如何使用 NumPy 用 non-overlapping 个矩形随机填充一个区域？
How to randomly fill a region with non-overlapping rectangles using NumPy?
如何使用 NumPy 用随机大小的矩形随机填充给定的矩形区域，而不让矩形相互重叠？
我的想法是创建一个与区域形状相同的二维数组，用零填充数组，然后对于每个需要的矩形，随机select数组内两个未设置的坐标，将这两个点做成一个矩形，然后用1.
填充矩形对应的数组里面的区域
不知何故它不起作用：
代码：
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Rectangle
from random import randbytes, randrange
def random_rectangles(width=1920, height=1080, number=24):
fig = plt.figure(figsize=(width/100, height/100), dpi=100, facecolor='black')
ax = fig.add_subplot(111)
ax.set_axis_off()
grid = np.zeros((height, width))
for i in range(number):
free = np.transpose(np.nonzero(grid == 0))
y1, x1 = free[randrange(free.shape[0])]
y2, x2 = free[randrange(free.shape[0])]
if x1 > x2: x1, x2 = x2, x1
if y1 > y2: y1, y2 = y2, y1
grid[y1:y2, x1:x2] = 1
w, h = x2-x1, y2-y1
x, y = x1, -y2
color = '#'+randbytes(3).hex()
ax.add_patch(Rectangle((x, y), w, h, fill=True,facecolor=color,edgecolor='#808080',lw=1))
plt.xlim(0, width)
plt.ylim(-height, 0)
plt.axis('scaled')
fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.show()
我不明白，我试过这个：
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Rectangle
import random
class Grid:
def __init__(self, x1, x2, y1, y2):
assert x2 > x1 and y2 > y1
self.x1 = x1
self.x2 = x2
self.y1 = y1
self.y2 = y2
self.subgrids = []
self.divisions = dict()
self.last_subgrid = None
def random(self):
if not self.subgrids:
x = self.x1 + random.random() * (self.x2 - self.x1)
y = self.y1 + random.random() * (self.y2 - self.y1)
return x, y
else:
if not self.last_subgrid:
subgrid = random.choice(self.subgrids)
self.last_subgrid = subgrid
return subgrid.random()
else:
x, y = self.last_subgrid.random()
self.last_subgrid = None
return x, y
def set_subgrid(self, shape):
x1, x2, y1, y2 = shape
assert x2 > x1 and y2 > y1
assert self.x1 <= x2 <= self.x2 and self.y1 <= y2 <= self.y2
if not self.subgrids:
eight = [
(self.x1, x1, self.y1, y1),
(x1, x2, self.y1, y1),
(x2, self.x2, self.y1, y1),
(x1, x2, y1, y2),
(x2, self.x2, y1, y2),
(self.x1, x1, y2, self.y2),
(x1, x2, y2, self.y2),
(x2, self.x2, y2, self.y2)
]
for a, b, c, d in eight:
if a != b and c != d:
subgrid = Grid(a, b, c, d)
self.subgrids.append(subgrid)
self.divisions[(a, b, c, d)] = subgrid
else:
for a, b, c, d in self.divisions:
if a <= x1 < x2 <= b and c <= y1 < y2 <= d:
self.divisions[(a, b, c, d)].set_subgrid((x1, x2, y1, y2))
def random_rectangles(width=1920, height=1080, number=24):
fig = plt.figure(figsize=(width/100, height/100), dpi=100, facecolor='black')
ax = fig.add_subplot(111)
ax.set_axis_off()
grid = Grid(0, width, 0, height)
for i in range(number):
x1, y1 = grid.random()
x2, y2 = grid.random()
if x1 > x2: x1, x2 = x2, x1
if y1 > y2: y1, y2 = y2, y1
grid.set_subgrid((x1, x2, y1, y2))
w, h = x2-x1, y2-y1
color = '#'+random.randbytes(3).hex()
ax.add_patch(Rectangle((x1, y1), w, h, fill=True,facecolor=color,edgecolor='#808080',lw=1))
plt.xlim(0, width)
plt.ylim(0, height)
plt.axis('scaled')
fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.show()
没用：
我做到了
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import random
class Grid:
def __init__(self, x1, x2, y1, y2):
assert x2 > x1 and y2 > y1
