def haversine_distance(p1_lon, p1_lat, p2_lon, p2_lat):
""" Compute the haversine distances between an arbitrary list of lon/lat
pairs
Parameters
----------
p1_lon
longitude of first set of coords
p1_lat
latitude of first set of coords
p2_lon
longitude of second set of coords
p2_lat
latitude of second set of coords
Returns
-------
result : cudf.Series
The distance between all pairs of lon/lat coordinates
"""
p1_lon, p1_lat, p2_lon, p2_lat = normalize_point_columns(
as_column(p1_lon),
as_column(p1_lat),
as_column(p2_lon),
as_column(p2_lat),
)
return cpp_haversine_distance(p1_lon, p1_lat, p2_lon, p2_lat)
def polygon_bounding_boxes(poly_offsets, ring_offsets, xs, ys):
"""Compute the minimum bounding-boxes for a set of polygons.
Parameters
----------
poly_offsets
Begin indices of the first ring in each polygon (i.e. prefix-sum)
ring_offsets
Begin indices of the first point in each ring (i.e. prefix-sum)
xs
Polygon point x-coordinates
ys
Polygon point y-coordinates
Returns
-------
result : cudf.DataFrame
minimum bounding boxes for each polygon
x_min : cudf.Series
the minimum x-coordinate of each bounding box
y_min : cudf.Series
the minimum y-coordinate of each bounding box
x_max : cudf.Series
the maximum x-coordinate of each bounding box
y_max : cudf.Series
the maximum y-coordinate of each bounding box
"""
poly_offsets = as_column(poly_offsets, dtype="int32")
ring_offsets = as_column(ring_offsets, dtype="int32")
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
return DataFrame._from_table(
cpp_polygon_bounding_boxes(poly_offsets, ring_offsets, xs, ys)
)
def polyline_bounding_boxes(poly_offsets, xs, ys, expansion_radius):
"""Compute the minimum bounding-boxes for a set of polylines.
Parameters
----------
poly_offsets
Begin indices of the first ring in each polyline (i.e. prefix-sum)
xs
Polyline point x-coordinates
ys
Polyline point y-coordinates
expansion_radius
radius of each polyline point
Returns
-------
result : cudf.DataFrame
minimum bounding boxes for each polyline
x_min : cudf.Series
the minimum x-coordinate of each bounding box
y_min : cudf.Series
the minimum y-coordinate of each bounding box
x_max : cudf.Series
the maximum x-coordinate of each bounding box
y_max : cudf.Series
the maximum y-coordinate of each bounding box
"""
poly_offsets = as_column(poly_offsets, dtype="int32")
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
return DataFrame._from_data(
*cpp_polyline_bounding_boxes(poly_offsets, xs, ys, expansion_radius)
)
def trajectory_distances_and_speeds(
num_trajectories, object_ids, xs, ys, timestamps
):
"""
Compute the distance traveled and speed of sets of trajectories
Parameters
----------
num_trajectories
number of trajectories (unique object ids)
object_ids
column of object (e.g., vehicle) ids
xs
column of x-coordinates (in kilometers)
ys
column of y-coordinates (in kilometers)
timestamps
column of timestamps in any resolution
Returns
-------
result : cudf.DataFrame
meters : cudf.Series
trajectory distance (in kilometers)
speed : cudf.Series
trajectory speed (in meters/second)
Examples
--------
Compute the distances and speeds of derived trajectories
>>> objects, traj_offsets = cuspatial.derive_trajectories(...)
>>> dists_and_speeds = cuspatial.trajectory_distances_and_speeds(
len(traj_offsets)
objects['object_id'],
objects['x'],
objects['y'],
objects['timestamp']
)
>>> print(dists_and_speeds)
distance speed
trajectory_id
0 1000.0 100000.000000
1 1000.0 111111.109375
"""
object_ids = as_column(object_ids, dtype=np.int32)
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
timestamps = normalize_timestamp_column(as_column(timestamps))
df = DataFrame._from_table(
cpp_trajectory_distances_and_speeds(
num_trajectories, object_ids, xs, ys, timestamps
)
)
df.index.name = "trajectory_id"
return df
def trajectory_bounding_boxes(num_trajectories, object_ids, xs, ys):
""" Compute the bounding boxes of sets of trajectories.
