3D parametric curve in Matplotlib does not respect zorder. Workaround?

Question

I am designing a three-dimensional illustration using Matplotlib. All is working nicely, except that the (red) parametric curve gets the wrong zorder while the (green) parametric surface is drawn completely correctly.

Output generated by code below:

I know that Matplotlib has limited capabilities for accurately computing the zorder of objects, but since it can do it for the parametric surface, it seems like a bug in Matplotlib.

That said, is there any way to force correct z-ordering just to get things to work quickly? It seems that all I have to be able to say is that the right transparent blue plane is on top of everything else. However, putting a zorder argument into PolyCollection does not seem to have any effect, and putting an explicit zorder argument into the plot function which draws the read line will mess up its ordering relative to the green surface.

Is there a way to force the right blue transparent surface on top of everything? Here is the code I have so far:

#!/bin/env python3

from pylab import *
from mpl_toolkits.mplot3d import *

from matplotlib.collections import PolyCollection
from matplotlib.colors import colorConverter
from matplotlib.patches import FancyArrowPatch

rc('text', usetex=True)
rc('font', size=20)

fig = figure(figsize=(11,6))
ax = fig.gca(projection='3d')

ax.set_axis_off()

def f(x,t):
    return t/2 * 0.55*(sin(2*x)+0.4*x**2-0.65)

c_plane   = colorConverter.to_rgba('b', alpha=0.15)

N = 50
y = linspace(-1,1,N)
t = linspace(0,2,N)
yy, tt = meshgrid(y, t)
zz = f(yy,tt)

ax.plot(0*ones(y.shape), y, f(y,0), '-g', linewidth=3)
ax.plot(2*ones(y.shape), y, f(y,2), '-g', linewidth=3)

yt = 0.7*y
zt = f(yt, t) + 0.2*t

ax.plot(t, yt, zt, '-r', linewidth=3)
ax.plot((0,2), (yt[0], yt[-1]), (zt[0], zt[-1]), 'or')

ax.plot([2,2,2], [-1,yt[-1],yt[-1]], [zt[-1],zt[-1],-1], 'k--')
ax.plot(2*ones(y.shape), yt, f(yt,2)+0.1*(y+1), 'g:', linewidth=2)
ax.plot((2,2),
(yt[0], yt[-1]),
(f(yt[0], 2), f(yt[-1], 2) + 0.1*(y[-1]+1)), 'og')
ax.plot((0,2,2),
(-1,-1,zt[-1]),
(0,yt[-1],-1), 'ok')

ax.text(0, -1.1, 0, r'$p(0)=0$', ha='right', va='center')
ax.text(2, -1.05, zt[-1], r'$p(T)$', ha='right', va='center')
ax.text(0, -1.0, 1, r'$p$', ha='right', va='bottom')
ax.text(0, 1, -1.1, r'$q$', ha='center', va='top')
ax.text(0, -1, -1.1, r'$t=0$', ha='right', va='top')
ax.text(2, -1, -1.1, r'$t=T$', ha='right', va='top')
ax.text(2, yt[-1]-0.05, -1.05, r'$q(T)=q^*$', ha='left', va='top')
ax.text(0, 0.5, 0.05, r'$\mathcal{M}(0)$', ha='center', va='bottom')
ax.text(2, 0.1, -0.8, r'$\mathcal{M}(T)$', ha='center', va='bottom')

arrowprops = dict(mutation_scale=20,
linewidth=2,
arrowstyle='-|>',
color='k')

# For arrows, see
# https://stackoverflow.com/questions/29188612/arrows-in-matplotlib-using-mplot3d
class Arrow3D(FancyArrowPatch):
    def __init__(self, xs, ys, zs, *args, **kwargs):
        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
        self._verts3d = xs, ys, zs

    def draw(self, renderer):
        xs3d, ys3d, zs3d = self._verts3d
        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
        FancyArrowPatch.draw(self, renderer)

a = Arrow3D([0,2], [-1,-1], [-1,-1], **arrowprops)
ax.add_artist(a)
a = Arrow3D([0,0], [-1,-1], [-1,1], **arrowprops)
ax.add_artist(a)
a = Arrow3D([0,0], [-1,1], [-1,-1], **arrowprops)
ax.add_artist(a)