self.x1 = x1
self.x2 = x2
self.y1 = y1
self.y2 = y2
self.subgrids = []
def random(self):
if not self.subgrids:
x = self.x1 + random.random() * (self.x2 - self.x1)
y = self.y1 + random.random() * (self.y2 - self.y1)
four = [
(self.x1, x, self.y1, y),
(x, self.x2, self.y1, y),
(self.x1, x, y, self.y2),
(x, self.x2, y, self.y2)
]
for a, b, c, d in four:
if a != b and c != d:
subgrid = Grid(a, b, c, d)
self.subgrids.append(subgrid)
else:
random.choice(self.subgrids).random()
def flatten(self):
if not self.subgrids:
return
result = []
for subgrid in self.subgrids:
if not subgrid.subgrids:
result.append((subgrid.x1, subgrid.x2, subgrid.y1, subgrid.y2))
else:
result.extend(subgrid.flatten())
return result
def random_rectangles(width=1920, height=1080, number=24):
fig = plt.figure(figsize=(width/100, height/100), dpi=100, facecolor='black')
ax = fig.add_subplot(111)
ax.set_axis_off()
grid = Grid(0, width, 0, height)
for i in range(number): grid.random()
rectangles = grid.flatten()
for x1, x2, y1, y2 in rectangles:
w, h = x2-x1, y2-y1
color = '#'+random.randbytes(3).hex()
ax.add_patch(Rectangle((x1, y1), w, h, fill=True,facecolor=color,edgecolor='#808080',lw=1))
plt.xlim(0, width)
plt.ylim(0, height)
plt.axis('scaled')
fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.show()
我终于做到了，但是结果不是我想象的那样，我觉得我的实现还不够好。谁能帮帮我？
从另一个方向解决问题可以获得更好的结果。
你所做的是在每次采样时将样本 space 分成子 spaces，然后你再次在所述子spaces 中采样（或类似的东西类似于那个）。
如果您事先拆分样本 space，您可以获得均匀采样 space 的网格，您可以从中采样：
import numpy as np
from matplotlib import pyplot as plt
from matplotlib.patches import Rectangle
from numpy.typing import ArrayLike
from numpy.random import default_rng
rng = default_rng(42069)
def get_rects(n: int) -> np.ndarray:
"""
Params
------
n: number of rectangles
"""
ceilsqrtn = int(np.ceil(np.sqrt(n)))
n_grids = ceilsqrtn * ceilsqrtn
# Create rectangles in the "full space", that is the [0, 1] space
rects = rng.uniform(size = (n, 4))
# To ensure that the rectangles are in (x1, x2, y1, y2) format where
# Upper left corner is (x1, y1) and bottom right corner (x2, y2)
# Result looks fine without this, but it's a nice to have
rects[:,:2].sort(1)
rects[:,2:].sort(1)
# Create a ceilsqrtn x ceilsqrtn even grid space
flat_grid_indices = rng.choice(n_grids, n, False)
offsets = np.unravel_index(flat_grid_indices, (ceilsqrtn, ceilsqrtn))
# Move each rectangle into their own randomly assigned grid
# This will result with triangles in a space that is ceilsqrtn times larger than the [0, 1] space
rects[:,:2] += offsets[1][..., None]
rects[:,2:] += offsets[0][..., None]
# Scale everything down to the [0, 1] space
rects /= ceilsqrtn
return rects
def plot_rects(rects: ArrayLike, width: int = 10, height: int = 10):
fig, ax = plt.subplots(figsize=(width, height))
for x1, x2, y1, y2 in rects:
ax.add_patch(Rectangle((x1, y1), x2 - x1, y2 - y1, facecolor='gray', edgecolor='black', fill=True))
plt.show()
rects = get_rects(150)
plot_rects(rects)
结果：
至少这是一个好的开始。要获得具有其他特征的矩形，您可以简单地从另一个分布（例如高斯分布）中采样。这样，您将获得更多相似的矩形，但您需要将溢出的矩形剪裁到其他 subspaces 或类似的东西中。另一种选择是 [0,1] 域内的截断分布。
编辑：代码清理和更好的评论
如何使用 NumPy 用随机大小的矩形随机填充给定的矩形区域，而不让矩形相互重叠？
我的想法是创建一个与区域形状相同的二维数组，用零填充数组，然后对于每个需要的矩形，随机select数组内两个未设置的坐标，将这两个点做成一个矩形，然后用1.
