matplotlib 3D

# la ration habituelle d'imports
import matplotlib.pyplot as plt
# et aussi numpy, même si ça n'est pas strictement nécessaire
import numpy as np

# même si l'on n'utilise pas explicitement
# d'attributs du module Axes3D
# cet import est nécessaire pour faire
# des visualisations en 3D
from mpl_toolkits.mplot3d import Axes3D

# ce mode d'interaction va nous permettre de nous déplacer
# dans l'espace pour voir les courbes en 3D
# depuis plusieurs points de vue
%matplotlib ipympl

# je choisis une taille raisonnable compte tenu de l'espace
# disponible dans fun-mooc
fig = plt.figure(figsize=(6, 3))

# voici la façon de créer un *subplot*
# qui se prête à une visualisation en 3D
ax = fig.add_subplot(121, projection='3d')

# à présent, copié de
# https://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html#line-plots
# on crée une courbe paramétrique
# où x et y sont fonctions de z
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)
# on fait maitenant un appel à plot normal
# mais avec un troisième paramètre
ax.plot(x, y, z, label='parametric curve')
ax.legend()

# on peut tout à fait ajouter un plot usuel
# dans un subplot, comme on l'a vu pour la 2D
ax2 = fig.add_subplot(122)
x = np.linspace(0, 10)
y = x**2
ax2.plot(x, y)
plt.show()

'''
==============
3D scatterplot
==============

Demonstration of a basic scatterplot in 3D.
'''

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=(4, 4))

def randrange(n, vmin, vmax):
    '''
    Helper function to make an array of random numbers having shape (n, )
    with each number distributed Uniform(vmin, vmax).
    '''
    return (vmax - vmin)*np.random.rand(n) + vmin

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

n = 100

# For each set of style and range settings, plot n random points in the box
# defined by x in [23, 32], y in [0, 100], z in [zlow, zhigh].
for c, m, zlow, zhigh in [('r', 'o', -50, -25), ('b', '^', -30, -5)]:
    xs = randrange(n, 23, 32)
    ys = randrange(n, 0, 100)
    zs = randrange(n, zlow, zhigh)
    ax.scatter(xs, ys, zs, c=c, marker=m)

ax.set_xlabel('X Label')
plt.show()

from mpl_toolkits.mplot3d import axes3d

fig = plt.figure(figsize=(4, 4))

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

# Grab some test data.
X, Y, Z = axes3d.get_test_data(0.05)

# Plot a basic wireframe.
ax.plot_wireframe(X, Y, Z, rstride=10, cstride=10)
plt.show()

'''
======================
3D surface (color map)
======================

Demonstrates plotting a 3D surface colored with the coolwarm color map.
The surface is made opaque by using antialiased=False.

Also demonstrates using the LinearLocator and custom formatting for the
z axis tick labels.
'''

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np

fig = plt.figure(figsize=(4, 4))

# dans le tuto on trouve
# fig, ax = plt.subplots(subplot_kw=dict(projection='3d'))

# personnellement je trouve plus facile à retenir ceci
ax = fig.add_subplot(111, projection='3d')

# Make data.
X = np.arange(-5, 5, 0.25)
Y = np.arange(-5, 5, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)

# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,
                       linewidth=0, antialiased=False)

# Customize the z axis.
ax.set_zlim(-1.01, 1.01)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

'''
========================
3D surface (solid color)
========================

Demonstrates a very basic plot of a 3D surface using a solid color.
'''

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')

# Make data
u = np.linspace(0, 2 * np.pi, 30)
v = np.linspace(0, np.pi, 30)
x = 10 * np.outer(np.cos(u), np.sin(v))
y = 10 * np.outer(np.sin(u), np.sin(v))
z = 10 * np.outer(np.ones(np.size(u)), np.cos(v))

# Plot the surface
ax.plot_surface(x, y, z, color='b')

plt.show()

'''
=========================
3D surface (checkerboard)
=========================

Demonstrates plotting a 3D surface colored in a checkerboard pattern.
'''

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator
import numpy as np

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')

# Make data.
X = np.arange(-5, 5, 0.25)
xlen = len(X)
Y = np.arange(-5, 5, 0.25)
ylen = len(Y)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)

# Create an empty array of strings with the same shape as the meshgrid, and
# populate it with two colors in a checkerboard pattern.
colortuple = ('y', 'b')
colors = np.empty(X.shape, dtype=str)
for y in range(ylen):
    for x in range(xlen):
        colors[x, y] = colortuple[(x + y) % len(colortuple)]

# Plot the surface with face colors taken from the array we made.
surf = ax.plot_surface(X, Y, Z, facecolors=colors, linewidth=0)

# Customize the z axis.
ax.set_zlim(-1, 1)
# 2023 Dec: this line breaks the script, although it's still
# in matplotlib's examples; let's ignore it for now
# ax.w_zaxis.set_major_locator(LinearLocator(6))

plt.show()

'''
======================
Triangular 3D surfaces
======================

Plot a 3D surface with a triangular mesh.
'''

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')

n_radii = 8
n_angles = 36

# Make radii and angles spaces (radius r=0 omitted to eliminate duplication).
radii = np.linspace(0.125, 1.0, n_radii)
angles = np.linspace(0, 2*np.pi, n_angles, endpoint=False)

# Repeat all angles for each radius.
angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)

# Convert polar (radii, angles) coords to cartesian (x, y) coords.
# (0, 0) is manually added at this stage,  so there will be no duplicate
# points in the (x, y) plane.
x = np.append(0, (radii*np.cos(angles)).flatten())
y = np.append(0, (radii*np.sin(angles)).flatten())

# Compute z to make the pringle surface.
z = np.sin(-x*y)

ax.plot_trisurf(x, y, z, linewidth=0.2, antialiased=True)

plt.show()

'''
===========================
More triangular 3D surfaces
===========================

Two additional examples of plotting surfaces with triangular mesh.

