{"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":636,"title":"Spherical radius given four points","description":"Determine the radius of a sphere provided four non-coplanar points on the surface of the sphere.\r\n\r\n pts = [x1 y1 z1;\r\n        x2 y2 z2;\r\n        x3 y3 z3;\r\n        x4 y4 z4]\r\n\r\nHint: See \u003chttp://steve.hollasch.net/cgindex/geometry/sphere4pts.html\u003e\r\n\r\nExample: \r\n\r\n pts = [1 0 0;\r\n        0 1 0;\r\n        0 0 1;\r\n       -1 0 0]\r\n r=1","description_html":"\u003cp\u003eDetermine the radius of a sphere provided four non-coplanar points on the surface of the sphere.\u003c/p\u003e\u003cpre\u003e pts = [x1 y1 z1;\r\n        x2 y2 z2;\r\n        x3 y3 z3;\r\n        x4 y4 z4]\u003c/pre\u003e\u003cp\u003eHint: See \u003ca href=\"http://steve.hollasch.net/cgindex/geometry/sphere4pts.html\"\u003ehttp://steve.hollasch.net/cgindex/geometry/sphere4pts.html\u003c/a\u003e\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e pts = [1 0 0;\r\n        0 1 0;\r\n        0 0 1;\r\n       -1 0 0]\r\n r=1\u003c/pre\u003e","function_template":"function r = Sphere_radius(pts)\r\n  r = 1;\r\nend","test_suite":"%%\r\npts=[0 3 2;1 -1 1;2 1 0;5 1 3]; % c(2 1 3) r=3\r\ny_correct = 3;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\n pts=[1 0 0;0 1 0;0 0 1;-1 0 0]; % c(0 0 0) r=1\r\ny_correct = 1;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\npts=[1 0 -1;0 1 -1;0 0 0;-1 0 -1]; % c(0 0 -1) r=1\r\ny_correct = 1;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\npts=[2 0 -2;0 2 -2;0 0 0;-2 0 -2]; % c(0 0 -2) r=2\r\ny_correct = 2;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\npts=[-5 -1 -3;1 -1 -3;-2 -4 -3;-2 -1 0]; % c(-2 -1 -3) r=3\r\ny_correct = 3;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":254,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":17,"created_at":"2012-04-29T17:20:14.000Z","updated_at":"2026-03-13T04:56:44.000Z","published_at":"2012-04-29T17:20:14.000Z","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\u003eDetermine the radius of a sphere provided four non-coplanar points on the surface of the sphere.\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[ pts = [x1 y1 z1;\\n        x2 y2 z2;\\n        x3 y3 z3;\\n        x4 y4 z4]]]\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\u003eHint: 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://steve.hollasch.net/cgindex/geometry/sphere4pts.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://steve.hollasch.net/cgindex/geometry/sphere4pts.html\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eExample:\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[ pts = [1 0 0;\\n        0 1 0;\\n        0 0 1;\\n       -1 0 0]\\n r=1]]\u003e\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\\\" 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pts = [x1 y1 z1;\r\n        x2 y2 z2;\r\n        x3 y3 z3;\r\n        x4 y4 z4]\u003c/pre\u003e\u003cp\u003eHint: See \u003ca href=\"http://steve.hollasch.net/cgindex/geometry/sphere4pts.html\"\u003ehttp://steve.hollasch.net/cgindex/geometry/sphere4pts.html\u003c/a\u003e\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e pts = [1 0 0;\r\n        0 1 0;\r\n        0 0 1;\r\n       -1 0 0]\r\n r=1\u003c/pre\u003e","function_template":"function r = Sphere_radius(pts)\r\n  r = 1;\r\nend","test_suite":"%%\r\npts=[0 3 2;1 -1 1;2 1 0;5 1 3]; % c(2 1 3) r=3\r\ny_correct = 3;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\n pts=[1 0 0;0 1 0;0 0 1;-1 0 0]; % c(0 0 0) r=1\r\ny_correct = 1;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\npts=[1 0 -1;0 1 -1;0 0 0;-1 0 -1]; % c(0 0 -1) r=1\r\ny_correct = 1;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\npts=[2 0 -2;0 2 -2;0 0 0;-2 0 -2]; % c(0 0 -2) r=2\r\ny_correct = 2;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n%%\r\npts=[-5 -1 -3;1 -1 -3;-2 -4 -3;-2 -1 0]; % c(-2 -1 -3) r=3\r\ny_correct = 3;\r\nassert(isequal(Sphere_radius(pts),y_correct))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":254,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":17,"created_at":"2012-04-29T17:20:14.000Z","updated_at":"2026-03-13T04:56:44.000Z","published_at":"2012-04-29T17:20:14.000Z","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 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