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TitleCalculate a polygon's area
Keywordspolygon, area
CategoriesGraphics
 
Add the areas of the trapezoids defined by the polygon's edges dropped to the X-axis. When the program considers a bottom edge of a polygon, the calculation gives a negative area so the space between the polygon and the axis is subtracted, leaving the polygon's area. This method gives odd results for non-simple polygons (where edges cross).

The total calculated area is negative if the polygon is oriented clockwise. See also the HowTo Find the orientation of a polygon (clockwise or counterclockwise).

 
Private Function SignedPolygonArea() As Single
Dim pt As Integer
Dim area As Single

    ' Add the first point to the end.
    ReDim Preserve m_Points(1 To m_NumPoints + 1)
    m_Points(m_NumPoints + 1) = m_Points(1)

    ' Get the areas.
    For pt = 1 To m_NumPoints
        area = area + _
            (m_Points(pt + 1).X - m_Points(pt).X) * _
            (m_Points(pt + 1).Y + m_Points(pt).Y) / 2
    Next pt

    ' Return the result.
    SignedPolygonArea = area
End Function

' Find the polygon's area.
Public Function PolygonArea() As Single
    ' Return the absolute value of the signed area.
    PolygonArea = Abs(SignedPolygonArea())
End Function
 
For more information on graphics programming in Visual Basic, see my book Visual Basic Graphics Programming.
 
 
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