Python implementation from Graham Scan

Author: wmboyles

chapters/computational_geometry/gift_wrapping/graham_scan/code/python/grahamScan.py

@@ -0,0 +1,57 @@
+from math import atan2
+
+#Is the turn counter clockwise?
+def CCW(p1, p2, p3):
+    return (p3[1]-p1[1])*(p2[0]-p1[0]) >= (p2[1]-p1[1])*(p3[0]-p1[0])
+
+
+#Find the point with least y-value. If tie, use point with least x-value.
+def minYPoint(points):
+    minYPt = points[0]
+    
+    for point in points[1:]:
+        if point[1] < minYPt[1]:
+            minYPt = point
+        elif point[1] == minYPt[1] and point[0]<minYPt[0]:
+            minYPt = point
+            
+    return minYPt
+
+
+#Find the polar angle of each point in list relative to a reference point
+def polarAngles(ref, points):
+    return [atan2(point[1]-ref[0],point[0]-ref[0]) for point in points]
+
+
+#Sort the list of point by their polar angle
+def sortByPolar(ref, points):
+    return [x for _,x in sorted(zip(polarAngles(ref,points),points))]
+
+
+def grahamScan(gift):
+    start = minYPoint(gift) #Must be in hull
+    gift.remove(start)
+
+    S = sortByPolar(start,gift)
+    hull = [start,S[0],S[1]]
+
+    #Remove points from hull that make the hull concave
+    for pt in S[2:]:
+        while not CCW(hull[-2],hull[-1],pt):
+            del hull[-1]
+        hull.append(pt)
+
+    return hull
+
+
+def main():
+    testGift = [(-5,2),(5,7),(-6,-12),(-14,-14),(9,9),
+                (-1,-1),(-10,11),(-6,15),(-6,-8),(15,-9),
+                (7,-7),(-2,-9),(6,-5),(0,14),(2,8)]
+    hull = grahamScan(testGift)
+
+    print("The points in the hull are:")
+    for point in hull:
+        print(point)
+
+main()