esda.shape.second_areal_moment

esda.shape.second_areal_moment(collection)[source]

Using equation listed on en.wikipedia.org/Second_Moment_of_area, the second moment of area is actually the cross-moment of area between the X and Y dimensions:

I_xy = (1/24)sum^{i=N}^{i=1} (x_iy_{i+1} + 2*x_iy_i + 2*x_{i+1}y_{i+1} + x_{i+1}y_i)(x_iy_i - x_{i+1}y_i)

where x_i, y_i is the current point and x_{i+1}, y_{i+1} is the next point, and where x_{n+1} = x_1, y_{n+1} = 1.

This relation is known as the: - second moment of area - moment of inertia of plane area - area moment of inertia - second area moment

and is not the mass moment of inertia, a property of the distribution of mass around a shape.