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Area of a polygon- using numerical integration

  1. Jun 2, 2014 #1

    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?

  2. jcsd
  3. Jun 2, 2014 #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:

  4. Jun 2, 2014 #3


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    Staff Emeritus
    Science Advisor
    Homework Helper

    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:

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