From 69037ec7714d8fa5dcc8853dd4254f7bcda397f3 Mon Sep 17 00:00:00 2001
From: Alexander Munch-Hansen <alexmunchhansen@gmail.com>
Date: Thu, 20 Sep 2018 14:50:16 +0200
Subject: [PATCH] hmmmm

---
 h2/gift_wrapper.py |  28 ++++++++----
 h2/quick_hull.py   | 106 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 125 insertions(+), 9 deletions(-)
 create mode 100644 h2/quick_hull.py

diff --git a/h2/gift_wrapper.py b/h2/gift_wrapper.py
index b2a4e54..edc28dd 100644
--- a/h2/gift_wrapper.py
+++ b/h2/gift_wrapper.py
@@ -2,7 +2,7 @@
 import random
 from collections import namedtuple
 import matplotlib.pyplot as plt
-from math import atan2, degrees, tau, pi, acos, sqrt
+from math import acos, sqrt
 
 Point = namedtuple('Point', 'x y')
 Vector = namedtuple('Vector', 'x y')
@@ -18,8 +18,19 @@ def gen_point():
     return p_i
 
 
-def calc_angle(v: Vector, upside_down=False) -> float:
-    return (90 - degrees(atan2(v.y, v.x)) - 180*upside_down) % 360
+def calc_angle(v1: Vector, v2: Vector) -> float:
+    dot = (v1.x * v2.x) + (v1.y * v2.y)
+    len_1 = sqrt(v1.x**2 + v1.y**2)
+    len_2 = sqrt(v2.x**2 + v2.y**2)
+
+    tmp = dot / (len_1 * len_2)
+
+    # pls
+    hmmmmmmm = round(tmp, 6)
+
+    return acos(hmmmmmmm)
+
+
 
 
 def calc_vector(p1: Point, p2: Point) -> Vector:
@@ -41,16 +52,15 @@ def display(points, hull):
 
 def rapper(points: set):
     min_pt = min(points)
-    max_pt = max(points)
     hull = [min_pt]
-    upside_down = False
-
+    comp_vec = Vector(0, 1)
     while True:
         hull.append(min(points - {hull[-1]},
-                        key=lambda p: calc_angle(calc_vector(hull[-1], p), upside_down)))
-        if hull[-1].x == max_pt.x:
-            upside_down = True
+                        key=lambda p: calc_angle(comp_vec, calc_vector(hull[-1], p))))
+        comp_vec = calc_vector(hull[-2], hull[-1])
+
         display(points, hull)
+
         if hull[-1] == min_pt:
             break
 
diff --git a/h2/quick_hull.py b/h2/quick_hull.py
new file mode 100644
index 0000000..d84db6f
--- /dev/null
+++ b/h2/quick_hull.py
@@ -0,0 +1,106 @@
+import random
+from collections import namedtuple
+import matplotlib.pyplot as plt
+from enum import Enum, auto
+from math import atan2, degrees, tau, pi, acos, sqrt
+
+
+Point = namedtuple('Point', 'x y')
+
+
+class Side(Enum):
+    ON = auto()
+    ABOVE = auto()
+    BELOW = auto()
+
+
+def display(points, hull):
+    x = [point.x for point in points]
+    y = [point.y for point in points]
+
+    h_x = [point.x for point in hull]
+    h_y = [point.y for point in hull]
+
+    plt.plot(h_x, h_y, 'ro-')
+
+    plt.scatter(x, y)
+    plt.show()
+
+
+def gen_point():
+    a = random.uniform(1, 5)
+    b = random.uniform(1, 5)
+
+    x_i = random.uniform(1, 5)
+    p_i = Point(x_i, a * x_i + b)
+
+    return p_i
+
+
+def sidedness(p1, p2, p3, eps=0.0000001):
+    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
+
+    line = a*x+b
+
+    if y - eps < line < y + eps:
+        return [Side.ON, y - line]
+    elif y > line:
+        return [Side.ABOVE, y - line]
+    return [Side.BELOW, y - line]
+
+
+def prune_below_find_highest(points: set, line_segment, side = Side.BELOW, lel=max):
+    min_pt, max_pt = line_segment
+
+    above_pts = []
+
+    for point in points:
+        sidedness_res = sidedness(min_pt, max_pt, point)
+        if sidedness_res[0] != side:
+            above_pts.append(point)
+
+    highest_above = lel(above_pts, key=lambda pt: pt[1])
+
+    return above_pts, highest_above
+
+
+def find_line_segment(points):
+    min_pt = min(points, key=lambda pt: pt.x)
+    max_pt = max(points, key=lambda pt: pt.x)
+    return min_pt, max_pt
+
+
+def quick_hull(points, side=Side.BELOW, lel=max, hull=None):
+    if hull is None:
+        hull = set()
+
+    print(len(points))
+    if len(points) <= 2:
+        return hull
+
+    min_pt, max_pt = find_line_segment(points)
+
+    above_points, max_dist_pt = prune_below_find_highest(points, (min_pt, max_pt), side, lel)
+
+    left_side = prune_below_find_highest(points, (min_pt, max_dist_pt), side, lel)[0]
+    right_side = prune_below_find_highest(points, (max_dist_pt, max_pt), side, lel)[0]
+
+    hull.add(max_dist_pt)
+
+    quick_hull(left_side, side, lel, hull=hull).union(quick_hull(right_side, side, lel, hull=hull))
+
+    return hull
+
+points = {Point(2, 5), Point(3, 1), Point(3, 4), Point(9, 4), Point(1, 5), Point(5, 7)}
+#points = {gen_point() for _ in range(10)}
+
+line_segment = find_line_segment(points)
+uh_hull = quick_hull(points)
+lh_hull = quick_hull(points, Side.ABOVE, min)
+
+hull = uh_hull.union(lh_hull)
+
+display(points, hull)