Lol
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@ -1,7 +1,7 @@
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# Use atan2 instead of acos to calc angle; atan2(x,y) of the point we potentially want to add
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from math import acos, sqrt
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from util import Vector, Point, gen_point, display
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from util import Vector, Point, gen_point
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def calc_angle(v1: Vector, v2: Vector) -> float:
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@ -10,8 +10,7 @@ def calc_angle(v1: Vector, v2: Vector) -> float:
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len_2 = sqrt(v2.x**2 + v2.y**2)
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tmp = dot / (len_1 * len_2)
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return acos(round(tmp, 6))
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return acos(max(min(tmp, 1), -1)) # acos is only defined in [-1,1]
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def calc_vector(p1: Point, p2: Point) -> Vector:
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42
h2/mbc.py
42
h2/mbc.py
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@ -1,13 +1,17 @@
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import random
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import statistics
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from math import inf
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from typing import Set, List, Tuple
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from scipy.optimize import linprog
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import util
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from util import Side, Point, gen_point, display
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def sidedness(slope: float, intersection: float, p3: Point, linprog_flipper: callable, eps=0.0000001) -> Side:
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def sidedness(slope: float, intersection: float, p3: Point, flipper: callable, eps=0.0000001) -> Side:
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# finds where a point is in regards to a line
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if linprog_flipper(p3.y) - eps <= linprog_flipper(slope * p3.x + intersection) <= linprog_flipper(p3.y) + eps:
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if flipper(p3.y) - eps <= flipper(slope * p3.x + intersection) <= flipper(p3.y) + eps:
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return Side.ON
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elif p3.y > slope * p3.x + intersection:
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return Side.ABOVE
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@ -45,17 +49,16 @@ def solve_2dlp(c: Tuple[float, float], constraints: List[Tuple[Tuple[float, floa
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x1, x2 = (-inf, -inf) if c1 > 0 else (inf, inf)
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#random.shuffle(constraints)
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for i, ((a1, a2), b) in enumerate(constraints[1:], start=1):
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if a1*x1 + a2*x2 <= b:
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continue
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x1 = solve_1dlp(c1 - c2*a1/a2, [(ai1 - ai2*a1 / a2, bi - ai2*b / a2) for (ai1, ai2), bi in constraints[:i]])
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for i, ((a1, a2), b) in enumerate(constraints[1:], start=0):
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if not a1*x1 + a2*x2 <= b:
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x1 = solve_1dlp(c1 - c2*a1/a2,
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[(ai1 - ai2*a1 / a2, bi - ai2*b / a2) for (ai1, ai2), bi in constraints[:i]])
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x2 = (b - a1*x1) / a2
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return x1, x2
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def mbc_ch(points: Set[Point], linprog_flipper: callable) -> Set[Point]:
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def mbc_ch(points: Set[Point], flipper: callable) -> Set[Point]:
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if len(points) <= 2:
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return points
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@ -67,26 +70,19 @@ def mbc_ch(points: Set[Point], linprog_flipper: callable) -> Set[Point]:
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pr = {p for p in points if p.x >= med_x}
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# Find the bridge over the vertical line in pm
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c = (linprog_flipper(med_x), linprog_flipper(1))
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A = [(linprog_flipper(-p.x), linprog_flipper(-1)) for p in points]
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b = [linprog_flipper(-p.y) for p in points]
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#result = linprog(c, A, b, bounds=[(None, None), (None, None)], options={"tol": 0.00001})
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#slope, intercept = result.x[0], result.x[1]
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slope, intercept = solve_2dlp(c, list(zip(A, b)))
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#display_line_only(points, slope, intercept, [])
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slope, intercept = solve_2dlp((flipper(med_x), flipper(1)),
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[((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points])
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# Find the two points which are on the line, should work
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left_point = next(p for p in pl if sidedness(slope, intercept, p, linprog_flipper) == Side.ON)
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right_point = next(p for p in pr if sidedness(slope, intercept, p, linprog_flipper) == Side.ON)
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on = {p for p in points if sidedness(slope, intercept, p, flipper) == Side.ON}
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left_point = min(on)
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right_point = max(on)
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# Prune the points between the two line points
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pl = {p for p in pl if p.x <= left_point.x}
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pr = {p for p in pr if p.x >= right_point.x}
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pl = {p for p in points if p.x <= left_point.x}
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pr = {p for p in points if p.x >= right_point.x}
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return set.union(mbc_ch(pl, linprog_flipper), {left_point, right_point}, mbc_ch(pr, linprog_flipper))
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return set.union(mbc_ch(pl, flipper), {left_point, right_point}, mbc_ch(pr, flipper))
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def mbc(points: Set[Point]) -> Set[Point]:
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@ -7,16 +7,26 @@ from graham import graham_scan
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from mbc import mbc
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from quick_hull import quick_hull
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random.seed(1337_420)
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#random.seed(1337_420)
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points = {util.gen_point(-100, 100) for i in range(5_000)}
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while True:
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print("="*100)
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points = {util.gen_point(-100, 100) for i in range(100)}
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print("Points:", sorted(points))
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# Sanity check
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graham = set(graham_scan(points))
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gift = set(rapper(points))
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quick = quick_hull(points)
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mbch = set.union(mbc(points))
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assert gift == graham == quick == mbch
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# Sanity check
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graham = set(graham_scan(points))
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gift = set(rapper(points))
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quick = quick_hull(points)
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mbch = set.union(mbc(points))
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print("graham:", sorted(graham))
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print("gift :", sorted(gift))
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print("quick :", sorted(quick))
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print("mbch :", sorted(mbch))
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if not gift == graham == quick == mbch:
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util.display(points=points, hull=mbch)
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def time_it(f: callable, args: tuple = (), iterations=20):
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@ -32,7 +32,7 @@ def display(points: Set[Point], hull: Set[Point]):
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plt.show()
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def display_line_only(points: Set[Point], slope: int, intercept: int, line_points: Set[Point]):
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def display_line_only(points: Set[Point], slope: float, intercept: float, line_points: Set[Point]):
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x = [point.x for point in points]
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y = [point.y for point in points]
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