import contextlib
import warnings
import numpy as np
from .geometry import transform
from .geospatial_utils import GeoSpatialUtil
from .parse_version import Version
from .utl_import import import_optional_dependency
NUMPY_GE_121 = Version(np.__version__) >= Version("1.21")
shapely = import_optional_dependency("shapely", errors="silent")
if shapely is not None:
SHAPELY_GE_20 = Version(shapely.__version__) >= Version("2.0")
SHAPELY_LT_18 = Version(shapely.__version__) < Version("1.8")
else:
SHAPELY_GE_20 = False
SHAPELY_LT_18 = False
shapely_warning = None
if shapely is not None:
try:
from shapely.errors import ShapelyDeprecationWarning as shapely_warning
except ImportError:
pass
if shapely_warning is not None and not SHAPELY_GE_20:
@contextlib.contextmanager
def ignore_shapely_warnings_for_object_array():
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore",
"Iteration|The array interface|__len__",
shapely_warning,
)
if NUMPY_GE_121:
# warning from numpy for existing Shapely releases (this is
# fixed with Shapely 1.8)
warnings.filterwarnings(
"ignore",
"An exception was ignored while fetching",
DeprecationWarning,
)
yield
elif SHAPELY_LT_18 and NUMPY_GE_121:
@contextlib.contextmanager
def ignore_shapely_warnings_for_object_array():
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore",
"An exception was ignored while fetching",
DeprecationWarning,
)
yield
else:
[docs] @contextlib.contextmanager
def ignore_shapely_warnings_for_object_array():
yield
[docs]def parse_shapely_ix_result(collection, ix_result, shptyps=None):
"""Recursive function for parsing shapely intersection results. Returns a
list of shapely shapes matching shptyp.
Parameters
----------
collection : list
state variable for storing result, generally
an empty list
ix_result : shapely.geometry type
any shapely intersection result
shptyp : str, list of str, or None, optional
if None (default), return all types of shapes.
if str, return shapes of that type, if list of str,
return all types in list
Returns
-------
collection : list
list containing shapely geometries of type shptyp
"""
# convert shptyps to list if needed
if isinstance(shptyps, str):
shptyps = [shptyps]
elif shptyps is None:
shptyps = [None]
# if empty
if ix_result.is_empty:
return collection
# base case: geom_type is partial or exact match to shptyp
elif ix_result.geom_type in shptyps:
collection.append(ix_result)
return collection
# recursion for collections
elif hasattr(ix_result, "geoms"):
for ishp in ix_result.geoms:
parse_shapely_ix_result(collection, ishp, shptyps=shptyps)
# if collecting all types
elif shptyps[0] is None:
return collection.append(ix_result)
return collection
[docs]class GridIntersect:
"""Class for intersecting shapely shapes (Point, Linestring, Polygon, or
their Multi variants) with MODFLOW grids. Contains optimized search
routines for structured grids.
Notes
-----
- The STR-tree query is based on the bounding box of the shape or
collection, if the bounding box of the shape covers nearly the entire
grid, the query won't be able to limit the search space much, resulting
in slower performance. Therefore, it can sometimes be faster to
intersect each individual shape in a collection than it is to intersect
with the whole collection at once.
- Building the STR-tree can take a while for large grids. Once built the
intersect routines (for individual shapes) should be pretty fast. It
is possible to perform intersects without building the STR-tree by
setting `rtree=False`.
- The optimized routines for structured grids will often outperform
the shapely routines because of the reduced overhead of building and
parsing the STR-tree. However, for polygons the STR-tree implementation
is often faster than the optimized structured routines, especially
for larger grids.
"""
def __init__(self, mfgrid, method=None, rtree=True):
"""Intersect shapes (Point, Linestring, Polygon) with a modflow grid.
Parameters
----------
mfgrid : flopy modflowgrid
MODFLOW grid as implemented in flopy
method : str, optional
default is None, which determines intersection method based on
the grid type. Options are either 'vertex' which uses shapely
interesection operations or 'structured' which uses optimized
methods that only work for structured grids
rtree : bool, optional
whether to build an STR-Tree, default is True. If False no
STR-tree is built (which saves some time), but intersects will
loop through all model gridcells (which is generally slower).
Only read when `method='vertex'`.
"""
self.mfgrid = mfgrid
if method is None:
# determine method from grid_type
self.method = self.mfgrid.grid_type
else:
# set method
self.method = method
self.rtree = rtree
if self.method == "vertex":
# set method to get gridshapes depending on grid type
self._set_method_get_gridshapes()
# build STR-tree if specified
if self.rtree:
strtree = import_optional_dependency(
"shapely.strtree",
error_message="STRTree requires shapely",
)
self.strtree = strtree.STRtree(self._get_gridshapes())
elif self.method == "structured" and mfgrid.grid_type == "structured":
pass
else:
raise ValueError(
"Method '{0}' not recognized or "
"not supported "
"for grid_type '{1}'!".format(
self.method, self.mfgrid.grid_type
)
)
[docs] def intersect(
self, shp, shapetype=None, sort_by_cellid=True, keepzerolengths=False
):
"""Method to intersect a shape with a model grid.