填充矩形对应的数组里面的区域不知何故它不起作用：
代码：
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Rectangle
from random import randbytes, randrange
def random_rectangles(width=1920, height=1080, number=24):
fig = plt.figure(figsize=(width/100, height/100), dpi=100, facecolor='black')
ax = fig.add_subplot(111)
ax.set_axis_off()
grid = np.zeros((height, width))
for i in range(number):
free = np.transpose(np.nonzero(grid == 0))
y1, x1 = free[randrange(free.shape[0])]
y2, x2 = free[randrange(free.shape[0])]
if x1 > x2: x1, x2 = x2, x1
if y1 > y2: y1, y2 = y2, y1
grid[y1:y2, x1:x2] = 1
w, h = x2-x1, y2-y1
x, y = x1, -y2
color = '#'+randbytes(3).hex()
ax.add_patch(Rectangle((x, y), w, h, fill=True,facecolor=color,edgecolor='#808080',lw=1))
plt.xlim(0, width)
plt.ylim(-height, 0)
plt.axis('scaled')
fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.show()
我不明白，我试过这个：
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Rectangle
import random
class Grid:
def __init__(self, x1, x2, y1, y2):
assert x2 > x1 and y2 > y1
self.x1 = x1
self.x2 = x2
self.y1 = y1
self.y2 = y2
self.subgrids = []
self.divisions = dict()
self.last_subgrid = None
def random(self):
if not self.subgrids:
x = self.x1 + random.random() * (self.x2 - self.x1)
y = self.y1 + random.random() * (self.y2 - self.y1)
return x, y
else:
if not self.last_subgrid:
subgrid = random.choice(self.subgrids)
self.last_subgrid = subgrid
return subgrid.random()
else:
x, y = self.last_subgrid.random()
self.last_subgrid = None
return x, y
def set_subgrid(self, shape):
x1, x2, y1, y2 = shape
assert x2 > x1 and y2 > y1
assert self.x1 <= x2 <= self.x2 and self.y1 <= y2 <= self.y2
if not self.subgrids:
eight = [
(self.x1, x1, self.y1, y1),
(x1, x2, self.y1, y1),
(x2, self.x2, self.y1, y1),
(x1, x2, y1, y2),
(x2, self.x2, y1, y2),
(self.x1, x1, y2, self.y2),
(x1, x2, y2, self.y2),
(x2, self.x2, y2, self.y2)
]
for a, b, c, d in eight:
if a != b and c != d:
subgrid = Grid(a, b, c, d)
self.subgrids.append(subgrid)
self.divisions[(a, b, c, d)] = subgrid
else:
for a, b, c, d in self.divisions:
if a <= x1 < x2 <= b and c <= y1 < y2 <= d:
self.divisions[(a, b, c, d)].set_subgrid((x1, x2, y1, y2))
def random_rectangles(width=1920, height=1080, number=24):
fig = plt.figure(figsize=(width/100, height/100), dpi=100, facecolor='black')
ax = fig.add_subplot(111)
ax.set_axis_off()
grid = Grid(0, width, 0, height)
for i in range(number):
x1, y1 = grid.random()
x2, y2 = grid.random()
if x1 > x2: x1, x2 = x2, x1
if y1 > y2: y1, y2 = y2, y1
grid.set_subgrid((x1, x2, y1, y2))
w, h = x2-x1, y2-y1
color = '#'+random.randbytes(3).hex()
ax.add_patch(Rectangle((x1, y1), w, h, fill=True,facecolor=color,edgecolor='#808080',lw=1))
plt.xlim(0, width)
plt.ylim(0, height)
plt.axis('scaled')
fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.show()
没用：
我做到了
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import random
class Grid:
def __init__(self, x1, x2, y1, y2):
assert x2 > x1 and y2 > y1
self.x1 = x1
self.x2 = x2
self.y1 = y1
self.y2 = y2
self.subgrids = []
