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For my internship research I am trying to compare the surfacearea and length of geometric shapes and lines in one coordinate system to another. I have a SpatialPolygonDataFrame in the European equal area projection ETRS-LAEA and I have a function that can calculate the surfacearea and the length of all polygons. I can transform it to another projection and calculate the surfaceareas and the lengths of all polygons in that projection.

My next step would be to calculate the surfacearea and the length of the polygons in ETRS89(x,y,z). Since this is a 3D projection the functions I am using for the 2D projections are not working. Are there functions for 3D projections? I can not find them online.

I am hoping there has been some smart guy with a similar problem and already fixed it. I am expecting this is not the case and that it is (for me) impossible in R.

Zuenie
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  • Quite an interesting question. As a starting point you may study this code for computation of the area of a spherical polygon and try to adapt it in R. – SS_Rebelious Sep 03 '14 at 13:56
  • @SS_Rebelious That spherical formula is unlikely to be accurate enough for work of this sort, which is bound to focus on rather small differences. In fact, I do not understand why it would be relevant, since the objective is to compare areas and lengths as computed in particular [projected] coordinate systems. – whuber Sep 03 '14 at 16:30
  • @whuber, if I understood question correctly, the CRS that was mentioned (ETRS89(x,y,z)) actually has no projection (it is lat/lon). That is why I pointed at spherical polygons. – SS_Rebelious Sep 03 '14 at 17:26
  • Yes I need to calculate surfaceareas and lengths of spherical polygons. The link you gave is nice, however it is hard to understand. Even harder to implement in R. – Zuenie Sep 03 '14 at 21:02
  • @whuber isnt a spherical calculation more accurate than a calculation of the area of a polygon on a 2D projection? The earth is not flat. This is exactly the thing I am trying to test. I do not know the answer yet. I however do assume that it is correct that on 3D projections calculations would be more accurate. Also more difficult, but also more accurate. – Zuenie Sep 04 '14 at 06:43
  • Creating 1:10 000 scale map is far more difficult than 1:100 000, and the result will be more precise... But what a point in wasting resources for 1:10 000 when 1:100 000 is suitable for your needs? Your precision with spherical polygons will only be relevant if your polygon has a size of a continent. – SS_Rebelious Sep 04 '14 at 08:45
  • That is not necessarily the case, Zuenie. Elsewhere I have documented the linear errors occurring in using a spherical model; they are up to one part in 300. On the other hand, with an equal-area projection based on an ellipsoidal earth model, areas computed in projected coordinates will be completely accurate. @SS_Rebelious Be careful: it is important in this conversation to distinguish precision from accuracy. Scale is relevant to precision but at best has only a small indirect relationship to accuracy. – whuber Sep 04 '14 at 14:26
  • @whuber why are you so eager to argue with me all the time? Reread my comment plz - I wrote about precision and didn't use word accuracy at all... – SS_Rebelious Sep 04 '14 at 15:14
  • @SS_Rebelious I raise issues where I think they need to be called out. It has nothing to do with you personally, but only concerns the comments and answers you post. In this case, we agree that scale is a matter of precision, as you have said. But don't you also agree that the question is about accuracy? Because the two concepts are distinct, and that distinction bears on the question, I feel it is important to point out that your comment was potentially misleading. Whether you meant "accuracy" or "precision," the last sentence in your comment is incorrect: the spherical formula is crude. – whuber Sep 04 '14 at 17:17
  • @whuber, sometimes should just turn a blind eye to someone's mistakes in the internet. I know you are a smart person, you should have understand that I used analogy in that comment and it only has only indirect relation to the question. Yes, I used a wrong word in the last sentence, but does it really matter for the topic starter?!!! DOES IT? Of course not... You are a moderator and you should not ruin one's experience with this site. I find it quite annoying being involved in such fruitless disputes (not the first time with you). – SS_Rebelious Sep 04 '14 at 17:43

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