Parameters
----------
shp : shapely.geometry, geojson object, shapefile.Shape,
or flopy geometry object
shapetype : str, optional
type of shape (i.e. "point", "linestring", "polygon" or
their multi-variants), used by GeoSpatialUtil if shp is
passed as a list of vertices, default is None
sort_by_cellid : bool
sort results by cellid, ensures cell with lowest cellid is
returned for boundary cases when using vertex methods, default
is True
keepzerolengths : bool
boolean method to keep zero length intersections for
linestring intersection, used when shp is of type "linestring"
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
gu = GeoSpatialUtil(shp, shapetype=shapetype)
shp = gu.shapely
if gu.shapetype in ("Point", "MultiPoint"):
if (
self.method == "structured"
and self.mfgrid.grid_type == "structured"
):
rec = self._intersect_point_structured(shp)
else:
rec = self._intersect_point_shapely(shp, sort_by_cellid)
elif gu.shapetype in ("LineString", "MultiLineString"):
if (
self.method == "structured"
and self.mfgrid.grid_type == "structured"
):
rec = self._intersect_linestring_structured(
shp, keepzerolengths
)
else:
rec = self._intersect_linestring_shapely(
shp, keepzerolengths, sort_by_cellid
)
elif gu.shapetype in ("Polygon", "MultiPolygon"):
if (
self.method == "structured"
and self.mfgrid.grid_type == "structured"
):
rec = self._intersect_polygon_structured(shp)
else:
rec = self._intersect_polygon_shapely(shp, sort_by_cellid)
else:
err = f"Shapetype {gu.shapetype} is not supported"
raise TypeError(err)
return rec
def _set_method_get_gridshapes(self):
"""internal method, set self._get_gridshapes to the certain method for
obtaining gridcells."""
# Set method for obtaining grid shapes
if self.mfgrid.grid_type == "structured":
self._get_gridshapes = self._rect_grid_to_shape_generator
elif self.mfgrid.grid_type == "vertex":
self._get_gridshapes = self._vtx_grid_to_shape_generator
elif self.mfgrid.grid_type == "unstructured":
raise NotImplementedError()
def _rect_grid_to_shape_generator(self):
"""internal method, generator yielding shapely polygons for structured
grid cells.
Returns
-------
generator :
generator of shapely Polygons
"""
shapely_geo = import_optional_dependency("shapely.geometry")
for i in range(self.mfgrid.nrow):
for j in range(self.mfgrid.ncol):
xy = self.mfgrid.get_cell_vertices(i, j)
p = shapely_geo.Polygon(xy)
p.name = (i, j)
yield p
def _usg_grid_to_shape_generator(self):
"""internal method, convert unstructred grid to list of shapely
polygons.
Returns
-------
list
list of shapely Polygons
"""
raise NotImplementedError()
def _vtx_grid_to_shape_generator(self):
"""internal method, generator yielding shapely polygons for vertex
grids.
Returns
-------
generator :
generator of shapely Polygons
"""
shapely_geo = import_optional_dependency("shapely.geometry")
# for cell2d rec-arrays
if isinstance(self.mfgrid._cell2d, np.recarray):
for icell in self.mfgrid._cell2d.icell2d:
points = []
icverts = [
f"icvert_{i}"
for i in range(self.mfgrid._cell2d["ncvert"][icell])
]
for iv in self.mfgrid._cell2d[icverts][icell]:
points.append(
(
self.mfgrid._vertices.xv[iv],
self.mfgrid._vertices.yv[iv],
)
)
# close the polygon, if necessary
if points[0] != points[-1]:
points.append(points[0])
p = shapely_geo.Polygon(points)
p.name = icell
yield p
# for cell2d lists
elif isinstance(self.mfgrid._cell2d, list):
for icell in range(len(self.mfgrid._cell2d)):
points = []
for iv in self.mfgrid._cell2d[icell][4:]:
points.append(
(
self.mfgrid._vertices[iv][1],
self.mfgrid._vertices[iv][2],
)
)
# close the polygon, if necessary
if points[0] != points[-1]:
points.append(points[0])
p = shapely_geo.Polygon(points)
p.name = icell
yield p
def _rect_grid_to_shape_list(self):
"""internal method, list of shapely polygons for structured grid cells.
Returns
-------
list :
list of shapely Polygons
"""
return list(self._rect_grid_to_shape_generator())
def _usg_grid_to_shape_list(self):
"""internal method, convert unstructred grid to list of shapely
polygons.
Returns
-------
list
list of shapely Polygons
"""
raise NotImplementedError()
def _vtx_grid_to_shape_list(self):
"""internal method, list of shapely polygons for vertex grids.
Returns
-------
list :
list of shapely Polygons
"""
return list(self._vtx_grid_to_shape_generator())
[docs] def query_grid(self, shp):
"""Perform spatial query on grid with shapely geometry. If no spatial
query is possible returns all grid cells.
Parameters
----------
shp : shapely.geometry
shapely geometry
Returns
-------
list or generator expression
list or generator containing grid cells in query result
"""
if self.rtree:
result = self.strtree.query(shp)
else:
# no spatial query
result = self._get_gridshapes()
return result
[docs] @staticmethod
def filter_query_result(qresult, shp):
"""Filter query result to obtain grid cells that intersect with shape.
Used to (further) reduce query result to cells that definitely
intersect with shape.
Parameters
----------
qresult : iterable
query result, iterable of polygons
shp : shapely.geometry
shapely geometry that is prepared and used to filter
query result
Returns
-------
qfiltered
filter or generator containing polygons that intersect with shape
"""
# prepare shape for efficient batch intersection check
prepared = import_optional_dependency("shapely.prepared")
prepshp = prepared.prep(shp)
# get only gridcells that intersect
qfiltered = filter(prepshp.intersects, qresult)
return qfiltered
[docs] @staticmethod
def sort_gridshapes(shape_iter):
"""Sort query result by node id.
Parameters
----------
shape_iter : iterable
list or iterable of gridcells
Returns
-------
list
sorted list of gridcells
"""
if not isinstance(shape_iter, list):
shapelist = list(shape_iter)
else:
shapelist = shape_iter
def sort_key(o):
return o.name
shapelist.sort(key=sort_key)
return shapelist
def _intersect_point_shapely(self, shp, sort_by_cellid=True):
"""intersect grid with Point or MultiPoint.