Parameters
----------
num_trajectories
number of trajectories (unique object ids)
object_ids
column of object (e.g., vehicle) ids
xs
column of x-coordinates (in kilometers)
ys
column of y-coordinates (in kilometers)
Returns
-------
result : cudf.DataFrame
minimum bounding boxes (in kilometers) for each trajectory
x_min : cudf.Series
the minimum x-coordinate of each bounding box
y_min : cudf.Series
the minimum y-coordinate of each bounding box
x_max : cudf.Series
the maximum x-coordinate of each bounding box
y_max : cudf.Series
the maximum y-coordinate of each bounding box
Examples
--------
Compute the minimum bounding boxes of derived trajectories
>>> objects, traj_offsets = trajectory.derive_trajectories(
[0, 0, 1, 1], # object_id
[0, 1, 2, 3], # x
[0, 0, 1, 1], # y
[0, 10, 0, 10] # timestamp
)
>>> traj_bounding_boxes = cuspatial.trajectory_bounding_boxes(
len(traj_offsets),
objects['object_id'],
objects['x'],
objects['y']
)
>>> print(traj_bounding_boxes)
x_min y_min x_max y_max
0 0.0 0.0 2.0 2.0
1 1.0 1.0 3.0 3.0
"""
object_ids = as_column(object_ids, dtype=np.int32)
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
return DataFrame._from_table(
cpp_trajectory_bounding_boxes(num_trajectories, object_ids, xs, ys)
)
def derive_trajectories(object_ids, xs, ys, timestamps):
"""
Derive trajectories from object ids, points, and timestamps.
Parameters
----------
object_ids
column of object (e.g., vehicle) ids
xs
column of x-coordinates (in kilometers)
ys
column of y-coordinates (in kilometers)
timestamps
column of timestamps in any resolution
Returns
-------
result : tuple (objects, traj_offsets)
objects : cudf.DataFrame
object_ids, xs, ys, and timestamps sorted by
``(object_id, timestamp)``, used by ``trajectory_bounding_boxes``
and ``trajectory_distances_and_speeds``
traj_offsets : cudf.Series
offsets of discovered trajectories
Examples
--------
Compute sorted objects and discovered trajectories
>>> objects, traj_offsets = cuspatial.derive_trajectories(
[0, 1, 2, 3], # object_id
[0, 0, 1, 1], # x
[0, 0, 1, 1], # y
[0, 10, 0, 10] # timestamp
)
>>> print(traj_offsets)
0 0
1 2
>>> print(objects)
object_id x y timestamp
0 0 1 0 0
1 0 0 0 10
2 1 3 1 0
3 1 2 1 10
"""
object_ids = as_column(object_ids, dtype=np.int32)
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
timestamps = normalize_timestamp_column(as_column(timestamps))
objects, traj_offsets = cpp_derive_trajectories(
object_ids, xs, ys, timestamps
)
return DataFrame._from_table(objects), Series(data=traj_offsets)
def points_in_spatial_window(min_x, max_x, min_y, max_y, xs, ys):
""" Return only the subset of coordinates that fall within a
rectangular window.
A point `(x, y)` is inside the query window if and only if
``min_x < x < max_x AND min_y < y < max_y``
The window is specified by minimum and maximum x and y
coordinates.
Parameters
----------
min_x
lower x-coordinate of the query window
max_x
upper x-coordinate of the query window
min_y
lower y-coordinate of the query window
max_y
upper y-coordinate of the query window
xs
column of x-coordinates that may fall within the window
ys
column of y-coordinates that may fall within the window
Returns
-------
result : cudf.DataFrame
subset of `(x, y)` pairs above that fall within the window
Notes
-----
* Swaps ``min_x`` and ``max_x`` if ``min_x > max_x``
* Swaps ``min_y`` and ``max_y`` if ``min_y > max_y``
"""
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
return DataFrame._from_data(
*spatial_window.points_in_spatial_window(
min_x, max_x, min_y, max_y, xs, ys
)
)
def directed_hausdorff_distance(xs, ys, space_offsets):
"""Compute the directed Hausdorff distances between all pairs of
spaces.
Parameters
----------
xs
column of x-coordinates
ys
column of y-coordinates
space_offsets
beginning index of each space, plus the last space's end offset.
Returns
-------
result : cudf.DataFrame
The pairwise directed distance matrix with one row and one
column per input space; the value at row i, column j represents the
hausdorff distance from space i to space j.
