The second moments of area of the polygon in Python
Posted on 13 Apr 2015 SympyPython 添加评论
Sympy geometry module does not offer function to calculate second moments of area of an arbitrary polygon. However, the algorithm to calculate the moments are quite simple. I simply post the codes for calculating second moments of area here for those who maybe interested in this function.
def second_moments(self):
"""The second moments of area of the polygon.
Returns
=======
Ix, Iy, Ixy : Second moments of area
Examples
========
>>> from sympy import Point, Polygon, S
>>> from numpy import arange
>>> p=[(cos(i),sin(i)) for i in arange(6)/S.One/3*pi]
>>> poly = Polygon(*p)
>>> second_moments(poly)
(5*sqrt(3)/16, 5*sqrt(3)/16, 0)
"""
xc, yc = self.centroid.args
Ix, Iy, Ixy = 0, 0, 0
args = self.args
for i in xrange(len(args)):
x1, y1 = args[i - 1].args
x2, y2 = args[i].args
x1 -= xc; x2 -= xc
y1 -= yc; y2 -= yc
v = x1*y2 - x2*y1
Ix += v*(y1*y1 + y1*y2 +y2*y2)
Iy += v*(x1*x1 + x1*x2 +x2*x2)
Ixy += v*(x1*y2 + 2*x1*y1 + 2*x2*y2 + x2*y1)
Ix /= 12
Iy /= 12
Ixy /= 24
return (Ix, Iy, Ixy)You may also download the raw code here.
