{"action":"created","issue":{"url":"https://api.github.com/repos/rodluger/planetplanet/issues/63","repository_url":"https://api.github.com/repos/rodluger/planetplanet","labels_url":"https://api.github.com/repos/rodluger/planetplanet/issues/63/labels{/name}","comments_url":"https://api.github.com/repos/rodluger/planetplanet/issues/63/comments","events_url":"https://api.github.com/repos/rodluger/planetplanet/issues/63/events","html_url":"https://github.com/rodluger/planetplanet/issues/63","id":253114540,"number":63,"title":"(Even more) arbitrary surface 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think my integration method is more general than I had realized. Currently, because I'm restricting my calculations to ellipses, I need the radiance map to be radially symmetric about the hotspot, but I think that we can relax this assumption. The integration step would also work if our curves of constant radiance were *any other convex shape*. The only bit that would change is the intersection-finding routine, but this can easily be done numerically (as I pointed out [here](https://github.com/rodluger/planetplanet/issues/31#issuecomment-325056027)). We'd also need to compute the integral of the shape, but that's quite easy.\r\n\r\nI'm thinking that in **v2** the user could specify the functional form of the curves of constant radiance, say, as two polynomials: the upper part of the curve and the lower part of the curve, provided they intersect to form a closed shape. We could then easily compute their integrals, and we could still use the GSL root-finder to determine the points of intersection with the occultor.\r\n\r\nThe tricky bit will be to rotate the shape depending on the viewing angle, but I think this is a simple stretching transformation that can be generalized.\r\n\r\nThe reason this may be super useful is that the radiance map of a planet could have different longitudinal and latitudinal length scales because of rotation/winds: i.e., the hotspot may be elongated along the equator (currently we're effectively assuming it's a circle).\r\n\r\nIt will be a bit of work to code this up, but the code should be *just as fast*!\r\n\r\n@ericagol, @jlustigy: what do you think?"},"comment":{"url":"https://api.github.com/repos/rodluger/planetplanet/issues/comments/325646729","html_url":"https://github.com/rodluger/planetplanet/issues/63#issuecomment-325646729","issue_url":"https://api.github.com/repos/rodluger/planetplanet/issues/63","id":325646729,"user":{"login":"ericagol","id":243664,"avatar_url":"https://avatars2.githubusercontent.com/u/243664?v=4","gravatar_id":"","url":"https://api.github.com/users/ericagol","html_url":"https://github.com/ericagol","followers_url":"https://api.github.com/users/ericagol/followers","following_url":"https://api.github.com/users/ericagol/following{/other_user}","gists_url":"https://api.github.com/users/ericagol/gists{/gist_id}","starred_url":"https://api.github.com/users/ericagol/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ericagol/subscriptions","organizations_url":"https://api.github.com/users/ericagol/orgs","repos_url":"https://api.github.com/users/ericagol/repos","events_url":"https://api.github.com/users/ericagol/events{/privacy}","received_events_url":"https://api.github.com/users/ericagol/received_events","type":"User","site_admin":false},"created_at":"2017-08-29T12:22:25Z","updated_at":"2017-08-29T12:22:25Z","body":"This could be a cool extension of the code!\r\n\r\nSometimes, though, the iso-intensity contours can be non-convex, such as the chevron shapes or latitudinally symmetric spots, such as seen here: [http://www.exoclimes.com/wp-content/uploads/2012/02/showman-600x353.png](url)"}}
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