How are x,y,z coordinates defined for Mayavi's mlab.mesh? - enthought

Question

I'm trying to create a 3D box which would appear in a Mayavi mlab.points3d plot.
I figure this should be possible using the mlab.mesh function, something like this:
points = mlab.points3d(xp,yp,zp,sp)
3Dbox = mlab.mesh(xbox,ybox,zbox)
mlab.show()
I've looked at the mlab manual entry for mesh, but for the life of me can't understand how the x, y, z data points for the mesh are defined.
Could anyone enlighten me please? An example of the x,y,z data points for a 3D box would be particularly appreciated.

Answer 1

You can see that like 3D array split in 3 matrix for x, y and z axes. Each matrix index will depict a coordinates and each points of this coordinates will be connected with this neighbors. So you can start by define 6 planes to make your box :
import numpy
import mayavi.mlab
# pt1_ _ _ _ _ _ _ _ _pt2
# /| /|
# / | / |
# pt3/_ | _ _ _ _ _ _pt4/ |
# | | | |
# | | | |
# | pt5_ _ _ _ _ _ _|_ _|pt6
# | / | /
# | / | /
# pt7|/_ _ _ _ _ _ _ _ _|/pt8
# Where :
x1, y1, z1 = (0, 1, 1) # | => pt1
x2, y2, z2 = (1, 1, 1) # | => pt2
x3, y3, z3 = (0, 0, 1) # | => pt3
x4, y4, z4 = (1, 0, 1) # | => pt4
x5, y5, z5 = (0, 1, 0) # | => pt5
x6, y6, z6 = (1, 1, 0) # | => pt6
x7, y7, z7 = (0, 0, 0) # | => pt7
x8, y8, z8 = (1, 0, 0) # | => pt8
box_points = numpy.array([[x1, y1, z1], [x2, y2, z2], [x3, y3, z3],
[x4, y4, z4], [x5, y5, z5], [x6, y6, z6],
[x7, y7, z7], [x8, y8, z8]])
mayavi.mlab.points3d(box_points[:, 0], box_points[:, 1], box_points[:, 2],
mode="axes", color=(1, 0, 0))
mayavi.mlab.mesh([[x1, x2],
[x3, x4]], # | => x coordinate
[[y1, y2],
[y3, y4]], # | => y coordinate
[[z1, z2],
[z3, z4]], # | => z coordinate
color=(0, 0, 0)) # black
# Where each point will be connected with this neighbors :
# (link = -)
#
# x1 - x2 y1 - y2 z1 - z2 | => pt1 - pt2
# - - and - - and - - | => - -
# x3 - x4 y3 - y4 z3 - z4 | => pt3 - pt4
mayavi.mlab.mesh([[x5, x6], [x7, x8]],
[[y5, y6], [y7, y8]],
[[z5, z6], [z7, z8]],
color=(1, 0, 0)) # red
mayavi.mlab.mesh([[x1, x3], [x5, x7]],
[[y1, y3], [y5, y7]],
[[z1, z3], [z5, z7]],
color=(0, 0, 1)) # blue
mayavi.mlab.mesh([[x1, x2], [x5, x6]],
[[y1, y2], [y5, y6]],
[[z1, z2], [z5, z6]],
color=(1, 1, 0)) # yellow
mayavi.mlab.mesh([[x2, x4], [x6, x8]],
[[y2, y4], [y6, y8]],
[[z2, z4], [z6, z8]],
color=(1, 1, 1)) # white
mayavi.mlab.mesh([[x3, x4], [x7, x8]],
[[y3, y4], [y7, y8]],
[[z3, z4], [z7, z8]],
color=(1, 0, 1)) # pink
mayavi.mlab.show()
Otherwise, you can also make mesh who show in on go more faces with one call.
With two call to mayavi.mlab.mesh :
# Define 2 mesh objects with 3 planes connected among themselves :
#
# pt1 - pt2 - pt6 pt8 - pt6 - pt2
# - - - - - -
# pt3 - pt4 - pt8 AND pt7 pt5 - pt1
# - - - - - -
# pt7 - pt8 - pt8 pt3 - pt1 - pt1
mayavi.mlab.figure()
mayavi.mlab.mesh([[x1, x2, x6], [x3, x4, x8], [x7, x8, x8]],
[[y1, y2, y6], [y3, y4, y8], [y7, y8, y8]],
[[z1, z2, z6], [z3, z4, z8], [z7, z8, z8]],
color=(1, 0, 0)) # red
mayavi.mlab.mesh([[x8, x6, x2], [x7, x5, x1], [x3, x1, x1]],
[[y8, y6, y2], [y7, y5, y1], [y3, y1, y1]],
[[z8, z6, z2], [z7, z5, z1], [z3, z1, z1]],
color=(0, 0, 1)) # blue
mayavi.mlab.show()
With one call to mayavi.mlab.mesh:
# Merge previous mesh objects in single one:
#
# pt1 - pt2 - pt6 | => pt1 - pt2 - pt6 - pt6 - pt6
# - - - | => - - - - -
# pt3 - pt4 - pt8 | => pt3 - pt4 - pt8 - pt6 - pt2
# - - - | => - - - - -
# pt7 - pt8 - pt8 - pt6 - pt2 | => pt7 - pt8 - pt8 - pt6 - pt2
# - - - | => - - - - -
# pt7 pt5 - pt1 | => pt7 - pt7 - pt7 pt5 - pt1
# - - - | => - - - - -
# pt3 - pt1 - pt1 | => pt7 - pt3 - pt3 - pt1 - pt1
mayavi.mlab.figure()
mayavi.mlab.mesh([[x1, x2, x6, x6, x6],
[x3, x4, x8, x6, x2],
[x7, x8, x8, x6, x2],
[x7, x7, x7, x5, x1],
[x7, x3, x3, x1, x1]],
[[y1, y2, y6, y6, y6],
[y3, y4, y8, y6, y2],
[y7, y8, y8, y6, y2],
[y7, y7, y7, y5, y1],
[y7, y3, y3, y1, y1]],
[[z1, z2, z6, z6, z6],
[z3, z4, z8, z6, z2],
[z7, z8, z8, z6, z2],
[z7, z7, z7, z5, z1],
[z7, z3, z3, z1, z1]])
mayavi.mlab.show()