ok

h2/quick_hull.py

@@ -1,5 +1,7 @@
 import random
 from collections import namedtuple
+from typing import Set
+
 import matplotlib.pyplot as plt
 from enum import Enum, auto
 from math import atan2, degrees, tau, pi, acos, sqrt
@@ -37,70 +39,63 @@ def gen_point():
     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 distance(a, b, c):
+    try:
+        nom = abs((b.y - a.y) * c.x - (b.x - a.x) * c.y + b.x * a.y - b.y * a.x)
+        den = sqrt((b.y - a.y) ** 2 + (b.x - a.x) ** 2)
+        return nom / den
+    except ZeroDivisionError:
+        return 0
 
 
-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 is_left(a: Point, b: Point, c: Point):
+    return ((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)) > 0
 
 
-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: Set[Point]):
+    assert len(points) >= 2
 
+    left = min(points)
+    right = max(points)
 
-def quick_hull(points, side=Side.BELOW, lel=max, hull=None):
-    if hull is None:
-        hull = set()
+    hull = {left, right}
 
-    print(len(points))
-    if len(points) <= 2:
-        return hull
+    find_hull({p for p in points if not is_left(left, right, p)},
+              left,
+              right,
+              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))
+    find_hull({p for p in points if is_left(left, right, p)},
+              right,
+              left,
+              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)
+def find_hull(points: Set[Point], p: Point, q: Point, hull: Set[Point]):
+    if not points:
+        return
 
-hull = uh_hull.union(lh_hull)
+    farthest = max(points, key=lambda point: distance(p, q, point))
+    hull.add(farthest)
+
+    s1 = {point
+          for point in points
+          if not is_left(p, farthest, point)}
+    print("--")
+    print(s1)
+
+    s2 = {point
+          for point in points
+          if not is_left(farthest, q, point)}
+    print(s2)
+
+    find_hull(s1, p, farthest, hull)
+    find_hull(s2, farthest, q, hull)
+
+
+points = {gen_point() for _ in range(10)}
+hull = quick_hull(points)
 
 display(points, hull)