Parameters
----------
shp : Point or MultiPoint
shapely Point or MultiPoint to intersect with grid. Note,
it is generally faster to loop over a MultiPoint and intersect
per point than to intersect a MultiPoint directly.
sort_by_cellid : bool, optional
flag whether to sort cells by id, used to ensure node
with lowest id is returned, by default True
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
shapely_geo = import_optional_dependency("shapely.geometry")
prepared = import_optional_dependency("shapely.prepared")
# query grid
qresult = self.query_grid(shp)
# prepare shape for efficient batch intersection check
prepshp = prepared.prep(shp)
# get only gridcells that intersect
qfiltered = filter(prepshp.intersects, qresult)
# sort cells to ensure lowest cell ids are returned
if sort_by_cellid:
qfiltered = self.sort_gridshapes(qfiltered)
isectshp = []
cellids = []
vertices = []
parsed_points = [] # for keeping track of points
# loop over cells returned by filtered spatial query
for r in qfiltered:
name = r.name
# do intersection
intersect = shp.intersection(r)
# parse result per Point
collection = parse_shapely_ix_result(
[], intersect, shptyps=["Point"]
)
# loop over intersection result and store information
cell_verts = []
cell_shps = []
for c in collection:
verts = c.__geo_interface__["coordinates"]
# avoid returning multiple cells for points on boundaries
if verts in parsed_points:
continue
parsed_points.append(verts)
cell_shps.append(c) # collect only new points
cell_verts.append(verts)
# if any new ix found
if len(cell_shps) > 0:
# combine new points in MultiPoint
isectshp.append(
shapely_geo.MultiPoint(cell_shps)
if len(cell_shps) > 1
else cell_shps[0]
)
vertices.append(tuple(cell_verts))
cellids.append(name)
rec = np.recarray(
len(isectshp),
names=["cellids", "vertices", "ixshapes"],
formats=["O", "O", "O"],
)
with ignore_shapely_warnings_for_object_array():
rec.ixshapes = isectshp
rec.vertices = vertices
rec.cellids = cellids
return rec
def _intersect_linestring_shapely(
self, shp, keepzerolengths=False, sort_by_cellid=True
):
"""intersect with LineString or MultiLineString.
Parameters
----------
shp : shapely.geometry.LineString or MultiLineString
LineString to intersect with the grid
keepzerolengths : bool, optional
keep linestrings with length zero, default is False
sort_by_cellid : bool, optional
flag whether to sort cells by id, used to ensure node
with lowest id is returned, by default True
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
# query grid
qresult = self.query_grid(shp)
# filter result further if possible (only strtree and filter methods)
qfiltered = self.filter_query_result(qresult, shp)
# sort cells to ensure lowest cell ids are returned
if sort_by_cellid:
qfiltered = self.sort_gridshapes(qfiltered)
# initialize empty lists for storing results
isectshp = []
cellids = []
vertices = []
lengths = []
# loop over cells returned by filtered spatial query
for r in qfiltered:
name = r.name
# do intersection
intersect = shp.intersection(r)
# parse result
collection = parse_shapely_ix_result(
[], intersect, shptyps=["LineString", "MultiLineString"]
)
# loop over intersection result and store information
for c in collection:
verts = c.__geo_interface__["coordinates"]
# test if linestring was already processed (if on boundary)
if verts in vertices:
continue
# if keep zero don't check length
if not keepzerolengths:
if c.length == 0.0:
continue
isectshp.append(c)
lengths.append(c.length)
vertices.append(verts)
cellids.append(name)
rec = np.recarray(
len(isectshp),
names=["cellids", "vertices", "lengths", "ixshapes"],
formats=["O", "O", "f8", "O"],
)
with ignore_shapely_warnings_for_object_array():
rec.ixshapes = isectshp
rec.vertices = vertices
rec.lengths = lengths
rec.cellids = cellids
return rec
def _intersect_polygon_shapely(self, shp, sort_by_cellid=True):
"""intersect with Polygon or MultiPolygon.
Parameters
----------
shp : shapely.geometry.Polygon or MultiPolygon
shape to intersect with the grid
sort_by_cellid : bool, optional
flag whether to sort cells by id, used to ensure node
with lowest id is returned, by default True
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
shapely_geo = import_optional_dependency("shapely.geometry")
# query grid
qresult = self.query_grid(shp)
# filter result further if possible (only strtree and filter methods)
qfiltered = self.filter_query_result(qresult, shp)
# sort cells to ensure lowest cell ids are returned
if sort_by_cellid:
qfiltered = self.sort_gridshapes(qfiltered)
isectshp = []
cellids = []
vertices = []
areas = []
# loop over cells returned by filtered spatial query
for r in qfiltered:
name = r.name
# do intersection
intersect = shp.intersection(r)
# parse result
collection = parse_shapely_ix_result(
[], intersect, shptyps=["Polygon", "MultiPolygon"]
)
if len(collection) > 1:
collection = [shapely_geo.MultiPolygon(collection)]
# loop over intersection result and store information
for c in collection:
# don't store intersections with 0 area
if c.area == 0.0:
continue
verts = c.__geo_interface__["coordinates"]
isectshp.append(c)
areas.append(c.area)
vertices.append(verts)
cellids.append(name)
rec = np.recarray(
len(isectshp),
names=["cellids", "vertices", "areas", "ixshapes"],
formats=["O", "O", "f8", "O"],
)
with ignore_shapely_warnings_for_object_array():
rec.ixshapes = isectshp
rec.vertices = vertices
rec.areas = areas
rec.cellids = cellids
return rec
[docs] def intersects(self, shp, shapetype=None):
"""Return cellIDs for shapes that intersect with shape.