# For surface illumination, see
# http://physicalmodelingwithpython.blogspot.de/2015/08/illuminating-surface-plots.html

# Get lighting object for shading surface plots.
from matplotlib.colors import LightSource

# Get colormaps to use with lighting object.
from matplotlib import cm

# Create an instance of a LightSource and use it to illuminate the surface.
light = LightSource(70, -120)
white = np.ones((zz.shape[0], zz.shape[1], 3))
illuminated_surface = light.shade_rgb(white*(0,1,0), zz)

ax.plot_surface(tt, yy, zz,
cstride=1, rstride=1,
alpha=0.3, facecolors=illuminated_surface,
linewidth=0)

verts = [array([(-1,-1), (-1,1), (1,1), (1,-1), (-1,-1)])]

poly = PolyCollection(verts, facecolors=c_plane)
ax.add_collection3d(poly, zs=[0], zdir='x')
poly = PolyCollection(verts, facecolors=c_plane)
ax.add_collection3d(poly, zs=[2], zdir='x')

ax.set_xlim3d(0, 2)
ax.view_init(elev=18, azim=-54)

show()

Answer 1

Axes3D ignores zorder and draws all artists in the order it thinks they should be. However, you may set zorder=0 for red line and zorder=-1 for green surface (or vice-versa) to put they behind right blue panel.

My result:

You have to know:

The default drawing order for axes is patches, lines, text. This order is determined by the zorder attribute. The following defaults are set

Artist Z-order

Patch / PatchCollection 1

Line2D / LineCollection 2

Text 3

Answer 2

A way of changing the drawing order for plots using axis3d was added in Matplotlib 3.5.0. Setting the parameter 'computed_zorder' False allows manual control of the drawing order

ax = plt.axes(projection='3d',computed_zorder=False)
ax.plot_surface(X1, Y1, Z1,zorder=4.4)
ax.plot_surface(X2, Y2, Z2,zorder=4.5)

Higher 'zorders' are plotted on top. Some common artist z-orders (so you don't plot over your legend):

Artist	Z-order
Images (AxesImage, FigureImage, BboxImage)	0
Patch, PatchCollection	1
Line2D, LineCollection (including minor ticks, grid lines)	2
Major ticks	2.01
Text (including axes labels and titles)	3
Legend	5

From: https://matplotlib.org/stable/gallery/misc/zorder_demo.html

Source: https://github.com/matplotlib/matplotlib/commit/2db6a0429af47102456366f8d3a4df24352b252e (from: https://github.com/matplotlib/matplotlib/pull/14508)

Answer 3

After some more trial and error, I found a solution. If the right plane is drawn using plot_surface and I change the zorder on the red curve, matplotlib gets the overall order of objects right. Funny enough, the color of the planes changes slightly whether I draw them via PolyCollection or plot_surface, so I need to draw both planes using the same function. So the zorder handling of mplot3d is rather inconsistent, but the final result looks pretty good. I post it here for reference

with final code here:

#!/bin/env python3

from pylab import *
from mpl_toolkits.mplot3d import *

from matplotlib.collections import PolyCollection
from matplotlib.colors import colorConverter
from matplotlib.patches import FancyArrowPatch

rc('text', usetex=True)
rc('font', size=20)

fig = figure(figsize=(11,6))
ax = fig.gca(projection='3d')

ax.set_axis_off()

def f(x,t):
    return t/2 * 0.55*(sin(2*x)+0.4*x**2-0.65)

c_plane   = colorConverter.to_rgba('b', alpha=0.15)

