{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":60986,"title":"Mesh the convex hull of a random 3D point cloud","description":"Problem statement\r\n\r\nThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\r\nA triangulation, or triangulated mesh, is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\nUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; 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: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 795.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 397.617px; transform-origin: 408px 397.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 256.717px 8px; transform-origin: 256.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulation, or triangulated mesh, is simply a \u003c/span\u003e\u003c/span\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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\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: 229.017px 8px; transform-origin: 229.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 327.125px 8px; transform-origin: 327.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_convex_hull(V)\r\n  T = V;\r\nend","test_suite":"%% Point set #1\r\nV = [0.7253   -0.3789    0.5520\r\n     0.4471   -0.3044    0.8245\r\n     0.8241    0.6916    0.2092\r\n    -0.7553   -0.5126    0.2692\r\n    -0.2179   -0.8765   -0.3024\r\n    -0.0984    0.3260    0.8808\r\n    -0.9354   -0.0462    0.2274\r\n     0.2122   -0.6391    0.6226\r\n    -0.0248   -0.1993   -0.8833\r\n     0.0772    0.9644   -0.2436\r\n    -0.1098   -0.0333   -0.9851\r\n    -0.6662    0.0466    0.7499\r\n    -0.6866    0.5290   -0.5468\r\n     0.0357    0.0086   -0.9728\r\n     0.0829   -0.2777   -1.0373\r\n    -0.3445    0.5795    0.6257];\r\n\r\nT_correct = [1     2     8;\r\n             1     3     2;\r\n             1     5    15;\r\n             1     8     5;\r\n             1    15     3;\r\n             2     3     6;\r\n             2     6    12;\r\n             2    12     8;\r\n             3    10    16;\r\n             3    14    10;\r\n             3    15    14;\r\n             3    16     6;\r\n             4     5     8;\r\n             4     7    13;\r\n             4     8    12;\r\n             4    12     7;\r\n             4    13     5;\r\n             5    11    15;\r\n             5    13    11;\r\n             6    16    12;\r\n             7    12    16;\r\n             7    16    13;\r\n             10    13    16;\r\n             10    14    13;\r\n             11    13    14;\r\n             11    14    15];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Point set #2\r\nV = [-0.0775   -0.4239    0.9421;\r\n    -0.8154    0.0299   -0.4279;\r\n     0.6777   -0.4686   -0.6602;\r\n    -0.2960   -0.8871    0.5367;\r\n    -0.0034   -0.0899    0.9352;\r\n     0.8245   -0.5624    0.0630;\r\n     0.6048   -0.7364   -0.3692;\r\n     0.4215    0.9403   -0.2533;\r\n     0.3255    0.0593   -0.8884;\r\n     0.4979   -0.0671    0.8623;\r\n    -1.0254    0.1883   -0.0015;\r\n     0.7398    0.2020   -0.4934;\r\n     0.7488    0.5209   -0.0621;\r\n    -0.0994   -0.5682   -0.8936;\r\n    -0.8099   -0.0951   -0.4470;\r\n     0.3038   -0.9284   -0.4938];\r\n\r\nT_correct = [1     4     6;\r\n             1     5    11;\r\n             1     6    10;\r\n             1    10     5;\r\n             1    11     4;\r\n             2     8     9;\r\n             2     9    14;\r\n             2    11     8;\r\n             2    14    15;\r\n             2    15    11;\r\n             3     6     7;\r\n             3     7    16;\r\n             3     9    12;\r\n             3    12     6;\r\n             3    14     9;\r\n             3    16    14;\r\n             4    11    15;\r\n             4    14    16;\r\n             4    15    14;\r\n             4    16     6;\r\n             5     8    11;\r\n             5    10     8;\r\n             6    12    13;\r\n             6    13    10;\r\n             6    16     7;\r\n             8    10    13;\r\n             8    12     9;\r\n             8    13    12];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_convex_hull.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:46:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T20:10:16.000Z","updated_at":"2026-02-13T17:40:03.000Z","published_at":"2025-07-24T18:00:49.000Z","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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eA triangulation, or triangulated mesh, is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58872,"title":"Find the Points Tangent to a Circle from an External Point ","description":"From a point where do the lines touch a circle tangentially?. The loldrup solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\r\nGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u003eR.\r\nThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\r\nP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\r\nY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\r\nX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\r\nThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\r\n\r\n\r\nThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; 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: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 952.