Parameters
----------
shp : shapely.geometry, geojson geometry, shapefile.shape,
or flopy geometry object
shape to intersect with the grid
shapetype : str, optional
type of shape (i.e. "point", "linestring", "polygon" or
their multi-variants), used by GeoSpatialUtil if shp is
passed as a list of vertices, default is None
Returns
-------
rec : numpy.recarray
a record array containing cell IDs of the gridcells
the shape intersects with
"""
# query grid
shp = GeoSpatialUtil(shp, shapetype=shapetype).shapely
qresult = self.query_grid(shp)
# filter result further if possible (only strtree and filter methods)
qfiltered = self.filter_query_result(qresult, shp)
# get cellids
cids = [cell.name for cell in qfiltered]
# build rec-array
rec = np.recarray(len(cids), names=["cellids"], formats=["O"])
rec.cellids = cids
return rec
def _intersect_point_structured(self, shp):
"""intersection method for intersecting points with structured grids.
Parameters
----------
shp : shapely.geometry.Point or MultiPoint
point shape to intersect with grid
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
shapely_geo = import_optional_dependency("shapely.geometry")
nodelist = []
Xe, Ye = self.mfgrid.xyedges
if isinstance(shp, shapely_geo.Point):
shp = [shp]
elif isinstance(shp, shapely_geo.MultiPoint):
shp = list(shp.geoms)
else:
raise ValueError("expected Point or MultiPoint")
ixshapes = []
for p in shp:
# if grid is rotated or offset transform point to local coords
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
rx, ry = transform(
p.x,
p.y,
self.mfgrid.xoffset,
self.mfgrid.yoffset,
self.mfgrid.angrot_radians,
inverse=True,
)
else:
rx = p.x
ry = p.y
# two dimensional point
jpos = ModflowGridIndices.find_position_in_array(Xe, rx)
ipos = ModflowGridIndices.find_position_in_array(Ye, ry)
if jpos is not None and ipos is not None:
# three dimensional point
if p._ndim == 3:
# find k
kpos = ModflowGridIndices.find_position_in_array(
self.mfgrid.botm[:, ipos, jpos], p.z
)
if kpos is not None:
nodelist.append((kpos, ipos, jpos))
ixshapes.append(p)
else:
nodelist.append((ipos, jpos))
ixshapes.append(p)
# remove duplicates
tempnodes = []
tempshapes = []
for node, ixs in zip(nodelist, ixshapes):
if node not in tempnodes:
tempnodes.append(node)
tempshapes.append(ixs)
else:
tempshapes[-1] = shapely_geo.MultiPoint([tempshapes[-1], ixs])
ixshapes = tempshapes
nodelist = tempnodes
rec = np.recarray(
len(nodelist), names=["cellids", "ixshapes"], formats=["O", "O"]
)
rec.cellids = nodelist
with ignore_shapely_warnings_for_object_array():
rec.ixshapes = ixshapes
return rec
def _intersect_linestring_structured(self, shp, keepzerolengths=False):
"""method for intersecting linestrings with structured grids.
Parameters
----------
shp : shapely.geometry.Linestring or MultiLineString
linestring to intersect with grid
keepzerolengths : bool, optional
if True keep intersection results with length=0, in
other words, grid cells the linestring does not cross
but does touch, by default False
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
shapely_geo = import_optional_dependency("shapely.geometry")
affinity_loc = import_optional_dependency("shapely.affinity")
# get local extent of grid
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
xmin = np.min(self.mfgrid.xyedges[0])
xmax = np.max(self.mfgrid.xyedges[0])
ymin = np.min(self.mfgrid.xyedges[1])
ymax = np.max(self.mfgrid.xyedges[1])
else:
xmin, xmax, ymin, ymax = self.mfgrid.extent
pl = shapely_geo.box(xmin, ymin, xmax, ymax)
# rotate and translate linestring to local coords
if self.mfgrid.xoffset != 0.0 or self.mfgrid.yoffset != 0.0:
shp = affinity_loc.translate(
shp, xoff=-self.mfgrid.xoffset, yoff=-self.mfgrid.yoffset
)
if self.mfgrid.angrot != 0.0:
shp = affinity_loc.rotate(
shp, -self.mfgrid.angrot, origin=(0.0, 0.0)
)
# clip line to mfgrid bbox
lineclip = shp.intersection(pl)
if lineclip.length == 0.0: # linestring does not intersect modelgrid
return np.recarray(
0,
names=["cellids", "vertices", "lengths", "ixshapes"],
formats=["O", "O", "f8", "O"],
)
if lineclip.geom_type == "MultiLineString": # there are multiple lines
nodelist, lengths, vertices = [], [], []
ixshapes = []
for ls in lineclip.geoms:
n, l, v, ixs = self._get_nodes_intersecting_linestring(ls)
nodelist += n
lengths += l
# if necessary, transform coordinates back to real
# world coordinates
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
v_realworld = []
for pt in v:
pt = np.array(pt)
rx, ry = transform(
pt[:, 0],
pt[:, 1],
self.mfgrid.xoffset,
self.mfgrid.yoffset,
self.mfgrid.angrot_radians,
inverse=False,
)
