Add docs about converting between shapely and cf (#512)

* Add docs about converting between shapely and cf

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Add shapely to docs env

* Apply suggestions from code review

Co-authored-by: Deepak Cherian <[email protected]>

* Update doc/geometry.md

* Update doc/geometry.md

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Deepak Cherian <[email protected]>

cf_xarray/geometry.py

@@ -94,9 +94,10 @@ def shapely_to_cf(geometries: xr.DataArray | Sequence, grid_mapping: str | None
         A dataset with shapely geometry objects translated into CF-compliant variables :
          - 'x', 'y' : the node coordinates
          - 'crd_x', 'crd_y' : the feature coordinates (might have different names if `grid_mapping` is available).
-         - 'node_count' : The number of nodes per feature. Absent if all instances are Points.
+         - 'node_count' : The number of nodes per feature. Always present for Lines and Polygons. For Points: only present if there are multipart geometries.
+         - 'part_node_count' : The number of nodes per individual geometry. Only for Lines with multipart geometries and for Polygons with multipart geometries or holes.
+         - 'interior_ring' : Integer boolean indicating whether rings are interior or exterior. Only for Polygons with holes.
          - 'geometry_container' : Empty variable with attributes describing the geometry type.
-         - Other variables are not implemented as only Points are currently understood.
 
     References
     ----------

ci/doc.yml

@@ -19,6 +19,7 @@ dependencies:
   - pooch
   - pint
   - regex
+  - shapely
   - furo
   - myst-nb
   - pip:

doc/geometry.md

@@ -1,7 +1,99 @@
+---
+jupytext:
+  text_representation:
+    format_name: myst
+kernelspec:
+  display_name: Python 3
+  name: python3
+---
+
 ```{eval-rst}
 .. currentmodule:: xarray
 ```
 
 # Geometries
 
-See {py:func}`cf_xarray.shapely_to_cf`,  {py:func}`cf_xarray.cf_to_shapely`
+```{seealso}
+1. [The CF conventions on Geometries](http://cfconventions.org/Data/cf-conventions/cf-conventions-1.11/cf-conventions.html#geometries)
+1. {py:func}`cf_xarray.shapely_to_cf`
+1. {py:func}`cf_xarray.cf_to_shapely`
+```
+
+`cf_xarray` can convert between vector geometries represented as shapely objects
+and CF-compliant array representations of those geometries.
+
+Let's start by creating an xarray object containing some shapely geometries. This example uses
+a `xr.DataArray` but these functions also work with a `xr.Dataset` where one of the data variables
+contains an array of shapes.
+
+```{code-cell}
+import cf_xarray as cfxr
+import xarray as xr
+
+from shapely.geometry import MultiPoint, Point
+
+da = xr.DataArray(
+    [
+        MultiPoint([(1.0, 2.0), (2.0, 3.0)]),
+        Point(3.0, 4.0),
+        Point(4.0, 5.0),
+        Point(3.0, 4.0),
+    ],
+    dims=("index",),
+    name="geometry"
+)
+```
+
+```{warning}
+`cf_xarray` does not support handle multiple types of shapes (Point, Line, Polygon) in one
+`xr.DataArray`, but multipart geometries are supported and can be mixed with single-part
+geometries of the same type.
+```
+
+Now we can take that `xr.DataArray` containing shapely geometries and convert it to cf:
+
+```{code-cell}
+ds_cf = cfxr.shapely_to_cf(da)
+ds_cf
+```
+
+This function returns a `xr.Dataset` containing the CF fields needed to reconstruct the
+geometries. In particular there are:
+
+- `'x'`, `'y'` : the node coordinates
+- `'crd_x'`, `'crd_y'` : the feature coordinates (might have different names if `grid_mapping` is available).
+- `'node_count'` : The number of nodes per feature. Always present for Lines and Polygons. For
+  Points: only present if there are multipart geometries.
+- `'part_node_count'` : The number of nodes per individual geometry. Only for Lines with multipart
+  geometries and for Polygons with multipart geometries or holes.
+- `'interior_ring'` : Integer boolean indicating whether ring is interior or exterior. Only for
+  Polygons with holes.
+- `'geometry_container`' : Empty variable with attributes describing the geometry type.
+
+Here are the attributes on `geometry_container`. This pattern mimics the convention of
+specifying spatial reference information in the attrs of the empty array `spatial_ref`.
+
+```{code-cell}
+ds_cf.geometry_container.attrs
+```
+
+```{note}
+Z axis is not yet supported for any shapes.
+```
+
+This `xr.Dataset` can be converted back into a `xr.DataArray` of shapely geometries:
+
+```{code-cell}
+cfxr.cf_to_shapely(ds_cf)
+```
+
+This conversion adds coordinates that aren't in the `xr.DataArray` that we started with.
+By default these are called `crd_x` and `crd_y` unless `grid_mapping` is specified.
+
+## Gotchas
+
+For MultiPolygons with holes the CF notation is slightly ambiguous on which hole is associated
+with which polygon. This is problematic because shapely stores holes within the polygon
+object that they are associated with. `cf_xarray` assumes that the the shapes are interleaved
+such that the holes (interior rings) are associated with the exteriors (exterior rings) that
+immediately precede them.