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 476.25px; transform-origin: 407px 476.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 204px 8px; transform-origin: 204px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eloldrup\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 358px 8px; transform-origin: 358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 188px 8px; transform-origin: 188px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 211px 8px; transform-origin: 211px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 556.5px; 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 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 419px;height: 551px\" 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\" data-image-state=\"image-loaded\" width=\"419\" height=\"551\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n%Find points on circle that when drawn to a point only touches circle at the circle point.\r\n%The line from the circle center to (x3 y3) is orthogonal to the line [(px,py) (x3,y3)]\r\n%A second point (x4,y4) also creates an orthogonal lines intersection\r\n\r\n  D=norm([px-cx py-cy])\r\n  \r\n  %Y=\r\n  %X=\r\n  \r\n  xy=[X Y;-X Y];\r\n \r\n %Rotation Angle: atan2\r\n theta=atan2(px-cx,py-cy); % (X,Y) output radians Neg Left of vert, Pos Right of Vert\r\n \r\n %Rotation Matrix: [cos(t) -sin(t);sin(t) cos(t)]\r\n %Translation matrix: [cx cy]\r\n %Check of (px,py) being regenerated from D, theta, and translation\r\n [pxyD]=[0 D]*[cos(theta) -sin(theta);sin(theta) cos(theta)]+[cx cy]\r\n [px py]\r\n \r\n %xy=\r\n \r\n \r\n  \r\nend %TangentPoints_onCircle","test_suite":"%%\r\nvalid=1;\r\npx=6;py=8;cx=0;cy=0;R=4;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=-6;py=-8;cx=2;cy=4;R=6;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=6;py=8;cx=1;cy=-2;R=5;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\n%px=6;py=8;cx=1;cy=-2;R=5;\r\ncx=-5*rand; cy=-5*rand; R=4+rand;\r\npx=3+2*rand; py=3+2*rand;\r\n[px py cx cy R]\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-12T23:33:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-12T21:15:25.000Z","updated_at":"2023-08-12T23:33:27.000Z","published_at":"2023-08-12T23:33:27.000Z","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\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eloldrup\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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 point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"419\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\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\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). 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the convex hull of a random 3D point cloud","description":"Problem statement\r\n\r\nThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\r\nA triangulation, or triangulated mesh, is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\nUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; 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: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 795.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 397.617px; transform-origin: 408px 397.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 256.717px 8px; transform-origin: 256.717px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; 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: 150.925px 8px; transform-origin: 150.925px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulation, or triangulated mesh, is simply a \u003c/span\u003e\u003c/span\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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\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: 229.017px 8px; transform-origin: 229.017px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\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: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\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: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 327.125px 8px; transform-origin: 327.