v_realworld.append(list(zip(rx, ry)))
ixs_realworld = []
for ix in ixs:
ix_realworld = affinity_loc.rotate(
ix, self.mfgrid.angrot, origin=(0.0, 0.0)
)
ix_realworld = affinity_loc.translate(
ix_realworld,
self.mfgrid.xoffset,
self.mfgrid.yoffset,
)
ixs_realworld.append(ix_realworld)
else:
v_realworld = v
ixs_realworld = ixs
vertices += v_realworld
ixshapes += ixs_realworld
else: # linestring is fully within grid
(
nodelist,
lengths,
vertices,
ixshapes,
) = self._get_nodes_intersecting_linestring(lineclip)
# if necessary, transform coordinates back to real
# world coordinates
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
v_realworld = []
for pt in vertices:
pt = np.array(pt)
rx, ry = transform(
pt[:, 0],
pt[:, 1],
self.mfgrid.xoffset,
self.mfgrid.yoffset,
self.mfgrid.angrot_radians,
inverse=False,
)
v_realworld.append(list(zip(rx, ry)))
vertices = v_realworld
ix_shapes_realworld = []
for ixs in ixshapes:
ixs = affinity_loc.rotate(
ixs, self.mfgrid.angrot, origin=(0.0, 0.0)
)
ixs = affinity_loc.translate(
ixs, self.mfgrid.xoffset, self.mfgrid.yoffset
)
ix_shapes_realworld.append(ixs)
ixshapes = ix_shapes_realworld
# bundle linestrings in same cell
tempnodes = []
templengths = []
tempverts = []
tempshapes = []
unique_nodes = list(set(nodelist))
if len(unique_nodes) < len(nodelist):
for inode in unique_nodes:
templengths.append(
sum([l for l, i in zip(lengths, nodelist) if i == inode])
)
tempverts.append(
[v for v, i in zip(vertices, nodelist) if i == inode]
)
tempshapes.append(
[ix for ix, i in zip(ixshapes, nodelist) if i == inode]
)
nodelist = unique_nodes
lengths = templengths
vertices = tempverts
ixshapes = tempshapes
# eliminate any nodes that have a zero length
if not keepzerolengths:
tempnodes = []
templengths = []
tempverts = []
tempshapes = []
for i, _ in enumerate(nodelist):
if lengths[i] > 0:
tempnodes.append(nodelist[i])
templengths.append(lengths[i])
tempverts.append(vertices[i])
tempshapes.append(ixshapes[i])
nodelist = tempnodes
lengths = templengths
vertices = tempverts
ixshapes = tempshapes
rec = np.recarray(
len(nodelist),
names=["cellids", "vertices", "lengths", "ixshapes"],
formats=["O", "O", "f8", "O"],
)
rec.vertices = vertices
rec.lengths = lengths
rec.cellids = nodelist
with ignore_shapely_warnings_for_object_array():
rec.ixshapes = ixshapes
return rec
def _get_nodes_intersecting_linestring(self, linestring):
"""helper function, intersect the linestring with the a structured grid
and return a list of node indices and the length of the line in that
node.
Parameters
----------
linestring: shapely.geometry.LineString or MultiLineString
shape to intersect with the grid
Returns
-------
nodelist, lengths, vertices: lists
lists containing node ids, lengths of intersects and the
start and end points of the intersects
"""
shapely_geo = import_optional_dependency("shapely.geometry")
nodelist = []
lengths = []
vertices = []
ixshapes = []
# start at the beginning of the line
x, y = linestring.xy
# linestring already in local coords but
# because intersect_point does transform again
# we transform back to real world here if necessary
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
x0, y0 = transform(
[x[0]],
[y[0]],
self.mfgrid.xoffset,
self.mfgrid.yoffset,
self.mfgrid.angrot_radians,
inverse=False,
)
else:
x0 = [x[0]]
y0 = [y[0]]
(i, j) = self.intersect(shapely_geo.Point(x0[0], y0[0])).cellids[0]
Xe, Ye = self.mfgrid.xyedges
xmin = Xe[j]
xmax = Xe[j + 1]
ymax = Ye[i]
ymin = Ye[i + 1]
pl = shapely_geo.box(xmin, ymin, xmax, ymax)
intersect = linestring.intersection(pl)
# if linestring starts in cell, exits, and re-enters
# a MultiLineString is returned.
ixshapes.append(intersect)
length = intersect.length
lengths.append(length)
if hasattr(intersect, "geoms"):
x, y = [], []
for igeom in intersect.geoms:
x.append(igeom.xy[0])
y.append(igeom.xy[1])
x = np.concatenate(x)
y = np.concatenate(y)
else:
x = intersect.xy[0]
y = intersect.xy[1]
verts = [(ixy[0], ixy[1]) for ixy in zip(x, y)]
vertices.append(verts)
nodelist.append((i, j))
n = 0
while True:
(i, j) = nodelist[n]
(
node,
length,
verts,
ixshape,
) = self._check_adjacent_cells_intersecting_line(
linestring, (i, j), nodelist
)
for inode, ilength, ivert, ix in zip(node, length, verts, ixshape):
if inode is not None:
if ivert not in vertices:
nodelist.append(inode)
lengths.append(ilength)
vertices.append(ivert)
ixshapes.append(ix)
if n == len(nodelist) - 1:
break
n += 1
return nodelist, lengths, vertices, ixshapes
def _check_adjacent_cells_intersecting_line(
self, linestring, i_j, nodelist
):
"""helper method that follows a line through a structured grid.
