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How do you find the moment of inertia of a polygon?

  1. Mar 24, 2009 #1
    I'm working on an engine right now, and I'm having trouble calculating the moment of inertia for a polygon. Is there any way to easily do this without decomposing the polygon into triangles?

    edit: I've looked at the wikipedia page with examples on the subject (http://en.wikipedia.org/wiki/List_of_moments_of_inertia) and I'm having trouble understanding the last example, which seems to be what I need.
    Last edited: Mar 24, 2009
  2. jcsd
  3. Mar 24, 2009 #2


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    Dearly Missed

    That last example is, indeed, the moment of inertia formula for the polygon, and is the final result of having decomposed the polygon into triangles.

    I derived it once for myself, I'm sorry that I'm not inm the mood to do it once again.
  4. Mar 25, 2009 #3
    Any particular reason your polygons are not triangles in the first place? Polygons of 4 or more sides complicates everything.

    4 or more sides means your polygon does not need to have all vertexes on the same plane, which complicates shading.

    Building a BSP-tree gets more complicated the more sides your polygons have (you will end up splitting a whole lot).

    and so on.

  5. Mar 25, 2009 #4
    I'm sorry if I wasn't clear, but I'm doing everything on a 2D plane. I'm not sure what you mean by stating that the vertexes won't be on the same plane, but I think you may be confusing 3D graphics with my problem (shading?). In addition, finding a way to solve this problem for convex polygons will achieve what I'm going for, which is why I'm avoiding BSP-trees or any other kind of decomposition of the polygon.
  6. Mar 31, 2009 #5
    Yep, I was thinking 3D, sorry.

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