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; 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: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_convex_hull(V)\r\n  T = V;\r\nend","test_suite":"%% Point set #1\r\nV = [0.7253   -0.3789    0.5520\r\n     0.4471   -0.3044    0.8245\r\n     0.8241    0.6916    0.2092\r\n    -0.7553   -0.5126    0.2692\r\n    -0.2179   -0.8765   -0.3024\r\n    -0.0984    0.3260    0.8808\r\n    -0.9354   -0.0462    0.2274\r\n     0.2122   -0.6391    0.6226\r\n    -0.0248   -0.1993   -0.8833\r\n     0.0772    0.9644   -0.2436\r\n    -0.1098   -0.0333   -0.9851\r\n    -0.6662    0.0466    0.7499\r\n    -0.6866    0.5290   -0.5468\r\n     0.0357    0.0086   -0.9728\r\n     0.0829   -0.2777   -1.0373\r\n    -0.3445    0.5795    0.6257];\r\n\r\nT_correct = [1     2     8;\r\n             1     3     2;\r\n             1     5    15;\r\n             1     8     5;\r\n             1    15     3;\r\n             2     3     6;\r\n             2     6    12;\r\n             2    12     8;\r\n             3    10    16;\r\n             3    14    10;\r\n             3    15    14;\r\n             3    16     6;\r\n             4     5     8;\r\n             4     7    13;\r\n             4     8    12;\r\n             4    12     7;\r\n             4    13     5;\r\n             5    11    15;\r\n             5    13    11;\r\n             6    16    12;\r\n             7    12    16;\r\n             7    16    13;\r\n             10    13    16;\r\n             10    14    13;\r\n             11    13    14;\r\n             11    14    15];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Point set #2\r\nV = [-0.0775   -0.4239    0.9421;\r\n    -0.8154    0.0299   -0.4279;\r\n     0.6777   -0.4686   -0.6602;\r\n    -0.2960   -0.8871    0.5367;\r\n    -0.0034   -0.0899    0.9352;\r\n     0.8245   -0.5624    0.0630;\r\n     0.6048   -0.7364   -0.3692;\r\n     0.4215    0.9403   -0.2533;\r\n     0.3255    0.0593   -0.8884;\r\n     0.4979   -0.0671    0.8623;\r\n    -1.0254    0.1883   -0.0015;\r\n     0.7398    0.2020   -0.4934;\r\n     0.7488    0.5209   -0.0621;\r\n    -0.0994   -0.5682   -0.8936;\r\n    -0.8099   -0.0951   -0.4470;\r\n     0.3038   -0.9284   -0.4938];\r\n\r\nT_correct = [1     4     6;\r\n             1     5    11;\r\n             1     6    10;\r\n             1    10     5;\r\n             1    11     4;\r\n             2     8     9;\r\n             2     9    14;\r\n             2    11     8;\r\n             2    14    15;\r\n             2    15    11;\r\n             3     6     7;\r\n             3     7    16;\r\n             3     9    12;\r\n             3    12     6;\r\n             3    14     9;\r\n             3    16    14;\r\n             4    11    15;\r\n             4    14    16;\r\n             4    15    14;\r\n             4    16     6;\r\n             5     8    11;\r\n             5    10     8;\r\n             6    12    13;\r\n             6    13    10;\r\n             6    16     7;\r\n             8    10    13;\r\n             8    12     9;\r\n             8    13    12];\r\n\r\nassert(isequal(mesh_the_convex_hull(V),T_correct))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_convex_hull.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:46:23.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T20:10:16.000Z","updated_at":"2026-02-13T17:40:03.000Z","published_at":"2025-07-24T18:00:49.000Z","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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe convex hull of a 3D point set is actually a first -though rough- triangulation of it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eA triangulation, or triangulated mesh, is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eUse Matlab functions to compute the convex hull of the random point clouds given in the tests here below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc 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w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\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\u003cw:jc 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58872,"title":"Find the Points Tangent to a Circle from an External Point ","description":"From a point where do the lines touch a circle tangentially?. The loldrup solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\r\nGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u003eR.\r\nThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\r\nP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\r\nY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\r\nX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\r\nThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\r\n\r\n\r\nThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; 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: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 952.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 476.25px; transform-origin: 407px 476.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 204px 8px; transform-origin: 204px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eloldrup\u003c/span\u003e\u003c/span\u003e\u003c/a\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: 133px 8px; transform-origin: 133px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 358px 8px; transform-origin: 358px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 188px 8px; transform-origin: 188px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 211px 8px; transform-origin: 211px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; 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 10.5px; text-align: left; transform-origin: 384px 10.5px; 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 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 556.5px; 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 278.25px; text-align: left; transform-origin: 384px 278.