107 lines
2.4 KiB
Python
107 lines
2.4 KiB
Python
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import random
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from collections import namedtuple
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import matplotlib.pyplot as plt
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from enum import Enum, auto
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from math import atan2, degrees, tau, pi, acos, sqrt
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Point = namedtuple('Point', 'x y')
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class Side(Enum):
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ON = auto()
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ABOVE = auto()
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BELOW = auto()
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def display(points, hull):
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x = [point.x for point in points]
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y = [point.y for point in points]
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h_x = [point.x for point in hull]
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h_y = [point.y for point in hull]
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plt.plot(h_x, h_y, 'ro-')
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plt.scatter(x, y)
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plt.show()
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def gen_point():
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a = random.uniform(1, 5)
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b = random.uniform(1, 5)
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x_i = random.uniform(1, 5)
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p_i = Point(x_i, a * x_i + b)
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return p_i
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def sidedness(p1, p2, p3, eps=0.0000001):
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y = p1.y * (p3.x - p2.x)
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x = p1.x
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a = (p3.y - p2.y)
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b = p3.y * (p3.x - p2.x) - a * p3.x
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line = a*x+b
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if y - eps < line < y + eps:
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return [Side.ON, y - line]
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elif y > line:
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return [Side.ABOVE, y - line]
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return [Side.BELOW, y - line]
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def prune_below_find_highest(points: set, line_segment, side = Side.BELOW, lel=max):
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min_pt, max_pt = line_segment
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above_pts = []
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for point in points:
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sidedness_res = sidedness(min_pt, max_pt, point)
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if sidedness_res[0] != side:
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above_pts.append(point)
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highest_above = lel(above_pts, key=lambda pt: pt[1])
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return above_pts, highest_above
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def find_line_segment(points):
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min_pt = min(points, key=lambda pt: pt.x)
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max_pt = max(points, key=lambda pt: pt.x)
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return min_pt, max_pt
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def quick_hull(points, side=Side.BELOW, lel=max, hull=None):
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if hull is None:
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hull = set()
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print(len(points))
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if len(points) <= 2:
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return hull
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min_pt, max_pt = find_line_segment(points)
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above_points, max_dist_pt = prune_below_find_highest(points, (min_pt, max_pt), side, lel)
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left_side = prune_below_find_highest(points, (min_pt, max_dist_pt), side, lel)[0]
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right_side = prune_below_find_highest(points, (max_dist_pt, max_pt), side, lel)[0]
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hull.add(max_dist_pt)
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quick_hull(left_side, side, lel, hull=hull).union(quick_hull(right_side, side, lel, hull=hull))
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return hull
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points = {Point(2, 5), Point(3, 1), Point(3, 4), Point(9, 4), Point(1, 5), Point(5, 7)}
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#points = {gen_point() for _ in range(10)}
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line_segment = find_line_segment(points)
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uh_hull = quick_hull(points)
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lh_hull = quick_hull(points, Side.ABOVE, min)
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hull = uh_hull.union(lh_hull)
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display(points, hull)
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