Merge branch 'update_readme' into 'main'

docs: update README with examples

See merge request !6

README.md

@@ -2,12 +2,190 @@
 
 Python module containing useful functions and classes for Spatial Analysis.
 
-This package supports Python 3.11 and beyond.
+Tested on Python versions 3.11, 3.12, and 3.13. Not expected to work with Python 3.9 or below due
+to usage of type annotations.
 
 ## Installation
 
 As a dependency with `pip`
 
 ```bash
-pip install git+git@git.noc.ac.uk:josidd/geospatialtools.git
+pip install git+git@git.noc.ac.uk:nocsurfaceprocesses/geospatialtools.git
+```
+
+## Neighbours
+
+### 1d neighbours
+
+For example, finding the closest time value in a list of _sorted_ time values:
+
+```python
+def find_nearest(vals: list[Numeric], test: list[Numeric]) -> list[int]:
+    ...
+```
+
+Example:
+
+```python
+from GeoSpatialTools import find_nearest
+import numpy as np
+
+# Generate random neighbours and test points
+potential_neighbours = list(np.random.randn(100))
+potential_neighbours.sort()
+test_values = list(np.random.randn(3))
+
+neighbour_i = find_nearest(potential_neighbours, test_values)
+```
+
+Returns the index of the value in `potential_neighbours` that is closest to each value in
+`test_values`. This function makes use of `bisect.bisect` from the python standard library and
+requires that the list `potential_neighbours` is sorted. No check on sorted-ness is performed, if
+the list is unsorted then the incorrect answer will be returned.
+
+This calculation is performed in `O(log(n))` time.
+
+### 2d neighbours
+
+An implementation of `KDTree` (specifically a `2DTree`) using Haversine distance as the query
+distance and accounting for longitudinal wrapping at -180, 180.
+
+Uses a `Record` class:
+
+```python
+Record(
+    lon: float,
+    lat: float,
+    datetime: datetime.datetime | None,
+    uid: str | None,
+    **data
+)
+```
+
+Fast look-up of nearest neighbours in 2 spatial dimensions (longitude and latitude).
+
+```python
+KDTree(
+    points: list[Record],
+    max_depth: int,
+    depth: int = 0  # Internal parameter
+)
+```
+
+```python
+from GeoSpatialTools import KDTree, Record
+from random import choice
+
+lon_range = list(range(-180, 180))
+lat_range = list(range(-90, 90))
+N_samples = 1000
+
+records: list[Record] = [Record(choice(lon_range), choice(lat_range)) for _ in range(N_samples)]
+# Construct Tree
+kt = KDTree(records)
+
+test_value: Record = Record(lon=47.6, lat=-31.1)
+neighbours: list[Record] = []
+neighbours, dist = kt.query(test_value)
+```
+
+### Points within distance (2d \& 3d)
+
+Also included is an implementation of `QuadTree` and `OctTree` using Haversine distance for querying
+with a test `Record` and distance.
+
+```python
+QuadTree(
+    boundary: Rectangle,
+    capacity: int,
+    max_depth: int,
+    depth: int = 0  # Internal parameter
+)
+
+Rectangle(
+    lon: float,  # Centre longitude
+    lat: float,  # Centre latitude
+    lon_range: float,  # Full width of rectangle (degrees)
+    lat_range: float,  # Full height of rectangle (degrees)
+)
+```
+
+```python
+from GeoSpatialTools import QuadTree, Record, Rectangle
+from random import choice
+
+lon_range = list(range(-180, 180))
+lat_range = list(range(-90, 90))
+N_samples = 1000
+
+# Construct Tree
+boundary = Rectangle(0, 0, 360, 180)  # Full domain
+qt = QuadTree(boundary)
+
+records: list[Record] = [Record(choice(lon_range), choice(lat_range)) for _ in range(N_samples)]
+for record in records:
+    qt.insert(record)
+
+test_value: Record = Record(lon=47.6, lat=-31.1)
+dist: float = 340  # km
+
+neighbours: list[Record] = qt.nearby_points(test_value, dist)
+```
+
+#### OctTree - 3d QuadTree
+
+Adds `SpaceTimeRecord`, `SpaceTimeRectangle` and `OctTree` classes.
+
+```python
+SpaceTimeRecord(
+    lon: float,
+    lat: float,
+    datetime: datetime.datetime,  # datetime no longer optional
+    uid: str | None,
+    **data
+)
+
+SpaceTimeRectangle(
+    lon: float,          # Centre longitude
+    lat: float,          # Centre latitude
+    datetime: datetime,  # Central datetime
+    w: float,            # Full width of rectangle (degrees)
+    h: float,            # Full height of rectangle (degrees)
+    dt: timedelta,       # Time extent of rectangle
+)
+```
+
+Example
+
+```python
+from GeoSpatialTools.octtree import OctTree, SpaceTimeRecord, SpaceTimeRectangle
+from datetime import datetime, timedelta
+from random import choice
+from pandas import date_range
+
+lon_range = list(range(-180, 180))
+lat_range = list(range(-90, 90))
+
+dates = date_range(
+    start=datetime(2009, 1, 1, 0, 0),
+    end=datetime(2009, 2, 1, 0, 0),
+    interval=timedelta(hours=1),
+    inclusive="left",
+)
+N_samples = 1000
+
+# Construct Tree
+boundary = SpaceTimeRectangle(0, 0, datetime(2009, 1, 15, 12), 360, 180, timedelta(days=31))  # Full domain
+ot = OctTree(boundary)
+
+records: list[SpaceTimeRecord] = [
+    SpaceTimeRecord(choice(lon_range), choice(lat_range), choice(dates)) for _ in range(N_samples)]
+for record in records:
+    ot.insert(record)
+
+test_value: SpaceTimeRecord = SpaceTimeRecord(lon=47.6, lat=-31.1, datetime=datetime(2009, 1, 23, 17, 41))
+dist: float = 340  # km
+t_dist = timedelta(hours=4)
+
+neighbours: list[Record] = ot.nearby_points(test_value, dist, t_dist)
 ```