def second_areal_moment(collection):
"""
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.
"""
ga = _cast(collection)
result = numpy.zeros(len(ga))
n_holes_per_geom = pygeos.get_num_interior_rings(ga)
for i, geometry in enumerate(ga):
n_holes = n_holes_per_geom[i]
for hole_ix in range(n_holes):
hole = pygeos.get_coordinates(pygeos.get_interior_ring(
ga, hole_ix))
result[i] -= _second_moa_ring(hole)
n_parts = pygeos.get_num_geometries(geometry)
for part in pygeos.get_parts(geometry):
result[i] += _second_moa_ring(pygeos.get_coordinates(part))
# must divide everything by 24 and flip if polygon is clockwise.
signflip = numpy.array([-1, 1])[pygeos.is_ccw(ga).astype(int)]
return result * (1 / 24) * signflip
def test_is_ccw(geom, expected):
assert pygeos.is_ccw(geom) == expected