{"action":"created","comment":{"url":"https://api.github.com/repos/dealii/dealii/pulls/comments/73426426","id":73426426,"diff_hunk":"@@ -127,6 +116,131 @@ class SphericalManifold : public ChartManifold<dim, spacedim, spacedim>\n \n \n /**\n+ * Manifold description for a spherical space coordinate system.\n+ *\n+ * You can use this Manifold object to describe any sphere, circle,\n+ * hypersphere or hyperdisc in two or three dimensions, both as a co-dimension\n+ * one manifold descriptor or as co-dimension zero manifold descriptor.\n+ *\n+ * The two template arguments match the meaning of the two template arguments\n+ * in Triangulation<dim, spacedim>, however this Manifold can be used to\n+ * describe both thin and thick objects, and the behavior is identical when\n+ * dim <= spacedim, i.e., the functionality of SphericalManifold<2,3> is\n+ * identical to SphericalManifold<3,3>.\n+ *\n+ * While PolarManifold reflects the usual notion of polar coordinates,\n+ * it may not be suitable for domains that contain either the north\n+ * pole, the south pole or the center.  Consider for instance the pair\n+ * of points \\f$x_1=(1,\\pi/3,0)\\f$ and \\f$x_2=(1,\\pi/3,\\pi)\\f$ in\n+ * polar coordinates (laying on the surface of a sphere with radius\n+ * one, on a parallel at height $\\pi/3$. In this case connecting the\n+ * points with a straight line in polar coordinates would take the\n+ * long road around the globe, without passing through the north pole.\n+ *\n+ * These two points would be connented (using a PolarManifold) by the curve\n+ * \\$[\n+ * \\begin{align}\n+ *   s: [0,1]  & \\rightarrow &  \\mathbb S^3 \\\\\n+ *           t & \\mapsto     &  (1,\\pi/3,0) + (0,0,t\\pi)\n+ * \\$]\n+ * This curve is not a geodesic on the sphere, and it is not how we\n+ * would connect those two points. A better curve, would be the one\n+ * passing through the North pole:\n+ * \\[\n+ *  s(t) = x_1 \\cos(\\alpha(t)) + \\kappa \\times x_1 \\sin(\\alpha(t)) +\n+ *  \\kappa ( \\kappa \\cdot x_1) (1-\\cos(\\alpha(t))).\n+ * \\]\n+ * where $\\kappa = \\frac{x_1 \\times \\x_2}{\\Vert x_1 \\times \\x_2 \\Vert}$\n+ * and $\\alpha(t) = t * \\arccos(x_1 * x_2) $ for $t\\in[0,1]$.\n+ * Indeed, this is a geodesic, and it is the natural choice when\n+ * connecting points on the surface of the sphere.\n+ *\n+ * If the codimension of the Manifold is one, than this Manifold\n+ * connects points using geodesics. In all other cases it is a\n+ * continuus extension of the codimension one case.","path":"include/deal.II/grid/manifold_lib.h","position":138,"original_position":138,"commit_id":"455f7bf5c7d289ac6343d5059f2bd82810e85274","original_commit_id":"455f7bf5c7d289ac6343d5059f2bd82810e85274","user":{"login":"bangerth","id":7504421,"avatar_url":"https://avatars.githubusercontent.com/u/7504421?v=3","gravatar_id":"","url":"https://api.github.com/users/bangerth","html_url":"https://github.com/bangerth","followers_url":"https://api.github.com/users/bangerth/followers","following_url":"https://api.github.com/users/bangerth/following{/other_user}","gists_url":"https://api.github.com/users/bangerth/gists{/gist_id}","starred_url":"https://api.github.com/users/bangerth/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/bangerth/subscriptions","organizations_url":"https://api.github.com/users/bangerth/orgs","repos_url":"https://api.github.com/users/bangerth/repos","events_url":"https://api.github.com/users/bangerth/events{/privacy}","received_events_url":"https://api.github.com/users/bangerth/received_events","type":"User","site_admin":false},"body":"-> continuous\r\n\r\nWhat does this actually mean? That it finds the geodesic in (phi,theta) space, and then continuously interpolates this geodesic in radial direction between the two points?","created_at":"2016-08-03T21:38:28Z","updated_at":"2016-08-03T21:38:28Z","html_url":"https://github.com/dealii/dealii/pull/2810#discussion_r73426426","pull_request_url":"https://api.github.com/repos/dealii/dealii/pulls/2810","_links":{"self":{"href":"https://api.github.com/repos/dealii/dealii/pulls/comments/73426426"},"html":{"href":"https://github.com/dealii/dealii/pull/2810#discussion_r73426426"},"pull_request":{"href":"https://api.github.com/repos/dealii/dealii/pulls/2810"}}},"pull_request":{"url":"https://api.github.com/repos/dealii/dealii/pulls/2810","id":77104498,"html_url":"https://github.com/dealii/dealii/pull/2810","diff_url":"https://github.com/dealii/dealii/pull/2810.diff","patch_url":"https://github.com/dealii/dealii/pull/2810.patch","issue_url":"https://api.github.com/repos/dealii/dealii/issues/2810","number":2810,"state":"open","locked":false,"title":"SphericalManifold -> PolarManifold","user":{"login":"luca-heltai","id":2919756,"avatar_url":"https://avatars.githubusercontent.com/u/2919756?v=3","gravatar_id":"","url":"https://api.github.com/users/luca-heltai","html_url":"https://github.com/luca-heltai","followers_url":"https://api.github.com/users/luca-heltai/followers","following_url":"https://api.github.com/users/luca-heltai/following{/other_user}","gists_url":"https://api.github.com/users/luca-heltai/gists{/gist_id}","starred_url":"https://api.github.com/users/luca-heltai/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/luca-heltai/subscriptions","organizations_url":"https://api.github.com/users/luca-heltai/orgs","repos_url":"https://api.github.com/users/luca-heltai/repos","events_url":"https://api.github.com/users/luca-heltai/events{/privacy}","received_events_url":"https://api.github.com/users/luca-heltai/received_events","type":"User","site_admin":false},"body":"Still