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I have a list of coordinates of latitude and longitude which make an 'S' shape if I join the coordinates sequentially. My task is to make a parallel 'S' translated 0.1 nautical miles from the original one. Please give me some hints or tell me any mathematical formula to do this.

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Please try to clarify your question. Do you mean that you have a set of points, with coordinates given as latitude and longitude, which form an "S" shape, and you wish to find coordinates in latitude and longitude for the set of points translated by a distance of $.1$ NM? If so, translated in what direction, and what is "NM"? – Alex Becker Dec 30 '11 at 6:16
@AlexBecker, I want to make a parallel "S" with 0.1 NM difference from the original "S". Where "S" is the shape which I get from the given coordinates if I connect all the coordinates with line sequentially. And 'NM' is Nautical Miles (Unit of Distance). – Siddiqui Dec 30 '11 at 6:24
What is so complicated about this? You take your original coordinates in latitude and longitude and just translate those coordinates by 0.1 NM. Is that what seems to be a complicated task for you? I am not sure I understand. – Patrick Da Silva Dec 30 '11 at 7:44
Given that 0.1 NM is A) a small distance on the global scale, B) an approximate figure, C) it is unlikely that your teacher wants the app to be used anywhere near either of the poles, I dare guess that a "locally flat" approach will be adequate. In that case the NS direction has a fixed scale of 60 NM per degree, but the scale on the EW axis depends on latitude in the known way: 1 degree change in longitude amounts to $60*\cos\alpha$ NM, where $\alpha$ is the latitude. – Jyrki Lahtonen Dec 30 '11 at 8:12
What do you mean by parallel? There are no parallel straight lines (great circles) on a sphere. – Henry Dec 30 '11 at 8:14

I think what you are looking for is discussed under the subject of function transformation. Assuming that the points you have are in a 2-dimensional surface, you may use the technique below to do the desired shift (image source is:Shifting function) enter image description here

Here is another example (with an S-shaped function):

Sin(x) shifted

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