97 lines
2.0 KiB
Python
97 lines
2.0 KiB
Python
import random
|
|
from collections import namedtuple
|
|
from typing import Set
|
|
|
|
import matplotlib.pyplot as plt
|
|
from enum import Enum, auto
|
|
from math import atan2, degrees, tau, pi, acos, sqrt
|
|
|
|
|
|
Point = namedtuple('Point', 'x y')
|
|
|
|
|
|
class Side(Enum):
|
|
ON = auto()
|
|
ABOVE = auto()
|
|
BELOW = auto()
|
|
|
|
|
|
def display(points, hull):
|
|
x = [point.x for point in points]
|
|
y = [point.y for point in points]
|
|
|
|
h_x = [point.x for point in hull]
|
|
h_y = [point.y for point in hull]
|
|
|
|
plt.plot(h_x, h_y, 'ro-')
|
|
|
|
plt.scatter(x, y)
|
|
plt.show()
|
|
|
|
|
|
def gen_point():
|
|
a = random.uniform(1, 5)
|
|
b = random.uniform(1, 5)
|
|
|
|
x_i = random.uniform(1, 5)
|
|
p_i = Point(x_i, a * x_i + b)
|
|
|
|
return p_i
|
|
|
|
|
|
def distance(a, b, c):
|
|
nom = abs((b.y - a.y) * c.x - (b.x - a.x) * c.y + b.x * a.y - b.y * a.x)
|
|
den = sqrt((b.y - a.y) ** 2 + (b.x - a.x) ** 2)
|
|
return nom / den
|
|
|
|
|
|
def is_left(a: Point, b: Point, c: Point):
|
|
return ((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)) > 0
|
|
|
|
|
|
def quick_hull(points: Set[Point]):
|
|
assert len(points) >= 2
|
|
|
|
left = min(points)
|
|
right = max(points)
|
|
|
|
hull = {left, right}
|
|
points = points - hull
|
|
|
|
find_hull({p for p in points if not is_left(left, right, p)},
|
|
left,
|
|
right,
|
|
hull)
|
|
|
|
find_hull({p for p in points if not is_left(right, left, p)},
|
|
right,
|
|
left,
|
|
hull)
|
|
|
|
return hull
|
|
|
|
|
|
def find_hull(points: Set[Point], p: Point, q: Point, hull: Set[Point]):
|
|
if not points:
|
|
return
|
|
|
|
farthest = max(points, key=lambda point: abs(distance(p, q, point)))
|
|
hull.add(farthest)
|
|
points.remove(farthest)
|
|
|
|
find_hull({po for po in points if not is_left(p, farthest, po)},
|
|
p,
|
|
farthest,
|
|
hull)
|
|
|
|
find_hull({po for po in points if not is_left(farthest, q, po)},
|
|
farthest,
|
|
q,
|
|
hull)
|
|
|
|
|
|
peepees = {gen_point() for _ in range(30)}
|
|
hulliees = quick_hull(peepees)
|
|
|
|
display(peepees, hulliees)
|