Examples
--------
The directed Hausdorff distance from one space to another is the greatest
of all the distances between any point in the first space to the closest
point in the second.
`Wikipedia <https://en.wikipedia.org/wiki/Hausdorff_distance>`_
Consider a pair of lines on a grid::
:
x
-----xyy---
:
:
x\\ :sub:`0` = (0, 0), x\\ :sub:`1` = (0, 1)
y\\ :sub:`0` = (1, 0), y\\ :sub:`1` = (2, 0)
x\\ :sub:`0` is the closest point in ``x`` to ``y``. The distance from
x\\ :sub:`0` to the farthest point in ``y`` is 2.
y\\ :sub:`0` is the closest point in ``y`` to ``x``. The distance from
y\\ :sub:`0` to the farthest point in ``x`` is 1.414.
Compute the directed hausdorff distances between a set of spaces
>>> result = cuspatial.directed_hausdorff_distance(
[0, 1, 0, 0], # xs
[0, 0, 1, 2], # ys
[0, 2, 4], # space_offsets
)
>>> print(result)
0 1
0 0.0 1.414214
1 2.0 0.000000
"""
num_spaces = len(space_offsets)
if num_spaces == 0:
return DataFrame()
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
result = cpp_directed_hausdorff_distance(
xs, ys, as_column(space_offsets, dtype="uint32"),
)
result = result.data_array_view
result = result.reshape(num_spaces, num_spaces)
return DataFrame(result)
def point_in_polygon(
test_points_x,
test_points_y,
poly_offsets,
poly_ring_offsets,
poly_points_x,
poly_points_y,
):
""" Compute from a set of points and a set of polygons which points fall
within which polygons. Note that `polygons_(x,y)` must be specified as
closed polygons: the first and last coordinate of each polygon must be
the same.
Parameters
----------
test_points_x
x-coordinate of test points
test_points_y
y-coordinate of test points
poly_offsets
beginning index of the first ring in each polygon
poly_ring_offsets
beginning index of the first point in each ring
poly_points_x
x closed-coordinate of polygon points
poly_points_y
y closed-coordinate of polygon points
Examples
--------
Test whether 3 points fall within either of two polygons
>>> result = cuspatial.point_in_polygon(
[0, -8, 6.0], # test_points_x
[0, -8, 6.0], # test_points_y
cudf.Series([0, 1], index=['nyc', 'hudson river']), # poly_offsets
[0, 3], # ring_offsets
[-10, 5, 5, -10, 0, 10, 10, 0], # poly_points_x
[-10, -10, 5, 5, 0, 0, 10, 10], # poly_points_y
)
# The result of point_in_polygon is a DataFrame of Boolean
# values indicating whether each point (rows) falls within
# each polygon (columns).
>>> print(result)
nyc hudson river
0 True True
1 True False
2 False True
# Point 0: (0, 0) falls in both polygons
# Point 1: (-8, -8) falls in the first polygon
# Point 2: (6.0, 6.0) falls in the second polygon
note
input Series x and y will not be index aligned, but computed as
sequential arrays.
Returns
-------
result : cudf.DataFrame
A DataFrame of boolean values indicating whether each point falls
within each polygon.
"""
if len(poly_offsets) == 0:
return DataFrame()
(
test_points_x,
test_points_y,
poly_points_x,
poly_points_y,
) = normalize_point_columns(
as_column(test_points_x),
as_column(test_points_y),
as_column(poly_points_x),
as_column(poly_points_y),
)
result = cpp_point_in_polygon(
test_points_x,
test_points_y,
as_column(poly_offsets, dtype="int32"),
as_column(poly_ring_offsets, dtype="int32"),
poly_points_x,
poly_points_y,
)
result = gis_utils.pip_bitmap_column_to_binary_array(
polygon_bitmap_column=result, width=len(poly_offsets)
)
result = DataFrame(result)
result = DataFrame._from_data(
{name: col.astype("bool") for name, col in result._data.items()}
)
result.columns = [x for x in list(reversed(poly_offsets.index))]
result = result[list(reversed(result.columns))]
return result
def quadtree_point_in_polygon(
poly_quad_pairs,
quadtree,
point_indices,
points_x,
points_y,
poly_offsets,
ring_offsets,
poly_points_x,
poly_points_y,
):
""" Test whether the specified points are inside any of the specified
polygons.
