71 lines
1.9 KiB
Python
71 lines
1.9 KiB
Python
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from collections import namedtuple
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from itertools import chain
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from operator import itemgetter
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__all__ = ['bounding_box', 'convex_hull', 'Point', 'Rect']
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Point = namedtuple('Point', ['x', 'y'])
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Rect = namedtuple('Rect', ['left', 'top', 'width', 'height'])
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def bounding_box(locations):
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"""Computes the bounding box of an iterable of (x, y) coordinates.
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Args:
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locations: iterable of (x, y) tuples.
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Returns:
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`Rect`: Coordinates of the bounding box.
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"""
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x_values = list(map(itemgetter(0), locations))
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x_min, x_max = min(x_values), max(x_values)
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y_values = list(map(itemgetter(1), locations))
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y_min, y_max = min(y_values), max(y_values)
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return Rect(x_min, y_min, x_max - x_min, y_max - y_min)
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def convex_hull(points):
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"""Computes the convex hull of an iterable of (x, y) coordinates.
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Args:
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points: iterable of (x, y) tuples.
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Returns:
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`list`: instances of `Point` - vertices of the convex hull in
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counter-clockwise order, starting from the vertex with the
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lexicographically smallest coordinates.
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Andrew's monotone chain algorithm. O(n log n) complexity.
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https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
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"""
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def is_not_clockwise(p0, p1, p2):
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return 0 <= (
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(p1[0] - p0[0]) * (p2[1] - p0[1]) -
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(p1[1] - p0[1]) * (p2[0] - p0[0])
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)
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def go(points_):
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res = []
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for p in points_:
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while 1 < len(res) and is_not_clockwise(res[-2], res[-1], p):
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res.pop()
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res.append(p)
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# The last point in each list is the first point in the other list
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res.pop()
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return res
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# Discard duplicates and sort by x then y
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points = sorted(set(points))
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# Algorithm needs at least two points
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hull = (
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points if len(points) < 2 else chain(go(points), go(reversed(points)))
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)
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return list(map(Point._make, hull))
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