feat: gift wrapping

gift_wrapping/wrap.py

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