Parameters
----------
linestring : shapely.geometry.LineString
shape to intersect with the grid
i_j : tuple
tuple containing (nrow, ncol)
nodelist : list of tuples
list of node ids that have already been added
as intersections
Returns
-------
node, length, verts: lists
lists containing nodes, lengths and vertices of
intersections with adjacent cells relative to the
current cell (i, j)
"""
shapely_geo = import_optional_dependency("shapely.geometry")
i, j = i_j
Xe, Ye = self.mfgrid.xyedges
node = []
length = []
verts = []
ixshape = []
# check to left
if j > 0:
ii = i
jj = j - 1
if (ii, jj) not in nodelist:
xmin = Xe[jj]
xmax = Xe[jj + 1]
ymax = Ye[ii]
ymin = Ye[ii + 1]
pl = shapely_geo.box(xmin, ymin, xmax, ymax)
if linestring.intersects(pl):
intersect = linestring.intersection(pl)
ixshape.append(intersect)
length.append(intersect.length)
if hasattr(intersect, "geoms"):
x, y = [], []
for igeom in intersect.geoms:
x.append(igeom.xy[0])
y.append(igeom.xy[1])
x = np.concatenate(x)
y = np.concatenate(y)
else:
x = intersect.xy[0]
y = intersect.xy[1]
verts.append([(ixy[0], ixy[1]) for ixy in zip(x, y)])
node.append((ii, jj))
# check to right
if j < self.mfgrid.ncol - 1:
ii = i
jj = j + 1
if (ii, jj) not in nodelist:
xmin = Xe[jj]
xmax = Xe[jj + 1]
ymax = Ye[ii]
ymin = Ye[ii + 1]
pl = shapely_geo.box(xmin, ymin, xmax, ymax)
if linestring.intersects(pl):
intersect = linestring.intersection(pl)
ixshape.append(intersect)
length.append(intersect.length)
if hasattr(intersect, "geoms"):
x, y = [], []
for igeom in intersect.geoms:
x.append(igeom.xy[0])
y.append(igeom.xy[1])
x = np.concatenate(x)
y = np.concatenate(y)
else:
x = intersect.xy[0]
y = intersect.xy[1]
verts.append([(ixy[0], ixy[1]) for ixy in zip(x, y)])
node.append((ii, jj))
# check to back
if i > 0:
ii = i - 1
jj = j
if (ii, jj) not in nodelist:
xmin = Xe[jj]
xmax = Xe[jj + 1]
ymax = Ye[ii]
ymin = Ye[ii + 1]
pl = shapely_geo.box(xmin, ymin, xmax, ymax)
if linestring.intersects(pl):
intersect = linestring.intersection(pl)
ixshape.append(intersect)
length.append(intersect.length)
if hasattr(intersect, "geoms"):
x, y = [], []
for igeom in intersect.geoms:
x.append(igeom.xy[0])
y.append(igeom.xy[1])
x = np.concatenate(x)
y = np.concatenate(y)
else:
x = intersect.xy[0]
y = intersect.xy[1]
verts.append([(ixy[0], ixy[1]) for ixy in zip(x, y)])
node.append((ii, jj))
# check to front
if i < self.mfgrid.nrow - 1:
ii = i + 1
jj = j
if (ii, jj) not in nodelist:
xmin = Xe[jj]
xmax = Xe[jj + 1]
ymax = Ye[ii]
ymin = Ye[ii + 1]
pl = shapely_geo.box(xmin, ymin, xmax, ymax)
if linestring.intersects(pl):
intersect = linestring.intersection(pl)
ixshape.append(intersect)
length.append(intersect.length)
if hasattr(intersect, "geoms"):
x, y = [], []
for igeom in intersect.geoms:
x.append(igeom.xy[0])
y.append(igeom.xy[1])
x = np.concatenate(x)
y = np.concatenate(y)
else:
x = intersect.xy[0]
y = intersect.xy[1]
verts.append([(ixy[0], ixy[1]) for ixy in zip(x, y)])
node.append((ii, jj))
return node, length, verts, ixshape
def _intersect_rectangle_structured(self, rectangle):
"""intersect a rectangle with a structured grid to retrieve node ids of
intersecting grid cells.
Note: only works in local coordinates (i.e. non-rotated grid
with origin at (0, 0))
Parameters
----------
rectangle : list of tuples
list of lower-left coordinate and upper-right
coordinate: [(xmin, ymin), (xmax, ymax)]
Returns
-------
nodelist: list of tuples
list of tuples containing node ids with which
the rectangle intersects
"""
shapely_geo = import_optional_dependency("shapely.geometry")
nodelist = []
# return if rectangle does not contain any cells
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
minx = np.min(self.mfgrid.xyedges[0])
maxx = np.max(self.mfgrid.xyedges[0])
miny = np.min(self.mfgrid.xyedges[1])
maxy = np.max(self.mfgrid.xyedges[1])
local_extent = [minx, maxx, miny, maxy]
else:
local_extent = self.mfgrid.extent
xmin, xmax, ymin, ymax = local_extent
bgrid = shapely_geo.box(xmin, ymin, xmax, ymax)
(rxmin, rymin), (rxmax, rymax) = rectangle
b = shapely_geo.box(rxmin, rymin, rxmax, rymax)
if not b.intersects(bgrid):
# return with nodelist as an empty list
return []
Xe, Ye = self.mfgrid.xyedges
jmin = ModflowGridIndices.find_position_in_array(Xe, xmin)
if jmin is None:
if xmin <= Xe[0]:
jmin = 0
elif xmin >= Xe[-1]:
jmin = self.mfgrid.ncol - 1
jmax = ModflowGridIndices.find_position_in_array(Xe, xmax)
if jmax is None:
if xmax <= Xe[0]:
jmax = 0
elif xmax >= Xe[-1]:
jmax = self.mfgrid.ncol - 1
imin = ModflowGridIndices.find_position_in_array(Ye, ymax)
if imin is None:
if ymax >= Ye[0]:
imin = 0
elif ymax <= Ye[-1]:
imin = self.mfgrid.nrow - 1
imax = ModflowGridIndices.find_position_in_array(Ye, ymin)
if imax is None:
if ymin >= Ye[0]:
imax = 0
elif ymin <= Ye[-1]:
imax = self.mfgrid.nrow - 1
for i in range(imin, imax + 1):
for j in range(jmin, jmax + 1):
nodelist.append((i, j))
return nodelist
def _intersect_polygon_structured(self, shp):
"""intersect polygon with a structured grid. Uses bounding box of the
Polygon to limit search space.
