Solved

# Area of a closed GraphicsPath

Posted on 2010-09-03
940 Views
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

0
Question by:SniperX1

LVL 21

Expert Comment

ID: 33597196
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.
0

LVL 4

Accepted Solution

aaver earned 500 total points
ID: 33601127
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.
0

LVL 18

Expert Comment

ID: 33601496
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

``````
0

LVL 1

Author Closing Comment

ID: 33602485
thanks for the help, it is very much appreciated.
0

## Featured Post

### Suggested Solutions

Introduction Hi all and welcome to my first article on Experts Exchange. A while ago, someone asked me if i could do some tutorials on object oriented programming. I decided to do them on C#. Now you may ask me, why's that? Well, one of the re…
This article is for Object-Oriented Programming (OOP) beginners. An Interface contains declarations of events, indexers, methods and/or properties. Any class which implements the Interface should provide the concrete implementation for each Inter…
This demo shows you how to set up the containerized NetScaler CPX with NetScaler Management and Analytics System in a non-routable Mesos/Marathon environment for use with Micro-Services applications.
You have products, that come in variants and want to set different prices for them? Watch this micro tutorial that describes how to configure prices for Magento super attributes. Assigning simple products to configurable: We assigned simple products…