From d25f19e0924f2f9ad4a0e7eaa9f85a4429b836ef Mon Sep 17 00:00:00 2001
From: Alexander Munch-Hansen <alexmunchhansen@gmail.com>
Date: Sat, 15 Sep 2018 11:04:41 +0200
Subject: [PATCH] added code for Graham's Scan

---
 h2/sidedness.py | 83 +++++++++++++++++++++++++++++++++++--------------
 1 file changed, 60 insertions(+), 23 deletions(-)

diff --git a/h2/sidedness.py b/h2/sidedness.py
index 66daeb6..0defecc 100644
--- a/h2/sidedness.py
+++ b/h2/sidedness.py
@@ -1,6 +1,7 @@
 import random
 from collections import namedtuple
 from enum import Enum, auto
+import matplotlib.pyplot as plt
 
 Point = namedtuple('Point', ['x', 'y'])
 
@@ -11,17 +12,18 @@ class Side(Enum):
     BELOW = auto()
 
 
-def sidedness(p1, p2, p3, eps=0.00000001):
-    y = p1.y * (p3.x - p2.x)
-    x = p1.x
-    a = (p3.y - p2.y)
-    b = p3.y * (p3.x - p2.x) - a * p3.x
+def sidedness(p1, p2, p3, eps=0.0000001):
 
-    if y - eps < a * x + b < y + eps:
-        return Side.ON
-    elif y > a * x + b:
-        return Side.ABOVE
-    return Side.BELOW
+	y = p1.y * (p3.x - p2.x)
+	x = p1.x
+	a = (p3.y - p2.y)
+	b = p3.y * (p3.x - p2.x) - a * p3.x
+
+	if y - eps < a * x + b < y + eps:
+		return Side.ON
+	elif y > a * x + b:
+		return Side.ABOVE
+	return Side.BELOW
 
 
 # test
@@ -36,22 +38,57 @@ p3 = Point(5, 2)
 
 
 def genPoint():
-    a = random.uniform(1, 10)
-    b = random.uniform(1, 10)
+    a = random.uniform(1, 5)
+    b = random.uniform(1, 5)
 
-    p = []
-    for i in range(3):
-        x_i = random.uniform(1, 10)
-        p_i = Point(x_i, a * x_i + b)
-        p.append(p_i)
-    return p
+    x_i = random.uniform(1, 5)
+    p_i = Point(x_i, a * x_i + b)
+    
+    return p_i
 
 
-hej = genPoint()
-print(hej)
 
-print(sidedness(*hej))
+def graham_scan(points):
 
+	# A funky issue where both a and b become negative in the sidedness test causes us to have to use
+	# Side.ABOVE for both tests, regardless of UH or LH.
 
-def graham_scan():
-    3
+	
+	sorted_points = sorted(points, key=lambda p: p.x)
+	
+	UH = sorted_points[:2]
+	#del sorted_points[0]
+
+	for s in sorted_points[2:]:
+		while len(UH) > 1 and (sidedness(UH[-2], UH[-1], s) != Side.ABOVE):
+			del UH[-1]
+		UH.append(s)
+	reversed_list = list(reversed(sorted_points))
+	reversed_list.append(UH[0])
+	LH = reversed_list[:2]
+	#del reversed_list[0]
+
+	for s in reversed_list[2:]:
+		while len(LH) > 1 and (sidedness(LH[-2], LH[-1], s) != Side.ABOVE):
+			del LH[-1]
+		LH.append(s)
+
+	return UH, LH
+		
+p = [genPoint() for _ in range(30)]
+UH, LH = graham_scan(p)
+
+x = [point.x for point in p]
+y = [point.y for point in p]
+
+UH_x = [point.x for point in UH]
+UH_y = [point.y for point in UH]
+
+LH_x = [point.x for point in LH]
+LH_y = [point.y for point in LH]
+
+plt.plot(UH_x, UH_y, 'ro-')
+plt.plot(LH_x, LH_y, 'ro-')
+
+plt.scatter(x,y)
+plt.show()