Irregular Polygon Area

[icb12]

I have a need to calculate the area of an irregular polygon.
Using the area by coordinates method. Given that you have the x,y coordinates of every vertice.

The equation is as follows..
A=(1/2)[{(x1*y2)+(x2*y3)+(x3*y4)...(xN*y1)} - {(y1*x2)+(y2*x3)+(y3*x4)...(yN*x1)}]

Assuming the vertice coordinates are (x1,y1), (x2,y2),...(xN,YN)- listed in separate columns on sheet1

This is simple enough to do in excel when the polygon has just a few vertices.
But when the closed traverse (polygon) is huge with tons of vertices the equation becomes convoluted and a PITA.

I'd like to write a function in VB that would allow me to quickly and easily compute the area simply by selecting the coordinates I have entered on the sheet1.

This was suggested to me by someone more skilled than I... but I can't seem to make it work.

Public Function getArea(ByVal a As ListBox, ByVal b As ListBox)

' Make sure to add the first element to the end to close the polygon
a.Items.Add (a.Items(0))
b.Items.Add (b.Items(0))

Dim n, area, i
n = a.Items.Count

i = 0
area = 0

Do
area = (a.Items.Item(i) * b.Items.Item(i + 1) - a.Items.Item(i + 1) * b.Items.Item(i))

i = i + 1
Loop While i < n - 1

area = Math.Abs(area * 0.5)

' if you have a certain scale you can use this, or skip it
area = applyScale((9 / 64), area)

Return area
End Function

Any suggestions? On how to make the above work, or a better way?

I appreciate any and ALL assistance.

-Iain

 

[John_Clarke]

Thank you

 

[jrickards]

Would this formula work for a shape like the outline of the letter "L" or the letter "W"?

 

[pgc01]

Would this formula work for a shape like the outline of the letter "L" or the letter "W"?

Hi
Welcome to the board

I don't see why it would not work. I don't see anything special in those 2 polygons.

Did you test it and got a bad result?

Please post your test.

 

[jrickards]

Hi
Welcome to the board

I don't see why it would not work. I don't see anything special in those 2 polygons.

Did you test it and got a bad result?

Please post your test.

OK, I will when I run the test.

 

[jrickards]

I used the following (GPS) coordinates (simplified). By my calculations, the area should be 480,000 sq m but the formula gives me an area of 800,000. This is an L shape where the top block is 400x400 (160,000 sq m) and the lower block is 800x400 (320,000 sq m).

Post	Easting	Northing
CP1	540800	5396000
DP1	540800	5395600
DP2	541200	5395600
CP2	541200	5395200
CP3	540000	5395200
CP4	540000	5396000

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[jrickards]

Hah! Never mind, I put in the wrong co-ordinates. All is good!

The Easting for CP3 and CP4 should be 540400.

 

[pgc01]

I'm glad it's working OK. Cheers!

 

[timjjsmith]

OK--This thread is awesome! I have a slightly different data set. My data is a "cloud" of XY data, so only some xy locations are on the exterior, and should be used for calculating the area. Any ideas on VB to find just the XY locations that represent the outer edge, ignoring interior data points to find the area?

 

[shg]

There's a description of the Graham algorithm for finding the convex hull of a point cloud in http://www.cs.princeton.edu/~rs/AlgsDS07/16Geometric.pdf

 

[timjjsmith]

Perfect---i just needed to know what to serach for. Pope has an awesome macro to do this. Convex hull