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