How to extract a plane from a 3D variable in FiPy (3D to 2D)

问题

I have a variable on a 3D mesh and I am trying to cut a plan. I am surprised this question hasn't been asked before, it looks an easy and common problem but I haven't found any good way. I would appreciate any advice.

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Let's say that I have a parallelepiped 3x3x5 and that I am trying to extract a z-plane.

from fipy import *
from numpy import *
#Describes a 3x3x5 mesh
nx = 3
ny = 3
nz = 5

dx = 1
dy = 1
dz = 1

#Creates a 3D mesh and a 2D mesh to store the plane
mesh3D = Grid3D(dx, dy, dz, nx, ny, nz)
mesh2D = Grid2D(dx, dy, nx, ny)
#Defines the same variable, in 3D and in 2D
var2D = CellVariable(mesh = mesh2D)
var3D = CellVariable(mesh = mesh3D)

#Fills the 3D matrix
for i in xrange(nx*ny*nz*dx*dy*dz):
    var3D[i] = i

print var3D

Output:

[  0.   1.   2.   3.   4.   5.   6.   7.   8.   9.  10.  11.  12.  13.  14.  15.  16.  17.  18.  19.  20.  21.  22.  23.  24.  25.  26.  27.  28.  29.  30.  31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.]

The 3D variable looks correctly filled.

First, I tried to use the way described at this link http://permalink.gmane.org/gmane.comp.python.fipy/1576

The call method of a CellVariable enables interpolation to a set of coordinates passed in via the call method (the call method is just accessed using parentheses like in a function call). It returns a set of values for corresponding to each of the coordinates that were passed in. The order argument just determines the order of the interpolation.

I am not sure of how this actual works, but from what I understand this should interpolate a single plane with 0 order, so it should extract the exact value on a specific plane. Please correct me if I am wrong.

x3D, y3D, z3D = mesh3D.getCellCenters()
x2D, y2D =  mesh2D.getCellCenters()

for zcut in xrange(nz*dz):
    var2D.setValue(var3D((x2D, y2D, zcut * ones(var2D.getMesh().getNumberOfCells())), order=0))
    print "z-plane = %d" % zcut
    print var2D

raw_input("Press any key to close")

Strangely it doesn't work. The even indexes are ok but the odd ones are a copy of the contiguous planes.

z-plane = 0
[ 0.  1.  2.  3.  4.  5.  6.  7.  8.]
z-plane = 1
[ 0.  1.  2.  3.  4.  5.  6.  7.  8.]
z-plane = 2
[ 18.  19.  20.  21.  22.  23.  24.  25.  26.]
z-plane = 3
[ 18.  19.  20.  21.  22.  23.  24.  25.  26.]
z-plane = 4
[ 36.  37.  38.  39.  40.  41.  42.  43.  44.]

I think there must be a stupid mistake somewhere, but I have no clue. Any idea?

回答1:

The cell centers are located at z=0.5, 1.5, 2.5, ... so FiPy is doing it's best to find the nearest cells to z=0, 1, 2, ...

Try

var2D.setValue(var3D((x2D, y2D, 
                      zcut * ones(var2D.mesh.numberOfCells) + dx/2.), order=0))

来源：https://stackoverflow.com/questions/29863958/how-to-extract-a-plane-from-a-3d-variable-in-fipy-3d-to-2d