Uses the table of (polygon, quadrant) pairs returned by
``cuspatial.join_quadtree_and_bounding_boxes`` to ensure only the points
in the same quadrant as each polygon are tested for intersection.
This pre-filtering can dramatically reduce number of points tested per
polygon, enabling faster intersection-testing at the expense of extra
memory allocated to store the quadtree and sorted point_indices.
Parameters
----------
poly_quad_pairs: cudf.DataFrame
Table of (polygon, quadrant) index pairs returned by
``cuspatial.join_quadtree_and_bounding_boxes``.
quadtree : cudf.DataFrame
A complete quadtree for a given area-of-interest bounding box.
point_indices : cudf.Series
Sorted point indices returned by ``cuspatial.quadtree_on_points``
points_x : cudf.Series
x-coordinates of points used to construct the quadtree.
points_y : cudf.Series
y-coordinates of points used to construct the quadtree.
poly_offsets : cudf.Series
Begin index of the first ring in each polygon.
ring_offsets : cudf.Series
Begin index of the first point in each ring.
poly_points_x : cudf.Series
Polygon point x-coodinates.
poly_points_y : cudf.Series
Polygon point y-coodinates.
Returns
-------
result : cudf.DataFrame
Indices for each intersecting point and polygon pair.
point_offset : cudf.Series
Indices of each point that intersects with a polygon.
polygon_offset : cudf.Series
Indices of each polygon with which a point intersected.
"""
(
points_x,
points_y,
poly_points_x,
poly_points_y,
) = normalize_point_columns(
as_column(points_x),
as_column(points_y),
as_column(poly_points_x),
as_column(poly_points_y),
)
return DataFrame._from_table(
spatial_join.quadtree_point_in_polygon(
poly_quad_pairs,
quadtree,
as_column(point_indices, dtype="uint32"),
points_x,
points_y,
as_column(poly_offsets, dtype="uint32"),
as_column(ring_offsets, dtype="uint32"),
poly_points_x,
poly_points_y,
))
def quadtree_point_to_nearest_polyline(
poly_quad_pairs,
quadtree,
point_indices,
points_x,
points_y,
poly_offsets,
poly_points_x,
poly_points_y,
):
""" Finds the nearest polyline to each point in a quadrant, and computes
the distances between each point and polyline.
Uses the table of (polyline, quadrant) pairs returned by
``cuspatial.join_quadtree_and_bounding_boxes`` to ensure distances are
computed only for the points in the same quadrant as each polyline.
Parameters
----------
poly_quad_pairs: cudf.DataFrame
Table of (polyline, quadrant) index pairs returned by
``cuspatial.join_quadtree_and_bounding_boxes``.
quadtree : cudf.DataFrame
A complete quadtree for a given area-of-interest bounding box.
point_indices : cudf.Series
Sorted point indices returned by ``cuspatial.quadtree_on_points``
points_x : cudf.Series
x-coordinates of points used to construct the quadtree.
points_y : cudf.Series
y-coordinates of points used to construct the quadtree.
poly_offsets : cudf.Series
Begin index of the first point in each polyline.
poly_points_x : cudf.Series
Polyline point x-coodinates.
poly_points_y : cudf.Series
Polyline point y-coodinates.
Returns
-------
result : cudf.DataFrame
Indices for each point and its nearest polyline, and the distance
between the two.
point_offset : cudf.Series
Indices of each point that intersects with a polyline.
polyline_offset : cudf.Series
Indices of each polyline with which a point intersected.
distance : cudf.Series
Distances between each point and its nearest polyline.
"""
(
points_x,
points_y,
poly_points_x,
poly_points_y,
) = normalize_point_columns(
as_column(points_x),
as_column(points_y),
as_column(poly_points_x),
as_column(poly_points_y),
)
return DataFrame._from_table(
spatial_join.quadtree_point_to_nearest_polyline(
poly_quad_pairs,
quadtree,
as_column(point_indices, dtype="uint32"),
points_x,
points_y,
as_column(poly_offsets, dtype="uint32"),
poly_points_x,
poly_points_y,
))
def quadtree_on_points(xs, ys, x_min, x_max, y_min, y_max, scale, max_depth,
min_size):
""" Construct a quadtree from a set of points for a given area-of-interest
bounding box.
