{"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":55490,"title":"Rotation Matrix to Euler Angles","description":"Given a rotation matrix, generate the Euler Angles as output [phi,theta,psi]. [phi is a rotation around X-axis, theta is rotation around Y-axis, and psi is rotation around Z-axis].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a rotation matrix, generate the Euler Angles as output [phi,theta,psi]. [phi is a rotation around X-axis, theta is rotation around Y-axis, and psi is rotation around Z-axis].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function e = rotMat2euler(R)\r\nphi=acos(R(1,1));theta=asin(R(2,2));psi=atan(R(3,3));\r\ne=[phi,theta,psi];\r\nend","test_suite":"%%\r\nR =[0.495854215827297   0.217789379010378   0.840652355636128\r\n   0.639334284157749  -0.746671533981521  -0.183666255589267\r\n  -0.587690624178059  -0.628529559155301   0.509480444689732];\r\ne=rotMat2euler(R);\r\ne_correct=[-50.97,35.99,52.20];\r\nassert(isequal(e_correct,round(e,2)));\r\n%%\r\nrng(1);\r\nfor k=1:100\r\n   R=randOrthRotMat;\r\n   e(k,:)=rotMat2euler(R);\r\nend\r\ne_correct=[1.72,0.12,4.01];\r\nassert(isequal(e_correct,round(mean(e),2)));\r\n\r\nfunction M=randOrthRotMat()\r\nM = zeros(3); \r\nvi = 2*rand(3,1)-1;  \r\nM(:,1) = vi ./ norm(vi);\r\nfor i=2:3\r\n\tnrm = 0;\r\n\twhile nrm\u003c1e-10\r\n\t   vi = 2*rand(3,1)-1;\r\n\t   vi = vi -  M(:,1:i-1)  * ( M(:,1:i-1).' * vi )  ;\r\n\t   nrm = norm(vi);\r\n\tend\r\n\tM(:,i) = vi ./ nrm;\r\nend \r\nend\r\n%%\r\nrng(10);\r\nfor k=1:1000\r\n   R=randOrthRotMat;\r\n   e(k,:)=rotMat2euler(R);\r\nend\r\ne_correct=[-2.95,0.49,-3.43];\r\nassert(isequal(e_correct,round(mean(e),2)));\r\n\r\nfunction M=randOrthRotMat()\r\nM = zeros(3); \r\nvi = 2*rand(3,1)-1;  \r\nM(:,1) = vi ./ norm(vi);\r\nfor i=2:3\r\n\tnrm = 0;\r\n\twhile nrm\u003c1e-10\r\n\t   vi = 2*rand(3,1)-1;\r\n\t   vi = vi -  M(:,1:i-1)  * ( M(:,1:i-1).' * vi )  ;\r\n\t   nrm = norm(vi);\r\n\tend\r\n\tM(:,i) = vi ./ nrm;\r\nend \r\nend\r\n%%\r\nrng(100);\r\nfor k=1:100000\r\n   R=randOrthRotMat;\r\n   e(k,:)=rotMat2euler(R);\r\nend\r\ne_correct=[-0.24,0.22,0.22];\r\nassert(isequal(e_correct,round(mean(e),2)));\r\n\r\nfunction M=randOrthRotMat()\r\nM = zeros(3); \r\nvi = 2*rand(3,1)-1;  \r\nM(:,1) = vi ./ norm(vi);\r\nfor i=2:3\r\n\tnrm = 0;\r\n\twhile nrm\u003c1e-10\r\n\t   vi = 2*rand(3,1)-1;\r\n\t   vi = vi -  M(:,1:i-1)  * ( M(:,1:i-1).' * vi )  ;\r\n\t   nrm = norm(vi);\r\n\tend\r\n\tM(:,i) = vi ./ nrm;\r\nend \r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-05T14:52:16.000Z","updated_at":"2026-06-02T02:26:21.000Z","published_at":"2022-09-05T14:52:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a rotation matrix, generate the Euler Angles as output [phi,theta,psi]. [phi is a rotation around X-axis, theta is rotation around Y-axis, and psi is rotation around Z-axis].