def random(self):
if not self.subgrids:
x = self.x1 + random.random() * (self.x2 - self.x1)
y = self.y1 + random.random() * (self.y2 - self.y1)
four = [
(self.x1, x, self.y1, y),
(x, self.x2, self.y1, y),
(self.x1, x, y, self.y2),
(x, self.x2, y, self.y2)
]
for a, b, c, d in four:
if a != b and c != d:
subgrid = Grid(a, b, c, d)
self.subgrids.append(subgrid)
else:
random.choice(self.subgrids).random()
def flatten(self):
if not self.subgrids:
return
result = []
for subgrid in self.subgrids:
if not subgrid.subgrids:
result.append((subgrid.x1, subgrid.x2, subgrid.y1, subgrid.y2))
else:
result.extend(subgrid.flatten())
return result
def random_rectangles(width=1920, height=1080, number=24):
fig = plt.figure(figsize=(width/100, height/100), dpi=100, facecolor='black')
ax = fig.add_subplot(111)
ax.set_axis_off()
grid = Grid(0, width, 0, height)
for i in range(number): grid.random()
rectangles = grid.flatten()
for x1, x2, y1, y2 in rectangles:
w, h = x2-x1, y2-y1
color = '#'+random.randbytes(3).hex()
ax.add_patch(Rectangle((x1, y1), w, h, fill=True,facecolor=color,edgecolor='#808080',lw=1))
plt.xlim(0, width)
plt.ylim(0, height)
plt.axis('scaled')
fig.subplots_adjust(left=0, bottom=0, right=1, top=1, wspace=0, hspace=0)
plt.show()
我终于做到了，但是结果不是我想象的那样，我觉得我的实现还不够好。谁能帮帮我？
从另一个方向解决问题可以获得更好的结果。
你所做的是在每次采样时将样本 space 分成子 spaces，然后你再次在所述子spaces 中采样（或类似的东西类似于那个）。
如果您事先拆分样本 space，您可以获得均匀采样 space 的网格，您可以从中采样：
import numpy as np
from matplotlib import pyplot as plt
from matplotlib.patches import Rectangle
from numpy.typing import ArrayLike
from numpy.random import default_rng
rng = default_rng(42069)
def get_rects(n: int) -> np.ndarray:
"""
Params
------
n: number of rectangles
"""
ceilsqrtn = int(np.ceil(np.sqrt(n)))
n_grids = ceilsqrtn * ceilsqrtn
# Create rectangles in the "full space", that is the [0, 1] space
rects = rng.uniform(size = (n, 4))
# To ensure that the rectangles are in (x1, x2, y1, y2) format where
# Upper left corner is (x1, y1) and bottom right corner (x2, y2)
# Result looks fine without this, but it's a nice to have
rects[:,:2].sort(1)
rects[:,2:].sort(1)
# Create a ceilsqrtn x ceilsqrtn even grid space
flat_grid_indices = rng.choice(n_grids, n, False)
offsets = np.unravel_index(flat_grid_indices, (ceilsqrtn, ceilsqrtn))
# Move each rectangle into their own randomly assigned grid
# This will result with triangles in a space that is ceilsqrtn times larger than the [0, 1] space
rects[:,:2] += offsets[1][..., None]
rects[:,2:] += offsets[0][..., None]
# Scale everything down to the [0, 1] space
rects /= ceilsqrtn
return rects
def plot_rects(rects: ArrayLike, width: int = 10, height: int = 10):
fig, ax = plt.subplots(figsize=(width, height))
for x1, x2, y1, y2 in rects:
ax.add_patch(Rectangle((x1, y1), x2 - x1, y2 - y1, facecolor='gray', edgecolor='black', fill=True))
plt.show()
rects = get_rects(150)
plot_rects(rects)
结果：
至少这是一个好的开始。要获得具有其他特征的矩形，您可以简单地从另一个分布（例如高斯分布）中采样。这样，您将获得更多相似的矩形，但您需要将溢出的矩形剪裁到其他 subspaces 或类似的东西中。另一种选择是 [0,1] 域内的截断分布。
编辑：代码清理和更好的评论