90 lines
2.3 KiB
Python
90 lines
2.3 KiB
Python
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# Gift wrapping algorithm
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# https://en.wikipedia.org/wiki/Gift_wrapping_algorithm
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# Date: 2021-11-16
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import matplotlib.pyplot as plt
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import math
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import random
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def generate_points(n=100):
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X = []
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Y = []
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for i in range(n):
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X.append(random.random())
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Y.append(random.random())
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plt.plot(X, Y, '.')
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return [(X[i],Y[i]) for i in range(n)]
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# def angle(p1, p2, p3):
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# p1, p2, p3 = p3, p2, p1
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# print(p1, p2, p3)
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# if p1 == p3: return math.pi
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# x1, y1 = p2[0]-p1[0], p2[1]-p1[1]
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# x2, y2 = p3[0]-p2[0], p3[1]-p2[1]
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# d = x1*y2-y1*x2
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# n1 = math.hypot(x1, y1)
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# n2 = math.hypot(x2, y2)
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# if d == 0 or n1*n2 == 0:
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# l = x1/x2
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# if l >= 0: return 0
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# return math.pi
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# dp = x1*x2 + y1*y2
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# c = math.acos(dp/(n1*n2))
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# b = (c if d > 0 else -c) % 2*math.pi
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# return math.pi*2-b
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def cross_product(u, v):
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x1, y1 = u
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x2, y2 = v
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n1 = math.hypot(x1, y1)
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n2 = math.hypot(x2, y2)
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return (x1*y2-x2*y1)
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# def angle(p1, p2, p3):
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# x1, y1 = p2[0]-p1[0], p2[1]-p1[1]
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# x2, y2 = p3[0]-p2[0], p3[1]-p2[1]
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# a = (math.atan2(y1, x1) - math.atan2(y2, x2))
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# if a < 0:
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# a = math.pi
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# return a
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def gift_wrapping(points):
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convex_hull = []
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x_sorted = list(sorted(points, key=lambda point: point[0]))
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left_most = x_sorted[0]
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point_on_hull = left_most
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endpoint = None
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while endpoint != left_most:
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convex_hull.append(point_on_hull)
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endpoint = points[0]
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for point in points:
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cp = cross_product((
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endpoint[0] - point_on_hull[0],
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endpoint[1] - point_on_hull[1]
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), (
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point[0] - point_on_hull[0],
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point[1] - point_on_hull[1]
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))
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if endpoint == point_on_hull or cp < 0:
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endpoint = point
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point_on_hull = endpoint
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return convex_hull
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def draw_points(points, with_edge=False):
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X, Y = [], []
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for p in points:
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X.append(p[0])
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Y.append(p[1])
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plt.plot(X, Y, '.' if not with_edge else '')
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pts = generate_points(50)
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#pts = [(0.1, 1), (0.2, 0.4), (0.2, 0.15), (0.4, 0.25), (0.6, 0.8), (0.55, 0.3), (0.7, 0.2), (0.5, 0.5), (0.4, 0.7), (0.3, 0.1)]
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print(pts)
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draw_points(pts)
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hull=gift_wrapping(pts)
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draw_points(hull+[hull[0]], True)
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plt.show()
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