have to check all tests, but this is ready to review. Will add many changed output once this has been accepted as the \"right\" version of SphericalManifold.","created_at":"2016-07-12T11:35:59Z","updated_at":"2016-08-03T21:38:28Z","closed_at":null,"merged_at":null,"merge_commit_sha":"ce6b643c65626768d3f196152f28aa0c96295316","assignee":null,"assignees":[],"milestone":null,"commits_url":"https://api.github.com/repos/dealii/dealii/pulls/2810/commits","review_comments_url":"https://api.github.com/repos/dealii/dealii/pulls/2810/comments","review_comment_url":"https://api.github.com/repos/dealii/dealii/pulls/comments{/number}","comments_url":"https://api.github.com/repos/dealii/dealii/issues/2810/comments","statuses_url":"https://api.github.com/repos/dealii/dealii/statuses/455f7bf5c7d289ac6343d5059f2bd82810e85274","head":{"label":"luca-heltai:spherical-manifold-only","ref":"spherical-manifold-only","sha":"455f7bf5c7d289ac6343d5059f2bd82810e85274","user":{"login":"luca-heltai","id":2919756,"avatar_url":"https://avatars.githubusercontent.com/u/2919756?v=3","gravatar_id":"","url":"https://api.github.com/users/luca-heltai","html_url":"https://github.com/luca-heltai","followers_url":"https://api.github.com/users/luca-heltai/followers","following_url":"https://api.github.com/users/luca-heltai/following{/other_user}","gists_url":"https://api.github.com/users/luca-heltai/gists{/gist_id}","starred_url":"https://api.github.com/users/luca-heltai/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/luca-heltai/subscriptions","organizations_url":"https://api.github.com/users/luca-heltai/orgs","repos_url":"https://api.github.com/users/luca-heltai/repos","events_url":"https://api.github.com/users/luca-heltai/events{/privacy}","received_events_url":"https://api.github.com/users/luca-heltai/received_events","type":"User","site_admin":false},"repo":{"id":22053864,"name":"dealii","full_name":"luca-heltai/dealii","owner":{"login":"luca-heltai","id":2919756,"avatar_url":"https://avatars.githubusercontent.com/u/2919756?v=3","gravatar_id":"","url":"https://api.github.com/users/luca-heltai","html_url":"https://github.com/luca-heltai","followers_url":"https://api.github.com/users/luca-heltai/followers","following_url":"https://api.github.com/users/luca-heltai/following{/other_user}","gists_url":"https://api.github.com/users/luca-heltai/gists{/gist_id}","starred_url":"https://api.github.com/users/luca-heltai/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/luca-heltai/subscriptions","organizations_url":"https://api.github.com/users/luca-heltai/orgs","repos_url":"https://api.github.com/users/luca-heltai/repos","events_url":"https://api.github.com/users/luca-heltai/events{/privacy}","received_events_url":"https://api.github.com/users/luca-heltai/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/luca-heltai/dealii","description":"","fork":true,"url":"https://api.github.com/repos/luca-heltai/dealii","forks_url":"https://api.github.com/repos/luca-heltai/dealii/forks","keys_url":"https://api.github.com/repos/luca-heltai/dealii/keys{/key_id}","collaborators_url":"https://api.github.com/repos/luca-heltai/dealii/collaborators{/collaborator}","teams_url":"https://api.github.com/repos/luca-heltai/dealii/teams","hooks_url":"https://api.github.com/repos/luca-heltai/dealii/hooks","issue_events_url":"https://api.github.com/repos/luca-heltai/dealii/issues/events{/number}","events_url":"https://api.github.com/repos/luca-heltai/dealii/events","assignees_url":"https://api.github.com/repos/luca-heltai/dealii/assignees{/user}","branches_url":"https://api.github.com/repos/luca-heltai/dealii/branches{/branch}","tags_url":"https://api.github.com/repos/luca-heltai/dealii/tags","blobs_url":"https://api.github.com/repos/luca-heltai/dealii/git/blobs{/sha}","git_tags_url":"https://api.github.com/repos/luca-heltai/dealii/git/tags{/sha}","git_refs_url":"https://api.github.com/repos/luca-heltai/dealii/git/refs{/sha}","trees_url":"https://api.github.com/repos/luca-heltai/dealii/git/trees{/sha}","statuses_url":"https://api.github.com/repos/luca-heltai/dealii/statuses/{sha}","languages_url":"https://api.github.com/repos/luca-heltai/dealii/languages","stargazers_url":"https://api.github.com/repos/luca-heltai/dealii/stargazers","contributors_url":"https://api.github.com/repos/luca-heltai/dealii/contributors","subscribers_url":"https://api.github.com/repos/luca-heltai/dealii/subscribers","subscription_url":"https://api.github.com/repos/luca-heltai/dealii/subscription","commits_url":"https://api.github.com/repos/luca-heltai/dealii/commits{/sha}","git_commits_url":"https://api.github.com/repos/luca-heltai/dealii/git/commits{/sha}","comments_url":"https://api.github.com/repos/luca-heltai/dealii/comments{/number}","issue_comment_url":"https://api.github.com/repos/luca-heltai/dealii/issues/comments{/number}","contents_url":"https://api.github.com/repos/luca-heltai/dealii/contents/{+path}","compare_url":"https://api.github.com/repos/luca-heltai/dealii/compare/{base}...{head}","merges_url":"https://api.github.com/repos/luca-h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