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How do you calculate the area of ​​a series of random points?

So I'm working on a code snippet to take positional data for the RC Plane Crop Duster and calculate the total surface area (without double counting any area). I can’t understand how to calculate the area for a certain period of work.

According to the table below. Calculate the area in which the points are located.

x,y 1,2 1,5 4,3 6,6 3,4 3,1

Any ideas? I looked through the Green Theorem, and I was left without a practical concept in which to code.

Thanks for any advice.

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6 answers
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Someone than me may need to check the information here. But it looks legitimate: http://www.wikihow.com/Calculate-the-Area-of-a-Polygon and is pretty easy to apply in code.

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I'm not quite sure what you are looking for "Surface area" as much as you are looking for. It looks like you want to calculate the distance between one point and the next for this list. If so, just use the Distance Formula .

If the plane drops a constant width of dust when flying between these points, then the area is simply the distance between these points multiplied by the width of the spray.

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If your points are guaranteed to be on an integer grid - as they are in your example - (and you are really looking for a closed area), does Pick Theorem help?

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You will need to divide the complex polygon into approximately standard polygons (triangles, rectangles, etc.), and then find the area of ​​all of them. This is like regular integration (the only difference is that you still have to find a formula to approximate your data).

The above points are when you assume that you are forming a closed polygon with your data.

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Use for QHull to triangulate the area, then sum the areas of the resulting triangles.

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