如何将n，y，z坐标数组转换为numpy中的3D路径

Question

给定三个X，Y和Z坐标的1D阵列，如何使用numpy转换为3D网格路径？

我设法使用numpy为2D做了这个（即没有for循环）：

import numpy

def path_2d_numpy(x, y):
    m1, m2 = numpy.meshgrid(x, y)
    m1[1::2] = m1[1::2,::-1]
    r = numpy.append(m1, m2)
    r.shape = 2,-1
    return r.T

from matplotlib import lines
from matplotlib import pyplot

def plot_path_2d(path):
    x, y = path.T
    pyplot.plot(x, y, '-ro', lw=3)
    pyplot.show()

x = numpy.linspace(4, 1, 4)
y = numpy.linspace(1, 5, 5)
path = path_2d_numpy(x, y)
plot_path_2d(path)

输出：

...但是无法为3D做到这一点。显示纯python解决方案（即没有numpy）：

import numpy

def path_3d(x, y, z):
    nb_points =len(x)*len(y)*len(z)
    path = numpy.empty((nb_points, 3))

    xord, yord, i = True, True, 0
    for zi in z:
        for yi in y[::1 if yord else -1]:
            for xi in x[::1 if xord else -1]:
                path[i] = xi, yi, zi
                i += 1
            xord = not xord
        yord = not yord
    return path

from matplotlib import pyplot
from mpl_toolkits.mplot3d import Axes3D

def plot_path_3d(path):
    fig = pyplot.figure()
    ax = fig.gca(projection='3d')
    xx, yy, zz = path.T
    ax.plot(xx, yy, zz, '-bo', lw=3)
    pyplot.show()

x = numpy.linspace(4, 1, 4)
y = numpy.linspace(1, 5, 5)
z = numpy.linspace(-3, 0, 3)

path = path_3d(x, y, z)
plot_path_3d(path)

输出：

Essencialy，我正在寻找的是 path_3d 的numpy实现，正如我为 path_2d_numpy 所做的那样。

我需要这个，因为我正在处理的实际数组非常大。没有numpy这样做太慢了。

Answer 1

这看起来怎么样？

import numpy as np

def path_3d_numpy(x, y, z):
    coords = np.stack(np.meshgrid(x, y, z), axis=-1)  # shape = (nx, ny, nz, 3)
    coords[1::2,:,:] = coords[1::2,::-1,:]
    coords[:,1::2,:] = coords[:,1::2,::-1]
    return coords.reshape(-1, 3)  # flatten out the other axes

不会以与你的顺序相同的顺序迭代这些点，但你可以简单地通过交换一些索引来解决这个问题

同样，您的2d案例可以写成

def path_2d_numpy(x, y):
    coords = np.stack(np.meshgrid(x, y), axis=-1)
    coords[1::2] = coords[1::2,::-1]
    return coords.reshape(-1, 2)

对于某些真正的矫枉过正，您可以将其扩展为N维：

def path_nd(*args):
    coords = np.stack(np.meshgrid(*args), axis=-1)
    N = len(args)

    axes = np.arange(N)
    for i in range(N-1):
        # the last axis isn't part of our mesh, so don't roll it
        rolled_axes = tuple(np.roll(axes, -i)) + (N,)
        rolled_view = np.transpose(coords, rolled_axes)
        rolled_view[1::2,:] = rolled_view[1::2,::-1]

    return coords.reshape(-1, N)