Map an array of indexes to an array of coordinates

Question

I'm playing a bit with scikit-image marching cubes algorithm. Here is a simplified version of the example given in the docs.

from matplotlib import pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from skimage import measure


x = np.linspace(-1, 1, 11)

X, Y, Z = np.meshgrid(x, x, x, indexing = 'ij')

def f(x, y, z):
    return x

verts, faces = measure.marching_cubes(f(X, Y, Z), 0.6)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

mesh = Poly3DCollection(verts[faces])
ax.add_collection3d(mesh)

ax.set_xlim(0, 10)
ax.set_ylim(0, 10)
ax.set_zlim(0, 10)

plt.show()

Here is the resulting surface:

It appears that coordinates of vertices are given in terms of array index rather than coordinates of the meshgrid. How can I transform the coordinates of vertices so that they map to the meshgrid, like in the image below?

I can do that by hand:

mesh = Poly3DCollection((verts[faces] / 5) - 1)

but there must be some numpy magic here.

Thanks.

B. M. · Accepted Answer · 2015-12-06 12:03:56Z

2

IMHO, no magic here. There is no 'plug and play' transformations in mplot3d.

for automation, you can just make your 'by hand' job with a function :

from matplotlib import pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from skimage import measure

x=y=z= np.linspace(-1, 1, 11)

grid=np.meshgrid(x,y,z)

def f(x, y, z):
    return x*x+y*y+z*z   # more fun ;)

def scale_marching(x,verts):
    return x[0]+ (x[-1]-x[0])/len(x)*verts

verts, faces = measure.marching_cubes(f(*grid), 1.5)    
verts=scale_marching(x,verts)

ax = plt.figure().add_subplot(111, projection='3d') 
ax.add_collection3d(Poly3DCollection(verts[faces]))
ax.auto_scale_xyz(*grid)

edited Dec 6, 2015 at 12:03

answered Dec 5, 2015 at 20:51

B. M.

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1 Comment

cjorssen Over a year ago

This is what I've done (more general)

def scale_marching(verts, x, y, z):     verts[:,0] = x[0] + (x[-1] - x[0]) / (len(x) - 1) * verts[:,0]     verts[:,1] = y[0] + (y[-1] - y[0]) / (len(y) - 1) * verts[:,1]     verts[:,2] = z[0] + (z[-1] - z[0]) / (len(z) - 1) * verts[:,2]

. Note len(x) - 1.

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