[英]Random uniform distribution of points with minimum spacing
我试图在二维空间中生成一组点的坐标,这些点随机均匀分布,但彼此不太接近。
我从np.random.uniform
开始,生成 nx 2 个值(x 和 y 坐标),然后使用两个嵌套的 for 循环在所有坐标上筛选坐标列表,以删除太近的点并将它们随机放置在某处别的:
# Generate xy coordinates for the grafting points
rng = np.random.RandomState(seed=self.rng_seed)
coordinates = rng.uniform(high=(self.box_size[0], self.box_size[1]), size=(n_chains, 2))
for count in range(0, self.max_overlap_iter):
moved_bead = False
# Search for overlapping beads by looping over the list doubly
for id_i, coord_i in enumerate(coordinates):
for id_j, coord_j in enumerate(coordinates):
if not id_i == id_j and np.sqrt(sum((coord_i - coord_j)**2)) < self.bead_size:
# Move the second point
coordinates[id_j] = rng.uniform(high=(self.box_size[0], self.box_size[1]), size=2)
moved_bead = True
if not moved_bead:
break
在一个点被移动到一个新的随机位置后,它必须再次通过外循环到达 go,因为它可能仍然重叠。
问题是当点的密度足够高时,这会变得非常慢,因为某些点“重叠”的概率会飙升。 因此,我必须构建最大数量的迭代,但这显然不是我问题的解决方案。
有没有更快、更有效的方法来做到这一点?
您是否尝试过使用 Poisson-Disc 采样算法?
我认为这可能是您正在寻找的东西。
以下是删除的代码
<!DOCTYPE html>
<meta charset="utf-8">
<body>
<script src="//d3js.org/d3.v3.min.js"></script>
<script>
var width = 960,
height = 500;
var sample = poissonDiscSampler(width, height, 10);
var svg = d3.select("body").append("svg")
.attr("width", width)
.attr("height", height);
d3.timer(function() {
for (var i = 0; i < 10; ++i) {
var s = sample();
if (!s) return true;
svg.append("circle")
.attr("cx", s[0])
.attr("cy", s[1])
.attr("r", 0)
.transition()
.attr("r", 2);
}
});
// Based on https://www.jasondavies.com/poisson-disc/
function poissonDiscSampler(width, height, radius) {
var k = 30, // maximum number of samples before rejection
radius2 = radius * radius,
R = 3 * radius2,
cellSize = radius * Math.SQRT1_2,
gridWidth = Math.ceil(width / cellSize),
gridHeight = Math.ceil(height / cellSize),
grid = new Array(gridWidth * gridHeight),
queue = [],
queueSize = 0,
sampleSize = 0;
return function() {
if (!sampleSize) return sample(Math.random() * width, Math.random() * height);
// Pick a random existing sample and remove it from the queue.
while (queueSize) {
var i = Math.random() * queueSize | 0,
s = queue[i];
// Make a new candidate between [radius, 2 * radius] from the existing sample.
for (var j = 0; j < k; ++j) {
var a = 2 * Math.PI * Math.random(),
r = Math.sqrt(Math.random() * R + radius2),
x = s[0] + r * Math.cos(a),
y = s[1] + r * Math.sin(a);
// Reject candidates that are outside the allowed extent,
// or closer than 2 * radius to any existing sample.
if (0 <= x && x < width && 0 <= y && y < height && far(x, y)) return sample(x, y);
}
queue[i] = queue[--queueSize];
queue.length = queueSize;
}
};
function far(x, y) {
var i = x / cellSize | 0,
j = y / cellSize | 0,
i0 = Math.max(i - 2, 0),
j0 = Math.max(j - 2, 0),
i1 = Math.min(i + 3, gridWidth),
j1 = Math.min(j + 3, gridHeight);
for (j = j0; j < j1; ++j) {
var o = j * gridWidth;
for (i = i0; i < i1; ++i) {
if (s = grid[o + i]) {
var s,
dx = s[0] - x,
dy = s[1] - y;
if (dx * dx + dy * dy < radius2) return false;
}
}
}
return true;
}
function sample(x, y) {
var s = [x, y];
queue.push(s);
grid[gridWidth * (y / cellSize | 0) + (x / cellSize | 0)] = s;
++sampleSize;
++queueSize;
return s;
}
}
</script>
我最终编写了一个泊松盘点集生成器算法,该算法可以生成非最大点集并在线性时间内运行,使用我从其他算法中获得的一些想法。
当然感谢@Kamil 给了我“泊松磁盘点集”这个词给谷歌;)
可以在这里找到: https://github.com/Compizfox/MDBrushGenerators/blob/master/PoissonDiskGenerator.py
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