Area of a polygon- using numerical integration

In summary, the most efficient way to calculate the area of an irregular polygon is to divide it into triangles. However, this can be a challenge if the polygon is not convex or has multiple loops in its border. Another option is to use polygon filling with scanlines. Alternatively, if you have the coordinates of the vertices, you can use the formulas provided in the Wikipedia article for calculating the area and centroid.
  • #1
atee
1
0
Hi,

I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques.

Please can anyone suggest any reference material / best way of going about this efficiently?

Akash
 
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  • #2
The most accurate method will be to divide the polygon into triangles.

You can choose any corner, and try to eliminate it by drawing a line between the adjacent corners.
Since the polygon isn't convex, you need to check.
-that the line drawn is on the inside of the polygon
-that the line doesn't intersect any of the edges.

It gets harder if the border of the polygon consists of more than one loop.

Another idea is to look at polygon filling using scanlines, for example here:

http://ezekiel.vancouver.wsu.edu/~cs442/lectures/raster/polyfill/poly.pdf
 
  • #3
Decomposing a general polygon into triangles is intuitive, but it can be problematic in practice.

If you know the coordinates of the vertices of a general polygon, this article has formulas for calculating the area and centroid:

http://en.wikipedia.org/wiki/Polygon
 

FAQ: Area of a polygon- using numerical integration

What is the definition of a polygon?

A polygon is a two-dimensional shape with straight sides and angles. It is formed by connecting multiple line segments together to create a closed shape.

How is the area of a polygon calculated using numerical integration?

Numerical integration is a method used to approximate the area under a curve. To find the area of a polygon using this method, the polygon is divided into smaller, simpler shapes (such as triangles or rectangles) and the area of each shape is calculated. The sum of these areas gives an approximation of the total area of the polygon.

Is numerical integration the only method for finding the area of a polygon?

No, there are other methods for finding the area of a polygon, such as using the formula A = 1/2 * base * height for triangles or A = length * width for rectangles. However, numerical integration is useful for finding the area of irregular or complex polygons where these formulas may not apply.

What are the steps involved in using numerical integration to find the area of a polygon?

The steps involved in using numerical integration to find the area of a polygon are:

  1. Divide the polygon into smaller, simpler shapes.
  2. Calculate the area of each shape using its respective formula.
  3. Add the areas of each shape together to get an approximation of the total area of the polygon.

Is numerical integration accurate for finding the area of a polygon?

Numerical integration can provide a close approximation of the area of a polygon, but it may not be completely accurate. The smaller and more numerous the shapes used, the more accurate the approximation will be. It is also important to consider the precision and accuracy of the measurements used in the calculation.

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