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The orientation of {B} is described in terms of roll-pitch-yaw angles defined as a sequence of rotations where yaw is about the Z, pitch is about the Y axis and roll is about the X axis.\r\n\r\nGiven an SO(3) rotation matrix describing the orientation of {B} with respect to {W} determine the roll-pitch-yaw angles.","description_html":"\u003cp\u003eConsider an aerospace application where the world reference coordinate frame {W} and a body-fixed coordinate frame {B}.  The origins of {W} and {B} are coincident.  The orientation of {B} is described in terms of roll-pitch-yaw angles defined as a sequence of rotations where yaw is about the Z, pitch is about the Y axis and roll is about the X axis.\u003c/p\u003e\u003cp\u003eGiven an SO(3) rotation matrix describing the orientation of {B} with respect to {W} determine the roll-pitch-yaw angles.\u003c/p\u003e","function_template":"function rpy = your_fcn_name(R)\r\n  % rpy is a 1x3 vector [roll pitch yaw]\r\n  rpy = 0;\r\nend","test_suite":"%% handle regular case\r\n\r\n% compute random SO(3)\r\nfor count = 1:5\r\n  rpy = (rand(1,3)-0.5)*pi;\r\n  r = rpy(1); p = rpy(2); y = rpy(3);\r\n\r\n  rpy2r = @(r,p,y) reshape([cos(p).*cos(y),cos(p).*sin(y),-sin(p),-cos(r).*sin(y)+cos(y).*sin(p).*sin(r),cos(r).*cos(y)+sin(p).*sin(r).*sin(y),cos(p).*sin(r),sin(r).*sin(y)+cos(r).*cos(y).*sin(p),-cos(y).*sin(r)+cos(r).*sin(p).*sin(y),cos(p).*cos(r)],[3,3]);\r\n  R_correct = rpy2r(r, p, y);\r\n\r\n  % user's estimate\r\n  rpy = your_fcn_name(R_correct);\r\n  r = rpy(1); p = rpy(2); y = rpy(3);\r\n\r\n  err = R_correct' * rpy2r(r,p,y) - eye(3,3);\r\n  assert(norm(err) \u003c 10*eps)\r\nend\r\n\r\n%% handle singular case\r\nrpy = (rand(1,3)-0.5)*pi;\r\nr = rpy(1); p = pi/2; y = rpy(3);\r\n\r\nrpy2r = @(r,p,y) reshape([cos(p).*cos(y),cos(p).*sin(y),-sin(p),-cos(r).*sin(y)+cos(y).*sin(p).*sin(r),cos(r).*cos(y)+sin(p).*sin(r).*sin(y),cos(p).*sin(r),sin(r).*sin(y)+cos(r).*cos(y).*sin(p),-cos(y).*sin(r)+cos(r).*sin(p).*sin(y),cos(p).*cos(r)],[3,3]);\r\nR_correct = rpy2r(r, p, y);\r\n\r\n% user's estimate\r\nrpy = your_fcn_name(R_correct);\r\nr = rpy(1); p = rpy(2); y = rpy(3);\r\n\r\nerr = R_correct' * rpy2r(r,p,y) - eye(3,3);\r\nassert(norm(err) \u003c 10*eps)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2019-04-24T02:02:23.000Z","rescore_all_solutions":false,"group_id":629,"created_at":"2019-04-23T10:43:03.000Z","updated_at":"2026-05-30T01:41:22.000Z","published_at":"2019-04-23T10:46:56.000Z","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\u003eConsider an aerospace application where the world reference coordinate frame {W} and a body-fixed coordinate frame {B}. The origins of {W} and {B} are coincident. 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The origins of {W} and {B} are coincident.  The orientation of {B} is described in terms of roll-pitch-yaw angles defined as a sequence of rotations where yaw is about the Z, pitch is about the Y axis and roll is about the X axis.\r\n\r\nGiven an SO(3) rotation matrix describing the orientation of {B} with respect to {W} determine the roll-pitch-yaw angles.","description_html":"\u003cp\u003eConsider an aerospace application where the world reference coordinate frame {W} and a body-fixed coordinate frame {B}.  The origins of {W} and {B} are coincident.  The orientation of {B} is described in terms of roll-pitch-yaw angles defined as a sequence of rotations where yaw is about the Z, pitch is about the Y axis and roll is about the X axis.\u003c/p\u003e\u003cp\u003eGiven an SO(3) rotation matrix describing the orientation of {B} with respect to {W} determine the roll-pitch-yaw angles.\u003c/p\u003e","function_template":"function rpy = your_fcn_name(R)\r\n  % rpy is a 1x3 vector [roll pitch yaw]\r\n  rpy = 0;\r\nend","test_suite":"%% handle regular case\r\n\r\n% compute random SO(3)\r\nfor count = 1:5\r\n  rpy = (rand(1,3)-0.5)*pi;\r\n  r = rpy(1); p = rpy(2); y = rpy(3);\r\n\r\n  rpy2r = @(r,p,y) reshape([cos(p).*cos(y),cos(p).*sin(y),-sin(p),-cos(r).*sin(y)+cos(y).*sin(p).*sin(r),cos(r).*cos(y)+sin(p).*sin(r).*sin(y),cos(p).*sin(r),sin(r).*sin(y)+cos(r).*cos(y).*sin(p),-cos(y).*sin(r)+cos(r).*sin(p).*sin(y),cos(p).*cos(r)],[3,3]);\r\n  R_correct = rpy2r(r, p, y);\r\n\r\n  % user's estimate\r\n  rpy = your_fcn_name(R_correct);\r\n  r = rpy(1); p = rpy(2); y = rpy(3);\r\n\r\n  err = R_correct' * rpy2r(r,p,y) - eye(3,3);\r\n  assert(norm(err) \u003c 10*eps)\r\nend\r\n\r\n%% handle singular case\r\nrpy = (rand(1,3)-0.5)*pi;\r\nr = rpy(1); p = pi/2; y = rpy(3);\r\n\r\nrpy2r = @(r,p,y) reshape([cos(p).*cos(y),cos(p).*sin(y),-sin(p),-cos(r).*sin(y)+cos(y).*sin(p).*sin(r),cos(r).*cos(y)+sin(p).*sin(r).*sin(y),cos(p).*sin(r),sin(r).*sin(y)+cos(r).*cos(y).*sin(p),-cos(y).*sin(r)+cos(r).*sin(p).*sin(y),cos(p).*cos(r)],[3,3]);\r\nR_correct = rpy2r(r, p, y);\r\n\r\n% user's estimate\r\nrpy = your_fcn_name(R_correct);\r\nr = rpy(1); p = rpy(2); y = rpy(3);\r\n\r\nerr = R_correct' * rpy2r(r,p,y) - eye(3,3);\r\nassert(norm(err) \u003c 10*eps)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":5,"created_by":13332,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":9,"test_suite_updated_at":"2019-04-24T02:02:23.000Z","rescore_all_solutions":false,"group_id":629,"created_at":"2019-04-23T10:43:03.000Z","updated_at":"2026-05-30T01:41:22.000Z","published_at":"2019-04-23T10:46:56.000Z","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\u003eConsider an aerospace application where the world reference coordinate frame {W} and a body-fixed coordinate frame {B}. The origins of {W} and {B} are coincident. 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