pointpats.minimum_bounding_circle¶

pointpats.minimum_bounding_circle(points)[source]¶

pointpats.minimum_bounding_circle(points: ndarray) → tuple[tuple[float, float], float]

pointpats.minimum_bounding_circle(points: GeoPandasBase) → Polygon

Implements Skyum (1990)’s algorithm for the minimum bounding circle in R^2.

Store points clockwise. Find p in S that maximizes angle(prec(p), p, succ(p) THEN radius(prec( p), p, succ(p)). This is also called the lexicographic maximum, and is the last entry of a list of (radius, angle) in lexicographical order.

If angle(prec(p), p, succ(p)) <= 90 degrees, then finish.
If not, remove p from set.

Parameters:

pointsarraylike: array representing a point pattern

Returns:

circle: minimum bounding circle

Examples

>>> import numpy as np
>>> import geopandas as gpd

Create an array of point coordinates.

>>> coords = np.array(
...     [
...         [66.22, 32.54],
...         [22.52, 22.39],
...         [31.01, 81.21],
...         [9.47, 31.02],
...         [30.78, 60.10],
...         [75.21, 58.93],
...         [79.26, 7.68],
...         [8.23, 39.93],
...         [98.73, 77.17],
...         [89.78, 42.53],
...         [65.19, 92.08],
...     ]
... )

Passing an array of coordinates returns an tuple of (x, y), radius.

>>> minimum_bounding_circle(coords)
((55.244520477497474, 51.88135107645883), np.float64(50.304102155590726))

Passing a GeoPandas object returns a shapely geometry.

>>> geoms = gpd.GeoSeries.from_xy(*coords.T)
>>> minimum_bounding_circle(geoms)
<POLYGON ((105.549 51.881, 105.306 46.951, 104.582 42.068, 103.383 37.279, 1...>