PolygonMoments

Computes any order moment of a (continuous or discontinuous) area defined by a set of vertices.

The user defines an area via s set of vertices with coordinates x,y. The area can be continuous or discontinuous, convex, non-convex, any shape possible, as long as the vertices are increasing their id with the area on their left. By default, the PolygonMoments function computes:
- Area
- Area moments Ix, Iy,
- Area moments of second degree (inertias) Ixx, Iyy, Ixy, Izz
- Giration radius wrt x,y,z
- Area centroid (AC) coordinates
- Area moments of second degree in x,y,z axes passing through the AC
- Giration radius wrt x,y,z axes passing through the AC
- Rotation angle of the principal axes
- Minimum and Maximum area moments of second degree
- Coordinates of the original vertices in the rotated principal axes.
And it can also compute any are moment of degree (m,n) defined as M(m,n)=integral( x^m * y^n * dxdy).
Several plotting options are controlled by the PlotFlag input argument.

Additionally, in this package there are two more functions:
- TranslateMoment: it takes the (m,n) moments from PolygonMoments and translate them to a point (x0, y0)
- VolumeAndMomentsUnderPolynomial: it computes the volume under a bi-variate polynomial of any degree acting
on an arbitrary polygon defined by vertices (as explained above). This can be used in civil engineering
for computing forces, moments in columns, beams, or to compute forces on water-submerged gates, or to
compute forces and moments on foundations, footings, etc.

Technical Reference:
Marin, Joaquin, 1984,
"Computing Columns, Footings and Gates through Moments of Area,"
Computers & Structures, Vol. 18., Nr. 2, pp. 343-349,1984.