{"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":42762,"title":"Is 3D point set Co-Planar?","description":"This Challenge is to determine if four 3D integer points are co-planar.\r\nGiven a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.\r\n\r\nExamples\r\n\r\n m = [0 0 0;1 0 0;0 1 0;0 0 1] \r\n Output: False, this point set is non-coplanar.\r\n\r\n m = [0 0 0;0 0 1;1 1 0;1 1 1]\r\n Output: True, this point set is co-planar.\r\n\r\nReference: The \u003chttp://68.173.157.131/Contest/Tetrahedra March 2016 Al Zimmermann Non-Coplanar contest\u003e is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.\r\n\r\nTheory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D\r\n","description_html":"\u003cp\u003eThis Challenge is to determine if four 3D integer points are co-planar.\r\nGiven a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.\u003c/p\u003e\u003cp\u003eExamples\u003c/p\u003e\u003cpre\u003e m = [0 0 0;1 0 0;0 1 0;0 0 1] \r\n Output: False, this point set is non-coplanar.\u003c/pre\u003e\u003cpre\u003e m = [0 0 0;0 0 1;1 1 0;1 1 1]\r\n Output: True, this point set is co-planar.\u003c/pre\u003e\u003cp\u003eReference: The \u003ca href = \"http://68.173.157.131/Contest/Tetrahedra\"\u003eMarch 2016 Al Zimmermann Non-Coplanar contest\u003c/a\u003e is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.\u003c/p\u003e\u003cp\u003eTheory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D\u003c/p\u003e","function_template":"function TF = iscoplanar(m)\r\n% m is a 4x3 matrix\r\n  TF=false;\r\nend","test_suite":"%%\r\nm=[0 0 1;1 1 0;1 0 1;2 0 0];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;2 1 2];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;0 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;2 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;2 0 1];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[2 0 0;1 2 0;2 1 1;2 2 2];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[2 0 0;1 2 0;2 1 1;2 1 2];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;1 0 0;0 1 0;0 0 1];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;1 0 0;0 1 0;1 1 1];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;1 0 0;0 1 0;1 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;0 0 1;1 1 1;1 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n\r\n%0 0 0 \r\n%1 0 0 \r\n%0 1 0 \r\n%0 0 1 \r\n%1 1 1","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-03-05T21:58:07.000Z","updated_at":"2026-05-28T14:48:11.000Z","published_at":"2016-03-06T19:31:31.000Z","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\u003eThis Challenge is to determine if four 3D integer points are co-planar. Given a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.\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\u003eExamples\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[ m = [0 0 0;1 0 0;0 1 0;0 0 1] \\n Output: False, this point set is non-coplanar.\\n\\n m = [0 0 0;0 0 1;1 1 0;1 1 1]\\n Output: True, this point set is co-planar.]]\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\u003eReference: The\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://68.173.157.131/Contest/Tetrahedra\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMarch 2016 Al Zimmermann Non-Coplanar contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.\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\u003eTheory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D\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":42762,"title":"Is 3D point set Co-Planar?","description":"This Challenge is to determine if four 3D integer points are co-planar.\r\nGiven a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.\r\n\r\nExamples\r\n\r\n m = [0 0 0;1 0 0;0 1 0;0 0 1] \r\n Output: False, this point set is non-coplanar.\r\n\r\n m = [0 0 0;0 0 1;1 1 0;1 1 1]\r\n Output: True, this point set is co-planar.\r\n\r\nReference: The \u003chttp://68.173.157.131/Contest/Tetrahedra March 2016 Al Zimmermann Non-Coplanar contest\u003e is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.\r\n\r\nTheory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D\r\n","description_html":"\u003cp\u003eThis Challenge is to determine if four 3D integer points are co-planar.\r\nGiven a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.\u003c/p\u003e\u003cp\u003eExamples\u003c/p\u003e\u003cpre\u003e m = [0 0 0;1 0 0;0 1 0;0 0 1] \r\n Output: False, this point set is non-coplanar.\u003c/pre\u003e\u003cpre\u003e m = [0 0 0;0 0 1;1 1 0;1 1 1]\r\n Output: True, this point set is co-planar.\u003c/pre\u003e\u003cp\u003eReference: The \u003ca href = \"http://68.173.157.131/Contest/Tetrahedra\"\u003eMarch 2016 Al Zimmermann Non-Coplanar contest\u003c/a\u003e is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.\u003c/p\u003e\u003cp\u003eTheory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D\u003c/p\u003e","function_template":"function TF = iscoplanar(m)\r\n% m is a 4x3 matrix\r\n  TF=false;\r\nend","test_suite":"%%\r\nm=[0 0 1;1 1 0;1 0 1;2 0 0];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;2 1 2];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;0 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;2 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 1;1 1 0;1 0 1;2 0 1];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[2 0 0;1 2 0;2 1 1;2 2 2];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[2 0 0;1 2 0;2 1 1;2 1 2];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;1 0 0;0 1 0;0 0 1];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;1 0 0;0 1 0;1 1 1];\r\ny_correct = false;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;1 0 0;0 1 0;1 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n%%\r\nm=[0 0 0;0 0 1;1 1 1;1 1 0];\r\ny_correct = true;\r\nassert(isequal(iscoplanar(m),y_correct))\r\n\r\n%0 0 0 \r\n%1 0 0 \r\n%0 1 0 \r\n%0 0 1 \r\n%1 1 1","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":27,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-03-05T21:58:07.000Z","updated_at":"2026-05-28T14:48:11.000Z","published_at":"2016-03-06T19:31:31.000Z","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\u003eThis Challenge is to determine if four 3D integer points are co-planar. Given a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.\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\u003eExamples\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[ m = [0 0 0;1 0 0;0 1 0;0 0 1] \\n Output: False, this point set is non-coplanar.\\n\\n m = [0 0 0;0 0 1;1 1 0;1 1 1]\\n Output: True, this point set is co-planar.]]\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\u003eReference: The\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://68.173.157.131/Contest/Tetrahedra\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMarch 2016 Al Zimmermann Non-Coplanar contest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.\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\u003eTheory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D\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:\"convhull\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}