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Area of a closed GraphicsPath

I have a graphicspath shape in a picturebox, created from a set of lines and some beizer curves. does anyone know how to find the area of the shape. I know how find the points along any of the sides of the shape, and i know what the bounding rectangle is

thanks for any help

example image

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SniperX1
1 Solution

Commented:
Thinking back many many years, if you have equations for each segment you take the integral to get the area.  But it sounds like you have specific data points?  The simplest is to just loop through x = min to max in steps of deltax.  The area = sum of (y2 - y1) * deltax where y2 and y1 are the upper and lower curve coordinates.  There are more refined approximations, but that gets it done.  If you have an x with more than two y's (like in the middle of the graph) you need to calculate the upper and lower areas separately.  There are probably open source codes out there to do this, but you'd have to try your google skills with that.
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Commented:
What you need is a "relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C." (i.e. Green's theorem: http://en.wikipedia.org/wiki/Green%27s_theorem)

A special case of Green's theorem when the closed curve C is given by discrete coordinates is often called "Surveyor's Formula" (see under the paragraph "Area and centroid" here: http://en.wikipedia.org/wiki/Polygon)

If you have all vertices for the straight lines and enough points on the curved ones, the sum (area) should be easy to calculate.
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Graphics ExpertCommented:
By looking at the shape as an image, then what you have is a lot of pixels.
Assuming, for ease, that the image is a black and white with just 1 bit, then each pixel is 0 or 1. So, just count the number of pixels equal to 1 and you have the area.
As in CODE 1.
If the pixels are 8 bit deep, then CODE 2 applies.
The same approach is ok for color images.
The area is given in pixels. If you need the area in inches, for example, just calculate the area (as in CODE 1 or 2) and divide it by (N*N), being N the number of pixels by inch of your image.

``````// CODE 1 ---> image 1 bit deep
area = 0
for x=1 to width
for y=1 to height
if pixel(x,y) not zero then area = area + 1
next y
next x
//---------------------------------
// CODE 2 ---> image 8 bit deep (256 levels)
area = 0
for x=1 to width
for y=1 to height
if pixel(x,y) not zero then area = area + pixel(x,y)
next y
next x
area = area/256

``````
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Author Commented:
thanks for the help, it is very much appreciated.
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