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"""

============================

Draw flat objects in 3D plot

============================

Demonstrate using `.pathpatch_2d_to_3d` to 'draw' shapes and text on a 3D plot.

"""

import matplotlib.pyplot as plt

import numpy as np

from matplotlib.patches import Circle, PathPatch

from matplotlib.text import TextPath

from matplotlib.transforms import Affine2D

import mpl_toolkits.mplot3d.art3d as art3d

def text3d(ax, xyz, s, zdir="z", size=None, angle=0, usetex=False, **kwargs):

"""

Plots the string *s* on the Axes *ax*, with position *xyz*, size *size*,

and rotation angle *angle*. *zdir* gives the axis which is to be treated as

the third dimension. *usetex* is a boolean indicating whether the string

should be run through a LaTeX subprocess or not. Any additional keyword

arguments are forwarded to `.transform_path`.

Note: zdir affects the interpretation of xyz.

"""

x, y, z = xyz

if zdir == "y":

xy1, z1 = (x, z), y

elif zdir == "x":

xy1, z1 = (y, z), x

else:

xy1, z1 = (x, y), z

text_path = TextPath((0, 0), s, size=size, usetex=usetex)

trans = Affine2D().rotate(angle).translate(xy1[0], xy1[1])

p1 = PathPatch(trans.transform_path(text_path), **kwargs)

ax.add_patch(p1)

art3d.pathpatch_2d_to_3d(p1, z=z1, zdir=zdir)

fig = plt.figure()

ax = fig.add_subplot(projection='3d')

# Draw a circle on the x=0 'wall'

p = Circle((5, 5), 3)

ax.add_patch(p)

art3d.pathpatch_2d_to_3d(p, z=0, zdir="x")

# Manually label the axes

text3d(ax, (4, -2, 0), "X-axis", zdir="z", size=.5, usetex=False,

ec="none", fc="k")

text3d(ax, (12, 4, 0), "Y-axis", zdir="z", size=.5, usetex=False,

angle=np.pi / 2, ec="none", fc="k")

text3d(ax, (12, 10, 4), "Z-axis", zdir="y", size=.5, usetex=False,

angle=np.pi / 2, ec="none", fc="k")

# Write a Latex formula on the z=0 'floor'

text3d(ax, (1, 5, 0),

r"$\displaystyle G_{\mu\nu} + \Lambda g_{\mu\nu} = "

r"\frac{8\pi G}{c^4} T_{\mu\nu} $",

zdir="z", size=1, usetex=True,

ec="none", fc="k")

ax.set_xlim(0, 10)

ax.set_ylim(0, 10)

ax.set_zlim(0, 10)

plt.show()