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 419px;height: 551px\" 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\" data-image-state=\"image-loaded\" width=\"419\" height=\"551\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; 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: 378.5px 8px; transform-origin: 378.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). D=2*P\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function xy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n%Find points on circle that when drawn to a point only touches circle at the circle point.\r\n%The line from the circle center to (x3 y3) is orthogonal to the line [(px,py) (x3,y3)]\r\n%A second point (x4,y4) also creates an orthogonal lines intersection\r\n\r\n  D=norm([px-cx py-cy])\r\n  \r\n  %Y=\r\n  %X=\r\n  \r\n  xy=[X Y;-X Y];\r\n \r\n %Rotation Angle: atan2\r\n theta=atan2(px-cx,py-cy); % (X,Y) output radians Neg Left of vert, Pos Right of Vert\r\n \r\n %Rotation Matrix: [cos(t) -sin(t);sin(t) cos(t)]\r\n %Translation matrix: [cx cy]\r\n %Check of (px,py) being regenerated from D, theta, and translation\r\n [pxyD]=[0 D]*[cos(theta) -sin(theta);sin(theta) cos(theta)]+[cx cy]\r\n [px py]\r\n \r\n %xy=\r\n \r\n \r\n  \r\nend %TangentPoints_onCircle","test_suite":"%%\r\nvalid=1;\r\npx=6;py=8;cx=0;cy=0;R=4;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=-6;py=-8;cx=2;cy=4;R=6;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\npx=6;py=8;cx=1;cy=-2;R=5;\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n\r\n%%\r\nvalid=1;\r\n%px=6;py=8;cx=1;cy=-2;R=5;\r\ncx=-5*rand; cy=-5*rand; R=4+rand;\r\npx=3+2*rand; py=3+2*rand;\r\n[px py cx cy R]\r\nxy=TangentPoints_onCircle(px,py,cx,cy,R)\r\n\r\n%Verify line from (cx,cy) to (x3,y3) slope is -1/slope of (px,py) to (x3,y3), orthogonal\r\nmexp=-(xy(2,1)-cx)/(xy(2,2)-cy)\r\nmp=(xy(2,2)-py)/(xy(2,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\nmexp=-(xy(1,1)-cx)/(xy(1,2)-cy)\r\nmp=(xy(1,2)-py)/(xy(1,1)-px)\r\nif abs(mexp)\u003e1e12 % Inf slope allow +/- match\r\n if ~(abs(mp)\u003e1e12)\r\n   valid=0\r\n end\r\nelse\r\n if abs(mp-mexp)\u003e1e-6\r\n  valid=0\r\n end\r\nend\r\n\r\n\r\nassert(valid)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":3097,"edited_at":"2023-08-12T23:33:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-08-12T21:15:25.000Z","updated_at":"2023-08-12T23:33:27.000Z","published_at":"2023-08-12T23:33:27.000Z","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\u003eFrom a point where do the lines touch a circle tangentially?. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://math.stackexchange.com/questions/913239/given-circle-and-point-where-does-the-tangential-line-through-the-point-touch-t\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eloldrup\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e solution may provide some guidance and alternate method. I will elaborate a more reference frame modification geometric solution utilizing Matlab specific functions, rotation matrix, and translation matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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 point(px,py) and circle [cx,cy,R] return the circle points [x3 y3;x4 y4] where lines thru the point are tangential to the circle.  The line ([px,py],[x3,y3]) is tangential to circle [cx,cy,R] at circle point [x3,y3]. D\u0026gt;R.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eThe below figure is created based upon h=P=distance([cx,cy],[px,py])/2=D/2, translating (cx,cy) to (0,0), and rotating (px,py) to be on the Y-axis. From this manipulation two right triangles are apparent: [X,Y,R] and [X,h-Y,P]. Subtracting and simplifying these triangles leads to Y and two X values after substituting back into R^2=X^+Y^2 equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eP^2=X^2+(h-Y)^2  and R^2=X^2+Y^2  after subtraction gives R^2-P^2=Y^2-(h-Y)^2 = Y^2-h^2+2hY-Y^2=2hY-h^2 thus\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eY=(R^2-P^2+h^2)/(2h) =(R^2-P^2+P^2)/(2P)=R^2/(2P)=R^2/D\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eX=+/- (R^2-Y^2)^.5=+/- (R^2-(R^2/(2P))^2)^0.5=+/- R*(1-(R/D)^2)^0.5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\u003eThe trick is to now un-rotate and translate this solution matrix using t=atan2(dx,dy), [cos(t) -sin(t);sin(t) cos(t)] and [cx cy]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\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\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"551\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"419\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\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\u003eThis figure shows the point (px,py) rotated onto the Y-axis at position 2P. The circle (cx,cy) has been shifted to the origin with radius R. The green line shows a tangent at (x,y) from (px,py). A second tangent point is at (-x.y). 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