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fix math formatting in second_areal_moment #264

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Aug 25, 2023
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fix math formatting in second_areal_moment #264

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10 changes: 7 additions & 3 deletions esda/shape.py
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Original file line number Diff line number Diff line change
Expand Up @@ -475,16 +475,20 @@ def second_areal_moment(collection):
moment of area is the sum of the inertia across the x and y axes:

The :math:`x` axis is given by:

.. math::

I_x = (1/12)\\sum^{N}_{i=1} (x_i y_{i+1} - x_{i+1}y_i) (x_i^2 + x_ix_{i+1} + x_{i+1}^2)

While the :math:`y` axis is in a similar form:

.. math::

I_y = (1/12)\\sum^{N}_{i=1} (x_i y_{i+1} - x_{i+1}y_i) (y_i^2 + y_iy_{i+1} + y_{i+1}^2)

where :math:`x_i`,:math:`y_i` is the current point and :math:`x_{i+1}`, :math:`y_{i+1}` is the next point,
and where :math:`x_{n+1} = x_1, y_{n+1} = y_1`. For multipart polygons with holes,
all parts are treated as separate contributions to the overall centroid, which
where :math:`x_i`, :math:`y_i` is the current point and :math:`x_{i+1}`, :math:`y_{i+1}` is the next point,
and where :math:`x_{n+1} = x_1, y_{n+1} = y_1`. For multipart polygons with holes,
all parts are treated as separate contributions to the overall centroid, which
provides the same result as if all parts with holes are separately computed, and then
merged together using the parallel axis theorem.

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