62 lines
1.4 KiB
Python
62 lines
1.4 KiB
Python
from math import sqrt
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from typing import Set
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from util import Point, gen_point, display
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def distance(a, b, c):
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nom = abs((b.y - a.y) * c.x - (b.x - a.x) * c.y + b.x * a.y - b.y * a.x)
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den = sqrt((b.y - a.y) ** 2 + (b.x - a.x) ** 2)
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return nom / den
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def is_left(a: Point, b: Point, c: Point):
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return ((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)) > 0
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def quick_hull(points: Set[Point]):
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assert len(points) >= 2
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left = min(points)
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right = max(points)
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hull = {left, right}
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points = points - hull
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find_hull({p for p in points if not is_left(left, right, p)},
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left,
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right,
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hull)
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find_hull({p for p in points if not is_left(right, left, p)},
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right,
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left,
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hull)
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return hull
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def find_hull(points: Set[Point], p: Point, q: Point, hull: Set[Point]):
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if not points:
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return
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farthest = max(points, key=lambda point: abs(distance(p, q, point)))
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hull.add(farthest)
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points.remove(farthest)
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find_hull({po for po in points if not is_left(p, farthest, po)},
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p,
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farthest,
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hull)
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find_hull({po for po in points if not is_left(farthest, q, po)},
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farthest,
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q,
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hull)
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points = {gen_point() for _ in range(30)}
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hull = quick_hull(points)
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display(points, hull)
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