Notes
-----
If performance is slow, try setting the method to 'vertex'
in the GridIntersect object. For polygons this is often
faster.
Parameters
----------
shp : shapely.geometry.Polygon
polygon to intersect with the grid
Returns
-------
numpy.recarray
a record array containing information about the intersection
"""
shapely_geo = import_optional_dependency("shapely.geometry")
affinity_loc = import_optional_dependency("shapely.affinity")
# initialize the result lists
nodelist = []
areas = []
vertices = []
ixshapes = []
# transform polygon to local grid coordinates
if self.mfgrid.xoffset != 0.0 or self.mfgrid.yoffset != 0.0:
shp = affinity_loc.translate(
shp, xoff=-self.mfgrid.xoffset, yoff=-self.mfgrid.yoffset
)
if self.mfgrid.angrot != 0.0:
shp = affinity_loc.rotate(
shp, -self.mfgrid.angrot, origin=(0.0, 0.0)
)
# use the bounds of the polygon to restrict the cell search
minx, miny, maxx, maxy = shp.bounds
rectangle = ((minx, miny), (maxx, maxy))
nodes = self._intersect_rectangle_structured(rectangle)
for (i, j) in nodes:
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
cell_coords = [
(self.mfgrid.xyedges[0][j], self.mfgrid.xyedges[1][i]),
(self.mfgrid.xyedges[0][j + 1], self.mfgrid.xyedges[1][i]),
(
self.mfgrid.xyedges[0][j + 1],
self.mfgrid.xyedges[1][i + 1],
),
(self.mfgrid.xyedges[0][j], self.mfgrid.xyedges[1][i + 1]),
]
else:
cell_coords = self.mfgrid.get_cell_vertices(i, j)
node_polygon = shapely_geo.Polygon(cell_coords)
if shp.intersects(node_polygon):
intersect = shp.intersection(node_polygon)
if intersect.area > 0.0:
nodelist.append((i, j))
areas.append(intersect.area)
# if necessary, transform coordinates back to real
# world coordinates
if (
self.mfgrid.angrot != 0.0
or self.mfgrid.xoffset != 0.0
or self.mfgrid.yoffset != 0.0
):
v_realworld = []
if intersect.geom_type.startswith("Multi"):
for ipoly in intersect:
v_realworld += (
self._transform_geo_interface_polygon(
ipoly
)
)
else:
v_realworld += (
self._transform_geo_interface_polygon(
intersect
)
)
intersect_realworld = affinity_loc.rotate(
intersect, self.mfgrid.angrot, origin=(0.0, 0.0)
)
intersect_realworld = affinity_loc.translate(
intersect_realworld,
self.mfgrid.xoffset,
self.mfgrid.yoffset,
)
else:
v_realworld = intersect.__geo_interface__[
"coordinates"
]
intersect_realworld = intersect
ixshapes.append(intersect_realworld)
vertices.append(v_realworld)
rec = np.recarray(
len(nodelist),
names=["cellids", "vertices", "areas", "ixshapes"],
formats=["O", "O", "f8", "O"],
)
rec.vertices = vertices
rec.areas = areas
rec.cellids = nodelist
with ignore_shapely_warnings_for_object_array():
rec.ixshapes = ixshapes
return rec
def _transform_geo_interface_polygon(self, polygon):
"""Internal method, helper function to transform geometry
__geo_interface__.
Used for translating intersection result coordinates back into
real-world coordinates.
Parameters
----------
polygon : shapely.geometry.Polygon
polygon to transform coordinates for
Returns
-------
geom_list : list
list containing transformed coordinates in same structure as
the original __geo_interface__.
"""
if polygon.geom_type.startswith("Multi"):
raise TypeError("Does not support Multi geometries!")
geom_list = []
for coords in polygon.__geo_interface__["coordinates"]:
geoms = []
try:
# test depth of list/tuple
_ = coords[0][0][0]
if len(coords) == 2:
shell, holes = coords
else:
raise ValueError("Cannot parse __geo_interface__")
except TypeError:
shell = coords
holes = None
except Exception as e:
raise e
# transform shell coordinates
shell_pts = []
for pt in shell:
rx, ry = transform(
[pt[0]],
[pt[1]],
self.mfgrid.xoffset,
self.mfgrid.yoffset,
self.mfgrid.angrot_radians,
inverse=False,
)
shell_pts.append((rx, ry))
geoms.append(shell_pts)
# transform holes coordinates if necessary
if holes:
holes_pts = []
for pt in holes:
rx, ry = transform(
[pt[0]],
[pt[1]],
self.mfgrid.xoffset,
self.mfgrid.yoffset,
self.mfgrid.angrot_radians,
inverse=False,
)
# append (shells, holes) to transformed coordinates list
geom_list.append(tuple(geoms))
return geom_list
[docs] @staticmethod
def plot_polygon(rec, ax=None, **kwargs):
"""method to plot the polygon intersection results from the resulting
numpy.recarray.
Note: only works when recarray has 'intersects' column!
Parameters
----------
rec : numpy.recarray
record array containing intersection results
(the resulting shapes)
ax : matplotlib.pyplot.axes, optional
axes to plot onto, if not provided, creates a new figure
**kwargs:
passed to the plot function
Returns
-------
ax: matplotlib.pyplot.axes
returns the axes handle
"""
import matplotlib.pyplot as plt
import_optional_dependency("descartes")
from descartes import PolygonPatch
if ax is None:
_, ax = plt.subplots()
for i, ishp in enumerate(rec.ixshapes):
if "facecolor" in kwargs:
fc = kwargs.pop("facecolor")
else:
fc = f"C{i % 10}"
ppi = PolygonPatch(ishp, facecolor=fc, **kwargs)
ax.add_patch(ppi)
return ax
[docs] @staticmethod
def plot_linestring(rec, ax=None, cmap=None, **kwargs):
"""method to plot the linestring intersection results from the
resulting numpy.recarray.