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":55490,"title":"Rotation Matrix to Euler Angles","description":"Given a rotation matrix, generate the Euler Angles as output [phi,theta,psi]. [phi is a rotation around X-axis, theta is rotation around Y-axis, and psi is rotation around Z-axis].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a rotation matrix, generate the Euler Angles as output [phi,theta,psi]. [phi is a rotation around X-axis, theta is rotation around Y-axis, and psi is rotation around Z-axis].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function e = rotMat2euler(R)\r\nphi=acos(R(1,1));theta=asin(R(2,2));psi=atan(R(3,3));\r\ne=[phi,theta,psi];\r\nend","test_suite":"%%\r\nR =[0.495854215827297   0.217789379010378   0.840652355636128\r\n   0.639334284157749  -0.746671533981521  -0.183666255589267\r\n  -0.587690624178059  -0.628529559155301   0.509480444689732];\r\ne=rotMat2euler(R);\r\ne_correct=[-50.97,35.99,52.20];\r\nassert(isequal(e_correct,round(e,2)));\r\n%%\r\nrng(1);\r\nfor k=1:100\r\n   R=randOrthRotMat;\r\n   e(k,:)=rotMat2euler(R);\r\nend\r\ne_correct=[1.72,0.12,4.01];\r\nassert(isequal(e_correct,round(mean(e),2)));\r\n\r\nfunction M=randOrthRotMat()\r\nM = zeros(3); \r\nvi = 2*rand(3,1)-1;  \r\nM(:,1) = vi ./ norm(vi);\r\nfor i=2:3\r\n\tnrm = 0;\r\n\twhile nrm\u003c1e-10\r\n\t   vi = 2*rand(3,1)-1;\r\n\t   vi = vi -  M(:,1:i-1)  * ( M(:,1:i-1).' * vi )  ;\r\n\t   nrm = norm(vi);\r\n\tend\r\n\tM(:,i) = vi ./ nrm;\r\nend \r\nend\r\n%%\r\nrng(10);\r\nfor k=1:1000\r\n   R=randOrthRotMat;\r\n   e(k,:)=rotMat2euler(R);\r\nend\r\ne_correct=[-2.95,0.49,-3.43];\r\nassert(isequal(e_correct,round(mean(e),2)));\r\n\r\nfunction M=randOrthRotMat()\r\nM = zeros(3); \r\nvi = 2*rand(3,1)-1;  \r\nM(:,1) = vi ./ norm(vi);\r\nfor i=2:3\r\n\tnrm = 0;\r\n\twhile nrm\u003c1e-10\r\n\t   vi = 2*rand(3,1)-1;\r\n\t   vi = vi -  M(:,1:i-1)  * ( M(:,1:i-1).' * vi )  ;\r\n\t   nrm = norm(vi);\r\n\tend\r\n\tM(:,i) = vi ./ nrm;\r\nend \r\nend\r\n%%\r\nrng(100);\r\nfor k=1:100000\r\n   R=randOrthRotMat;\r\n   e(k,:)=rotMat2euler(R);\r\nend\r\ne_correct=[-0.24,0.22,0.22];\r\nassert(isequal(e_correct,round(mean(e),2)));\r\n\r\nfunction M=randOrthRotMat()\r\nM = zeros(3); \r\nvi = 2*rand(3,1)-1;  \r\nM(:,1) = vi ./ norm(vi);\r\nfor i=2:3\r\n\tnrm = 0;\r\n\twhile nrm\u003c1e-10\r\n\t   vi = 2*rand(3,1)-1;\r\n\t   vi = vi -  M(:,1:i-1)  * ( M(:,1:i-1).' * vi )  ;\r\n\t   nrm = norm(vi);\r\n\tend\r\n\tM(:,i) = vi ./ nrm;\r\nend \r\nend","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-05T14:52:16.000Z","updated_at":"2026-06-02T02:26:21.000Z","published_at":"2022-09-05T14:52:15.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a rotation matrix, generate the Euler Angles as output [phi,theta,psi]. [phi is a rotation around X-axis, theta is rotation around Y-axis, and psi is rotation around Z-axis].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"euler angles\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}