Re: polygonal area on a sphere



moltilimits@xxxxxxxxx wrote:
Hi,
please, someone can tell me how can I to calculate the area of a
polygon on the earth's surface where I know the coordinates (lat/lon)
of its points?
Since you know the coordinates of every vertex, break it into
triangles. The area of every triangle is that triangle's base
times its height divided by two. Sum the areas.

It's ok like idea, but doesn't exists a formula that uses vertex
coordinates to obtain the result?
Break the area in small trangles is allright, but practically how can
I implement it? I must find a point internal to the polygon and then
consider all the triangles?

It does not need to be a point internal. You can use one of the points you have and then compute the area of the next 2 points, then from the second point to the third point, etc. until all the area is covered. This will work so long as all the points are in one direction around the area. If some points result in a triangle outside the polygon then they need to be subtracted.

So, the calculus of the areas isn't very
easy:

While tedious it is not very hard. It only requires high school level geometry or trigonometry to perform the calculation. No calculus is needed. You can get a rough idea simply by plotting the points on a piece of graph paper. You could even use a protractor (or drafting triangle for 90 degrees) and dividers to measure the distances. This is not as accurate but a good learning exercise so that you can get a handle on what is really going on.

I know the vertex of the triangle and the calculus of the height
can be difficult.
Must I use the Erone's formula?
Sorry for the questions but I see this problem very difficult for me :-
(
Bye,

moltilimits


Dale

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