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Math Help - Polygon Center Point

  1. #1
    rat
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    Polygon Center Point

    Hello .

    How can I calculate the polygon center point using its vertexes?

    Thanks
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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by rat
    Hello .

    How can I calculate the polygon center point using its vertexes?

    Thanks
    are these regular polygons?
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  3. #3
    rat
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    No, they also can be irregular...
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by rat
    No, they also can be irregular...
    Then don't we need to know what type of centre you are
    interested in?

    Centre of mass of unit weights at the vertices.

    Centre or mass of rods of unit mass per unit length making
    up the sides of the polygon.

    Centre of mass of a lamellar of unit mass per unit area in
    the form of the polygon.

    Or some other centre?
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  5. #5
    Super Member Rebesques's Avatar
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    Since the polygon may be irregular, rat must mean the center of mass, when every vertex point \vec r_1,\ldots,\vec r_n(plural: vertices ) has nonzero mass m_1,\ldots,m_n. Then the center of mass lies at the tip of the vector

    \vec r=\frac{m_1\vec r_1+\dots+m_n\vec r_n}{m_1+\ldots+m_n}.

    Hope this is ok.
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