{"action":"created","issue":{"url":"https://api.github.com/repos/kinnala/scikit-fem/issues/62","repository_url":"https://api.github.com/repos/kinnala/scikit-fem","labels_url":"https://api.github.com/repos/kinnala/scikit-fem/issues/62/labels{/name}","comments_url":"https://api.github.com/repos/kinnala/scikit-fem/issues/62/comments","events_url":"https://api.github.com/repos/kinnala/scikit-fem/issues/62/events","html_url":"https://github.com/kinnala/scikit-fem/issues/62","id":365703914,"node_id":"MDU6SXNzdWUzNjU3MDM5MTQ=","number":62,"title":"interpolate Morley","user":{"login":"gdmcbain","id":1588947,"node_id":"MDQ6VXNlcjE1ODg5NDc=","avatar_url":"https://avatars3.githubusercontent.com/u/1588947?v=4","gravatar_id":"","url":"https://api.github.com/users/gdmcbain","html_url":"https://github.com/gdmcbain","followers_url":"https://api.github.com/users/gdmcbain/followers","following_url":"https://api.github.com/users/gdmcbain/following{/other_user}","gists_url":"https://api.github.com/users/gdmcbain/gists{/gist_id}","starred_url":"https://api.github.com/users/gdmcbain/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/gdmcbain/subscriptions","organizations_url":"https://api.github.com/users/gdmcbain/orgs","repos_url":"https://api.github.com/users/gdmcbain/repos","events_url":"https://api.github.com/users/gdmcbain/events{/privacy}","received_events_url":"https://api.github.com/users/gdmcbain/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":17,"created_at":"2018-10-02T01:26:59Z","updated_at":"2018-10-08T05:41:49Z","closed_at":null,"author_association":"CONTRIBUTOR","body":"The problem is to interpolate a function defined on Morley elements at a specified (*x, y*) point which isn't necessarily a node; e.g. the deflection at the centre of the Kirchhoff plate in ex02, or the value of the stream-function at the centre of the circular-cylindrical cavity in ex18.\r\n\r\nAttempting `MeshTri.interpolator` with the `MeshTri` returned by `refinterp` fails #59; the mesh is invalid, having duplicate points.\r\n\r\nI think interpolation involves two steps:\r\n1. Find the element (if any) that contains the point.\r\n1. Evaluate the function based on the local basis functions of that element and the elemental degrees of freedom.\r\n\r\nand I suspect that in general the first is the harder.  \r\n\r\nThus far, this operation is only implemented in scikit-fem as `MeshTri.interpolator` (P1) and `MeshTri.const_interpolator` (P0) and makes use of :\r\n* [`matplotlib.tri.Triangulation`](https://matplotlib.org/api/tri_api.html?highlight=matplotlib%20tri%20triangulation#matplotlib.tri.Triangulation),\r\n* [`matplotlib.tri.LinearTriInterpolator`](https://matplotlib.org/api/tri_api.html?highlight=matplotlib%20tri%20triangulation#matplotlib.tri.LinearTriInterpolator)\r\n* [`matplotlib.tri.Triangulation.get_trifinder`](https://matplotlib.org/api/tri_api.html?highlight=matplotlib%20tri%20triangulation#matplotlib.tri.Triangulation.get_trifinder)\r\n\r\nPerhaps the [`TriFinder`](https://matplotlib.org/api/tri_api.html?highlight=matplotlib%20tri%20triangulation#matplotlib.tri.TriFinder) might be factored out of those so that it could also be used for other elements defined on linear simplicial meshes; e.g., besides Morley, also affine P2.  Looking ahead, with `MeshQuad._splitquads`, perhaps quadrilateral meshes too."},"comment":{"url":"https://api.github.com/repos/kinnala/scikit-fem/issues/comments/427726290","html_url":"https://github.com/kinnala/scikit-fem/issues/62#issuecomment-427726290","issue_url":"https://api.github.com/repos/kinnala/scikit-fem/issues/62","id":427726290,"node_id":"MDEyOklzc3VlQ29tbWVudDQyNzcyNjI5MA==","user":{"login":"kinnala","id":973268,"node_id":"MDQ6VXNlcjk3MzI2OA==","avatar_url":"https://avatars2.githubusercontent.com/u/973268?v=4","gravatar_id":"","url":"https://api.github.com/users/kinnala","html_url":"https://github.com/kinnala","followers_url":"https://api.github.com/users/kinnala/followers","following_url":"https://api.github.com/users/kinnala/following{/other_user}","gists_url":"https://api.github.com/users/kinnala/gists{/gist_id}","starred_url":"https://api.github.com/users/kinnala/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/kinnala/subscriptions","organizations_url":"https://api.github.com/users/kinnala/orgs","repos_url":"https://api.github.com/users/kinnala/repos","events_url":"https://api.github.com/users/kinnala/events{/privacy}","received_events_url":"https://api.github.com/users/kinnala/received_events","type":"User","site_admin":false},"created_at":"2018-10-08T05:41:49Z","updated_at":"2018-10-08T05:41:49Z","author_association":"OWNER","body":"When you read the source code in Github and mouse over the line number, three dots apper next to it. Pressing that gives you a URL."}}
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