我在Python中有一个浮点值的3D numpy数组.
我需要检索半径为r的球体中的所有元素,从
中心点P(x,y,z).然后,我要在球体上应用点函数
更新其值,并需要到中心点的距离才能执行此操作.我经常执行这些步骤,并且
大半径值,所以我想有一个同样有效的解决方案
尽可能.

我当前的解决方案仅检查球体边界框中的点,
如此处所示：Using a QuadTree to get all points within a bounding circle.
代码草图如下所示：

# P(x, y, z): center of the sphere
for k1 in range(x - r, x + r + 1):
    for k2 in range(y - r, y + r + 1):
        for k3 in range(z - r, z + r + 1):
            # Sphere center - current point distance
            dist = np.sum((np.array([k1, k2, k3]) - np.array([x, y, z])) ** 2)

            if (dist <= r * r):
                # computeUpdatedValue(distance, radius): function that computes the new value of the matrix in the current point 
                newValue = computeUpdatedValue(dist, r)

                # Update the matrix
                mat[k1, k2, k3] = newValue

但是,我认为应用遮罩来检索点,然后
基于距离以矢量化方式更新它们的效率更高.
我已经看到了如何应用循环内核
(How to apply a disc shaped mask to a numpy array?),
但是我不知道如何在蒙版的每个元素上有效地应用该函数(取决于索引).

解决方法:

编辑：如果与正在更新的区域相比,您的数组很大,则下面的解决方案将占用比必要更多的内存.您可以将相同的想法应用到球体可能掉落的区域：

def updateSphereBetter(mat, center, radius):
    # Find beginning and end of region of interest
    center = np.asarray(center)
    start = np.minimum(np.maximum(center - radius, 0), mat.shape)
    end = np.minimum(np.maximum(center + radius + 1, 0), mat.shape)
    # Slice region of interest
    mat_sub = mat[tuple(slice(s, e) for s, e in zip(start, end))]
    # Center coordinates relative to the region of interest
    center_rel = center - start
    # Same as before but with mat_sub and center_rel
    ind = np.indices(mat_sub.shape)
    ind = np.moveaxis(ind, 0, -1)
    dist_squared = np.sum(np.square(ind - center_rel), axis=-1)
    mask = dist_squared <= radius * radius
    mat_sub[mask] = computeUpdatedValue(dist_squared[mask], radius)

请注意,由于mat_sub是mat的视图,对其进行更新将更新原始数组,因此这将产生与以前相同的结果,但是资源较少.

这是概念的一点证明.我定义了computeUpdatedValue,以便显示距中心的距离,然后绘制了示例的一些“部分”：

import numpy as np
import matplotlib.pyplot as plt

def updateSphere(mat, center, radius):
    # Make array of all index coordinates
    ind = np.indices(mat.shape)
    # Compute the squared distances to each point
    ind = np.moveaxis(ind, 0, -1)
    dist_squared = np.sum(np.square(ind - center), axis=-1)
    # Make a mask for squared distances within squared radius
    mask = dist_squared <= radius * radius
    # Update masked values
    mat[mask] = computeUpdatedValue(dist_squared[mask], radius)

def computeUpdatedValue(dist_squared, radius):
    # 1 at the center of the sphere and 0 at the surface
    return np.clip(1 - np.sqrt(dist_squared) / radius, 0, 1)

mat = np.zeros((100, 60, 80))
updateSphere(mat, [50, 20, 40], 20)

plt.subplot(131)
plt.imshow(mat[:, :, 30], vmin=0, vmax=1)
plt.subplot(132)
plt.imshow(mat[:, :, 40], vmin=0, vmax=1)
plt.subplot(133)
plt.imshow(mat[:, :, 55], vmin=0, vmax=1)

输出：