Function Prop_poli(ByVal x As Variant) As Variant

'EXAMPLE OF SUB: HOW TO CALL THE FUNCTION Prop_poli
'Sub test()
'Dim x() As Variant
'Dim out As Variant
''input points
'ReDim x(1 To 10, 1 To 2) As Variant
'
''Secção em canal
'x(1, 1) = -1.8
'x(1, 2) = 2.4552
'x(2, 1) = -2.1
'x(2, 2) = -0.5448
'x(3, 1) = -2.1
'x(3, 2) = -1.1448
'x(4, 1) = 2.1
'x(4, 2) = -1.1448
'x(5, 1) = 2.1
'x(5, 2) = -0.5448
'x(6, 1) = 1.8
'x(6, 2) = 2.4552
'x(7, 1) = 1.5
'x(7, 2) = 2.4552
'x(8, 1) = 1.5
'x(8, 2) = -0.5448
'x(9, 1) = -1.5
'x(9, 2) = -0.5448
'x(10, 1) = -1.5
'x(10, 2) = 2.4552
'
'out = Prop_poli(x)
'
'End Sub

    Dim n_pts As Integer
    Dim i As Integer
    Dim Area As Double
    Dim Cx As Double
    Dim Cy As Double
    Dim Ix As Double
    Dim Iy As Double
    Dim Ixy As Double
    Dim PROP_OUT As Variant

    n_pts = UBound(x, 1)
    Area = 0
    Cx = 0
    Cy = 0
    Ix = 0
    Iy = 0
    Ixy = 0

    For i = 1 To (n_pts - 1)
        Area = Area + (x(i, 1) * x(i + 1, 2) - x(i + 1, 1) * x(i, 2))
        Cx = Cx + (x(i, 1) + x(i + 1, 1)) * (x(i, 1) * x(i + 1, 2) - x(i + 1, 1) * x(i, 2))
        Cy = Cy + (x(i, 2) + x(i + 1, 2)) * (x(i, 1) * x(i + 1, 2) - x(i + 1, 1) * x(i, 2))
        Ix = Ix + (x(i, 2) ^ 2 + x(i, 2) * x(i + 1, 2) + x(i + 1, 2) ^ 2) * (x(i, 1) * x(i + 1, 2) - x(i + 1, 1) * x(i, 2))
        Iy = Iy + (x(i, 1) ^ 2 + x(i, 1) * x(i + 1, 1) + x(i + 1, 1) ^ 2) * (x(i, 1) * x(i + 1, 2) - x(i + 1, 1) * x(i, 2))
        Ixy = Ixy + (x(i, 1) * x(i + 1, 2) + 2 * x(i, 1) * x(i, 2) + 2 * x(i + 1, 1) * x(i + 1, 2) + x(i + 1, 1) * x(i, 2)) * (x(i, 1) * x(i + 1, 2) - x(i + 1, 1) * x(i, 2))
    Next
    i = n_pts
    Area = Area + (x(i, 1) * x(1, 2) - x(1, 1) * x(i, 2))
    Cx = Cx + (x(i, 1) + x(1, 1)) * (x(i, 1) * x(1, 2) - x(1, 1) * x(i, 2))
    Cy = Cy + (x(i, 2) + x(1, 2)) * (x(i, 1) * x(1, 2) - x(1, 1) * x(i, 2))
    Ix = Ix + (x(i, 2) ^ 2 + x(i, 2) * x(1, 2) + x(1, 2) ^ 2) * (x(i, 1) * x(1, 2) - x(1, 1) * x(i, 2))
    Iy = Iy + (x(i, 1) ^ 2 + x(i, 1) * x(1, 1) + x(1, 1) ^ 2) * (x(i, 1) * x(1, 2) - x(1, 1) * x(i, 2))
    Ixy = Ixy + (x(i, 1) * x(1, 2) + 2 * x(i, 1) * x(i, 2) + 2 * x(1, 1) * x(1, 2) + x(1, 1) * x(i, 2)) * (x(i, 1) * x(1, 2) - x(1, 1) * x(i, 2))


    Area = Area / 2
    Cx = Cx / (6 * Area)
    Cy = Cy / (6 * Area)
    Ix = Ix / 12
    Iy = Iy / 12
    Ixy = Ixy / 24

    'montagem da saida
    ReDim PROP_OUT(1 To 6) As Variant
    PROP_OUT(1) = Area
    PROP_OUT(2) = Cx
    PROP_OUT(3) = Cy
    PROP_OUT(4) = Ix
    PROP_OUT(5) = Iy
    PROP_OUT(6) = Ixy

    Prop_poli = PROP_OUT
End Sub