149 lines
5.6 KiB
Python
149 lines
5.6 KiB
Python
import random
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from typing import Set
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from profile import Profiler
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from util import Side, Point, gen_point, display, gen_circular_point
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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 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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return Side.BELOW
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def solve_1dlp(c, constraints):
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c1, c2 = c
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((a1, a2), b) = constraints[-1]
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q, p = b / a2, a1 / a2
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interval = [-10_000, 10_000]
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for (lel_a1, lel_a2), lel_b in constraints:
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bj, aj = (lel_b - lel_a2 * q), (lel_a1 - lel_a2 * p)
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if aj < 0 and bj / aj > interval[0]:
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interval[0] = bj / aj
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elif aj > 0 and bj / aj < interval[1]:
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interval[1] = bj / aj
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c = -(c1 - c2 * p)
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if c < 0:
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return interval[0], q - (p * interval[0])
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elif c >= 0:
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return interval[1], q - (p * interval[1])
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@Profiler("solving LP")
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def solve_2dlp(c, constraints):
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c1, c2 = c
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x1 = -10_000 if c1 > 0 else 10_000
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x2 = -10_000 if c2 > 0 else 10_000
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for i, ((a1, a2), b) in enumerate(constraints, start=1):
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if not (a1*x1 + a2*x2 <= b):
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x1, x2 = solve_1dlp(c, constraints[:i])
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return x1, x2
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@Profiler("finding median")
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def find_median(points):
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num_candidates = min(5, len(points))
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candidates = random.sample(points, num_candidates)
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candidates.sort(key=lambda p: p.x)
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median_i = num_candidates // 2
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median = ((candidates[median_i - 1].x + candidates[median_i].x)/2,
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(candidates[median_i - 1].y + candidates[median_i].y)/2)
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return median[0]
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def is_left(a: Point, b: Point, c: Point):
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return ((b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)) > 0
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def mbc_ch(points: Set[Point], flipper: callable, extra_prune=False, shuffle=True) -> Set[Point]:
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if len(points) < 2:
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return points
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# Extra pruning step
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if extra_prune:
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with Profiler("extra pruning step"):
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left_point = min(points, key=lambda p: (p.x, -p.y))
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right_point = max(points, key=lambda p: (p.x, -p.y))
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if flipper(1) == 1:
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points = {p for p in points if is_left(left_point, right_point, p)}.union({left_point, right_point})
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else:
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points = {p for p in points if not is_left(left_point, right_point, p)}.union({left_point, right_point})
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# Find the point with median x-coordinate, and partition the points on this point
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med_x = find_median(points)
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# Find left and right points in regards to median
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with Profiler("partitioning set"):
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pl = {p for p in points if p.x < med_x}
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pr = {p for p in points if p.x >= med_x}
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# Shuffle
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with Profiler("building constraints"):
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constraints = [((flipper(-p.x), flipper(-1)), flipper(-p.y)) for p in points]
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if shuffle:
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with Profiler("shuffling constraints"):
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random.shuffle(constraints)
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# Find the bridge over the vertical line in pm
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slope, intercept = solve_2dlp((flipper(med_x), flipper(1)), constraints)
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with Profiler("finding bridge points"):
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left_point = next(p for p in pl if sidedness(slope, intercept, p, flipper) == Side.ON)
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right_point = next(p for p in pr if sidedness(slope, intercept, p, flipper) == Side.ON)
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# Prune the points between the two line points
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with Profiler("pruning between 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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return set.union(mbc_ch(pl, flipper, extra_prune=extra_prune, shuffle=shuffle),
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{left_point, right_point},
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mbc_ch(pr, flipper, extra_prune=extra_prune, shuffle=shuffle))
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@Profiler("mbc")
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def mbc(points: Set[Point]) -> Set[Point]:
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return set.union(mbc_ch(points, lambda x: x, extra_prune=False, shuffle=True),
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mbc_ch(points, lambda x: -x, extra_prune=False, shuffle=True))
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@Profiler("mbc2")
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def mbc2(points: Set[Point]) -> Set[Point]:
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return set.union(mbc_ch(points, lambda x: x, extra_prune=True, shuffle=True),
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mbc_ch(points, lambda x: -x, extra_prune=True, shuffle=True))
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@Profiler("mbc_no_shuffle")
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def mbc_no_shuffle(points: Set[Point]) -> Set[Point]:
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return set.union(mbc_ch(points, lambda x: x, extra_prune=False, shuffle=False),
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mbc_ch(points, lambda x: -x, extra_prune=False, shuffle=False))
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@Profiler("mbc2_no_shuffle")
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def mbc2_no_shuffle(points: Set[Point]) -> Set[Point]:
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return set.union(mbc_ch(points, lambda x: x, extra_prune=True, shuffle=False),
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mbc_ch(points, lambda x: -x, extra_prune=True, shuffle=False))
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if __name__ == '__main__':
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random.seed(1337_420)
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points = {gen_point(0, 20) for _ in range(20)}
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points = {gen_circular_point(1, 100, 50) for _ in range(200)}
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#points = {gen_triangular_point(Point(1,1), Point(51,1), Point(26, 30)) for _ in range(200)}
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#points = {Point(x=-33.11091053638924, y=38.88967778961347), Point(x=61.20269947424177, y=-78.96305419217254), Point(x=99.44053842147957, y=-89.11579172297581), Point(x=-92.40380889537532, y=84.33904351991652), Point(x=-90.63139185545595, y=-91.13793846505985)}
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#points = {Point(x=5.2, y=9.7), Point(x=5.3, y=4.9), Point(x=3.3, y=3.6), Point(x=9.2, y=4.8), Point(x=9.7, y=5.7), Point(x=5.6, y=8.7)}
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upper_hull_points = mbc_ch(points, lambda x: x)
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lower_hull_points = mbc_ch(points, lambda x: -x)
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display(points, upper_hull_points.union(lower_hull_points))
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