N = 50
y = linspace(-1,1,N)
t = linspace(0,2,N)
yy, tt = meshgrid(y, t)
zz = f(yy,tt)

ax.plot(0*ones(y.shape), y, f(y,0), '-g', linewidth=3)
ax.plot(2*ones(y.shape), y, f(y,2), '-g', linewidth=3)

yt = 0.7*y
zt = f(yt, t) + 0.2*t

ax.plot(t, yt, zt, '-r', linewidth=3, zorder = 1)

ax.plot([2,2,2], [-1,yt[-1],yt[-1]], [zt[-1],zt[-1],-1], 'k--')
ax.plot(2*ones(y.shape), yt, f(yt,2)+0.1*(y+1), 'g:', linewidth=2)
ax.plot((2,2),
        (yt[0], yt[-1]),
        (f(yt[0], 2), f(yt[-1], 2) + 0.1*(y[-1]+1)), 'og')
ax.plot((0,2,2),
        (-1,-1,zt[-1]),
        (0,yt[-1],-1), 'ok')

ax.text(0, -1.1, 0, r'$p(0)=0$', ha='right', va='center')
ax.text(2, -1.05, zt[-1], r'$p(T)$', ha='right', va='center')
ax.text(0, -1.0, 1, r'$p$', ha='right', va='bottom')
ax.text(0, 1, -1.1, r'$q$', ha='center', va='top')
ax.text(0, -1, -1.1, r'$t=0$', ha='right', va='top')
ax.text(2, -1, -1.1, r'$t=T$', ha='right', va='top')
ax.text(2, yt[-1]-0.05, -1.05, r'$q(T)=q^*$', ha='left', va='top')
ax.text(0, 0.5, 0.05, r'$\mathcal{M}(0)$', ha='center', va='bottom')
ax.text(2, 0.1, -0.8, r'$\mathcal{M}(T)$', ha='center', va='bottom')

arrowprops = dict(mutation_scale=20,
                  linewidth=2,
                  arrowstyle='-|>',
                  color='k')

# For arrows, see
# https://stackoverflow.com/questions/29188612/arrows-in-matplotlib-using-mplot3d
class Arrow3D(FancyArrowPatch):
    def __init__(self, xs, ys, zs, *args, **kwargs):
        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
        self._verts3d = xs, ys, zs

    def draw(self, renderer):
        xs3d, ys3d, zs3d = self._verts3d
        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
        FancyArrowPatch.draw(self, renderer)

a = Arrow3D([0,2], [-1,-1], [-1,-1], **arrowprops)
ax.add_artist(a)
a = Arrow3D([0,0], [-1,-1], [-1,1], **arrowprops)
ax.add_artist(a)
a = Arrow3D([0,0], [-1,1], [-1,-1], **arrowprops)
ax.add_artist(a)

# For surface illumination, see
# http://physicalmodelingwithpython.blogspot.de/2015/08/illuminating-surface-plots.html

# Get lighting object for shading surface plots.
from matplotlib.colors import LightSource

# Get colormaps to use with lighting object.
from matplotlib import cm

# Create an instance of a LightSource and use it to illuminate the surface.
light = LightSource(70, -120)
white = ones((zz.shape[0], zz.shape[1], 3))
illuminated_surface = light.shade_rgb(white*(0,1,0), zz)

ax.plot_surface(tt, yy, zz,
                cstride=1, rstride=1,
                alpha=0.3, facecolors=illuminated_surface,
                linewidth=0,
                zorder=10)

verts = [array([(-1,-1), (-1,1), (1,1), (1,-1), (-1,-1)])]

ax.plot_surface(((0,0),(0,0)), ((-1,-1),(1,1)), ((-1,1),(-1,1)),
                color=c_plane)

ax.plot_surface(((2,2),(2,2)), ((-1,-1),(1,1)), ((-1,1),(-1,1)),
                color=c_plane)

ax.plot((0,2), (yt[0], yt[-1]), (zt[0], zt[-1]), 'or')

ax.set_xlim3d(0, 2)
ax.view_init(elev=18, azim=-54)

show()