Parameters
----------
xs
Column of x-coordinates for each point
ys
Column of y-coordinates for each point
x_min
The lower-left x-coordinate of the area of interest bounding box
x_max
The upper-right x-coordinate of the area of interest bounding box
y_min
The lower-left y-coordinate of the area of interest bounding box
y_max
The upper-right y-coordinate of the area of interest bounding box
scale
Scale to apply to each point's distance from ``(x_min, y_min)``
max_depth
Maximum quadtree depth
min_size
Minimum number of points for a non-leaf quadtree node
Returns
-------
result : tuple (cudf.Series, cudf.DataFrame)
keys_to_points : cudf.Series(dtype=np.int32)
A column of sorted keys to original point indices
quadtree : cudf.DataFrame
A complete quadtree for the set of input points
key : cudf.Series(dtype=np.int32)
An int32 column of quadrant keys
level : cudf.Series(dtype=np.int8)
An int8 column of quadtree levels
is_quad : cudf.Series(dtype=np.bool_)
A boolean column indicating whether the node is a quad or leaf
length : cudf.Series(dtype=np.int32)
If this is a non-leaf quadrant (i.e. ``is_quad`` is ``True``),
this column's value is the number of children in the non-leaf
quadrant.
Otherwise this column's value is the number of points
contained in the leaf quadrant.
offset : cudf.Series(dtype=np.int32)
If this is a non-leaf quadrant (i.e. ``is_quad`` is ``True``),
this column's value is the position of the non-leaf quadrant's
first child.
Otherwise this column's value is the position of the leaf
quadrant's first point.
Notes
-----
* Swaps ``min_x`` and ``max_x`` if ``min_x > max_x``
* Swaps ``min_y`` and ``max_y`` if ``min_y > max_y``
Examples
--------
An example of selecting the ``min_size`` and ``scale`` based on input::
>>> np.random.seed(0)
>>> points = cudf.DataFrame({
"x": cudf.Series(np.random.normal(size=120)) * 500,
"y": cudf.Series(np.random.normal(size=120)) * 500,
})
>>> max_depth = 3
>>> min_size = 50
>>> min_x, min_y, max_x, max_y = (points["x"].min(),
points["y"].min(),
points["x"].max(),
points["y"].max())
>>> scale = max(max_x - min_x, max_y - min_y) // (1 << max_depth)
>>> print(
"min_size: " + str(min_size) + "\\n"
"num_points: " + str(len(points)) + "\\n"
"min_x: " + str(min_x) + "\\n"
"max_x: " + str(max_x) + "\\n"
"min_y: " + str(min_y) + "\\n"
"max_y: " + str(max_y) + "\\n"
"scale: " + str(scale) + "\\n"
)
min_size: 50
num_points: 120
min_x: -1577.4949079170394
max_x: 1435.877311993804
min_y: -1412.7015761122134
max_y: 1492.572387431971
scale: 301.0
>>> key_to_point, quadtree = cuspatial.quadtree_on_points(
points["x"],
points["y"],
min_x,
max_x,
min_y,
max_y,
scale, max_depth, min_size
)
>>> print(quadtree)
key level is_quad length offset
0 0 0 False 15 0
1 1 0 False 27 15
2 2 0 False 12 42
3 3 0 True 4 8
4 4 0 False 5 106
5 6 0 False 6 111
6 9 0 False 2 117
7 12 0 False 1 119
8 12 1 False 22 54
9 13 1 False 18 76
10 14 1 False 9 94
11 15 1 False 3 103
>>> print(key_to_point)
0 63
1 20
2 33
3 66
4 19
...
115 113
116 3
117 78
118 98
119 24
Length: 120, dtype: int32
"""
xs, ys = normalize_point_columns(as_column(xs), as_column(ys))
x_min, x_max, y_min, y_max = (
min(x_min, x_max),
max(x_min, x_max),
min(y_min, y_max),
max(y_min, y_max),
)
min_scale = max(x_max - x_min, y_max - y_min) / ((1 << max_depth) + 2)
if scale < min_scale:
warnings.warn("scale {} is less than required minimum ".format(scale) +
"scale {}. Clamping to minimum scale".format(min_scale))
key_to_point, quadtree = cpp_quadtree_on_points(
xs,
ys,
x_min,
x_max,
y_min,
y_max,
max(scale, min_scale),
max_depth,
min_size,
)
return Series(key_to_point), DataFrame._from_table(quadtree)
