How to convert arrays of x,y,z coordinates to 3D path in numpy

Question

Given three 1D arrays of X, Y and Z coordinates, how to convert into a 3D mesh path using numpy?

I managed to do this for 2D using numpy (ie no for loops):

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)

which outputs:

...but was unable to do it for 3D. Showing pure python solution (ie without 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)

which outputs:

Essencialy, what I am looking for is for a numpy implementation of path_3d as I did for path_2d_numpy.

I need this because the actual arrays I am dealing with are quite big. Doing it without numpy is just too slow.

Answer 1

How's this look?

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

Doesn't iterate the points in quite the same order as yours, but you could fix that simply by swapping some indices around

---

Similarly, your 2d case could be written as

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)

---

For some real overkill, you can extend this to N dimensions:

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)