\r\n  inLOS = false;\r\nend","test_suite":"\r\n%%\r\nx1 = [10e6 10e6 10e6];\r\nx2 = x1.*[-1 -1 1];\r\nassert(isequal(in_los(x1, x2), true))\r\n%%\r\nx1 = [10e6 10e6 10e6];\r\nx2 = 2*x1;\r\nassert(isequal(in_los(x1, x2), true))\r\n%%\r\nx1 = [10e6 10e6 10e6];\r\nx2 = -x1;\r\nassert(isequal(in_los(x1, x2), false))\r\n%%\r\nx1 = 2*(6378137+1e-3)/sqrt(3)*[1 1 0]/sqrt(2);\r\nx2 = 2*(6378137+1e-3)/sqrt(3)*[1 0 1]/sqrt(2);\r\nassert(isequal(in_los(x1, x2), true))\r\n%%\r\nx1 = 2*(6378137-1e-3)/sqrt(3)*[1 1 0]/sqrt(2);\r\nx2 = 2*(6378137-1e-3)/sqrt(3)*[1 0 1]/sqrt(2);\r\nassert(isequal(in_los(x1, x2), false))","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":20319,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2014-06-18T14:29:37.000Z","updated_at":"2026-05-28T02:36:33.000Z","published_at":"2014-06-18T14:30:50.000Z","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\":[],\"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\u003eGiven two points in\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://en.wikipedia.org/wiki/Earth-centered_inertial\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eECI\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e reference frame, check wheather they are in line-of-sight, i.e, they are not obscured by Earth. Note that the Earth is assumed as a sphere with 6,378,137.0 m radius (equatorial radius according 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://en.wikipedia.org/wiki/WGS84\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWGS-84\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\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex1: [x y z] ECI coordinates of the first reference point\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ex2: [x y z] ECI coordinates of the second reference point\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\u003eOutputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einLOS: true if the line-of-sight is not obscured by Earth\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 type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"aerospace\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}