Note: only works when recarray has 'intersects' column!
Parameters
----------
rec : numpy.recarray
record array containing intersection results
(the resulting shapes)
ax : matplotlib.pyplot.axes, optional
axes to plot onto, if not provided, creates a new figure
cmap : str
matplotlib colormap
**kwargs:
passed to the plot function
Returns
-------
ax: matplotlib.pyplot.axes
returns the axes handle
"""
import matplotlib.pyplot as plt
if ax is None:
_, ax = plt.subplots()
specified_color = True
if "c" in kwargs:
c = kwargs.pop("c")
elif "color" in kwargs:
c = kwargs.pop("color")
else:
specified_color = False
if cmap is not None:
colormap = plt.get_cmap(cmap)
colors = colormap(np.linspace(0, 1, rec.shape[0]))
for i, ishp in enumerate(rec.ixshapes):
if not specified_color:
if cmap is None:
c = f"C{i % 10}"
else:
c = colors[i]
if ishp.type == "MultiLineString":
for part in ishp:
ax.plot(part.xy[0], part.xy[1], ls="-", c=c, **kwargs)
else:
ax.plot(ishp.xy[0], ishp.xy[1], ls="-", c=c, **kwargs)
return ax
[docs] @staticmethod
def plot_point(rec, ax=None, **kwargs):
"""method to plot the point intersection results from the resulting
numpy.recarray.
Note: only works when recarray has 'intersects' column!
Parameters
----------
rec : numpy.recarray
record array containing intersection results
ax : matplotlib.pyplot.axes, optional
axes to plot onto, if not provided, creates a new figure
**kwargs:
passed to the scatter function
Returns
-------
ax: matplotlib.pyplot.axes
returns the axes handle
"""
import matplotlib.pyplot as plt
shapely_geo = import_optional_dependency("shapely.geometry")
if ax is None:
_, ax = plt.subplots()
x, y = [], []
geo_coll = shapely_geo.GeometryCollection(list(rec.ixshapes))
collection = parse_shapely_ix_result([], geo_coll, ["Point"])
for c in collection:
x.append(c.x)
y.append(c.y)
ax.scatter(x, y, **kwargs)
return ax
[docs]class ModflowGridIndices:
"""Collection of methods that can be used to find cell indices for a
structured, but irregularly spaced MODFLOW grid."""
[docs] @staticmethod
def find_position_in_array(arr, x):
"""If arr has x positions for the left edge of a cell, then return the
cell index containing x.
Parameters
----------
arr : A one dimensional array (such as Xe) that contains
coordinates for the left cell edge.
x : float
The x position to find in arr.
"""
jpos = None
if x == arr[-1]:
return len(arr) - 2
if x < min(arr[0], arr[-1]):
return None
if x > max(arr[0], arr[-1]):
return None
# go through each position
for j in range(len(arr) - 1):
xl = arr[j]
xr = arr[j + 1]
frac = (x - xl) / (xr - xl)
if 0.0 <= frac <= 1.0:
# if min(xl, xr) <= x < max(xl, xr):
jpos = j
return jpos
return jpos
[docs] @staticmethod
def kij_from_nodenumber(nodenumber, nlay, nrow, ncol):
"""Convert the modflow node number to a zero-based layer, row and
column format. Return (k0, i0, j0).
Parameters
----------
nodenumber: int
The cell nodenumber, ranging from 1 to number of
nodes.
nlay: int
The number of layers.
nrow: int
The number of rows.
ncol: int
The number of columns.
"""
if nodenumber > nlay * nrow * ncol:
raise Exception("Error in function kij_from_nodenumber...")
n = nodenumber - 1
k = int(n / nrow / ncol)
i = int((n - k * nrow * ncol) / ncol)
j = n - k * nrow * ncol - i * ncol
return (k, i, j)
[docs] @staticmethod
def nodenumber_from_kij(k, i, j, nrow, ncol):
"""Calculate the nodenumber using the zero-based layer, row, and column
values. The first node has a value of 1.
Parameters
----------
k : int
The model layer number as a zero-based value.
i : int
The model row number as a zero-based value.
j : int
The model column number as a zero-based value.
nrow : int
The number of model rows.
ncol : int
The number of model columns.
"""
return k * nrow * ncol + i * ncol + j + 1
[docs] @staticmethod
def nn0_from_kij(k, i, j, nrow, ncol):
"""Calculate the zero-based nodenumber using the zero-based layer, row,
and column values. The first node has a value of 0.
Parameters
----------
k : int
The model layer number as a zero-based value.
i : int
The model row number as a zero-based value.
j : int
The model column number as a zero-based value.
nrow : int
The number of model rows.
ncol : int
The number of model columns.
"""
return k * nrow * ncol + i * ncol + j
[docs] @staticmethod
def kij_from_nn0(n, nlay, nrow, ncol):
"""Convert the node number to a zero-based layer, row and column
format. Return (k0, i0, j0).
Parameters
----------
nodenumber : int
The cell nodenumber, ranging from 0 to number of
nodes - 1.
nlay : int
The number of layers.
nrow : int
The number of rows.
ncol : int
The number of columns.
"""
if n > nlay * nrow * ncol:
raise Exception("Error in function kij_from_nodenumber...")
k = int(n / nrow / ncol)
i = int((n - k * nrow * ncol) / ncol)
j = n - k * nrow * ncol - i * ncol
return (k, i, j)