The first demonstrates use of plot_trisurf's triangles argument, and the
second sets a Triangulation object's mask and passes the object directly
to plot_trisurf.
'''

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.tri as mtri

fig = plt.figure(figsize=(6, 3))

#============
# First plot
#============

# Make a mesh in the space of parameterisation variables u and v
u = np.linspace(0, 2.0 * np.pi, endpoint=True, num=50)
v = np.linspace(-0.5, 0.5, endpoint=True, num=10)
u, v = np.meshgrid(u, v)
u, v = u.flatten(), v.flatten()

# This is the Mobius mapping, taking a u, v pair and returning an x, y, z
# triple
x = (1 + 0.5 * v * np.cos(u / 2.0)) * np.cos(u)
y = (1 + 0.5 * v * np.cos(u / 2.0)) * np.sin(u)
z = 0.5 * v * np.sin(u / 2.0)

# Triangulate parameter space to determine the triangles
tri = mtri.Triangulation(u, v)

# Plot the surface.  The triangles in parameter space determine which x, y, z
# points are connected by an edge.
ax = fig.add_subplot(1, 2, 1, projection='3d')
ax.plot_trisurf(x, y, z, triangles=tri.triangles, cmap=plt.cm.Spectral)
ax.set_zlim(-1, 1)


#============
# Second plot
#============

# Make parameter spaces radii and angles.
n_angles = 36
n_radii = 8
min_radius = 0.25
radii = np.linspace(min_radius, 0.95, n_radii)

angles = np.linspace(0, 2*np.pi, n_angles, endpoint=False)
angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
angles[:, 1::2] += np.pi/n_angles

# Map radius, angle pairs to x, y, z points.
x = (radii*np.cos(angles)).flatten()
y = (radii*np.sin(angles)).flatten()
z = (np.cos(radii)*np.cos(angles*3.0)).flatten()

# Create the Triangulation; no triangles so Delaunay triangulation created.
triang = mtri.Triangulation(x, y)

# Mask off unwanted triangles.
xmid = x[triang.triangles].mean(axis=1)
ymid = y[triang.triangles].mean(axis=1)
mask = np.where(xmid**2 + ymid**2 < min_radius**2, 1, 0)
triang.set_mask(mask)

# Plot the surface.
ax = fig.add_subplot(1, 2, 2, projection='3d')
ax.plot_trisurf(triang, z, cmap=plt.cm.CMRmap)

plt.show()

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
cset = ax.contour(X, Y, Z, cmap=cm.coolwarm)
ax.clabel(cset, fontsize=9, inline=1)

plt.show()

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
cset = ax.contour(X, Y, Z, extend3d=True, cmap=cm.coolwarm)
ax.clabel(cset, fontsize=9, inline=1)

plt.show()

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3)
cset = ax.contour(X, Y, Z, zdir='z', offset=-100, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='x', offset=-40, cmap=cm.coolwarm)
cset = ax.contour(X, Y, Z, zdir='y', offset=40, cmap=cm.coolwarm)

ax.set_xlabel('X')
ax.set_xlim(-40, 40)
ax.set_ylabel('Y')
ax.set_ylim(-40, 40)
ax.set_zlabel('Z')
ax.set_zlim(-100, 100)

plt.show()

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
cset = ax.contourf(X, Y, Z, cmap=cm.coolwarm)
ax.clabel(cset, fontsize=9, inline=1)

plt.show()

"""
.. versionadded:: 1.1.0
   This demo depends on new features added to contourf3d.
"""

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3)
cset = ax.contourf(X, Y, Z, zdir='z', offset=-100, cmap=cm.coolwarm)
cset = ax.contourf(X, Y, Z, zdir='x', offset=-40, cmap=cm.coolwarm)
cset = ax.contourf(X, Y, Z, zdir='y', offset=40, cmap=cm.coolwarm)

ax.set_xlabel('X')
ax.set_xlim(-40, 40)
ax.set_ylabel('Y')
ax.set_ylim(-40, 40)
ax.set_zlabel('Z')
ax.set_zlim(-100, 100)

plt.show()

"""
=============================================
Generate polygons to fill under 3D line graph
=============================================

Demonstrate how to create polygons which fill the space under a line
graph. In this example polygons are semi-transparent, creating a sort
of 'jagged stained glass' effect.
"""

from mpl_toolkits.mplot3d import Axes3D
from matplotlib.collections import PolyCollection
import matplotlib.pyplot as plt
from matplotlib import colors as mcolors
import numpy as np

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')

def cc(arg):
    return mcolors.to_rgba(arg, alpha=0.6)

xs = np.arange(0, 10, 0.4)
verts = []
zs = [0.0, 1.0, 2.0, 3.0]
for z in zs:
    ys = np.random.rand(len(xs))
    ys[0], ys[-1] = 0, 0
    verts.append(list(zip(xs, ys)))

poly = PolyCollection(verts, facecolors=[cc('r'), cc('g'), cc('b'),
                                         cc('y')])
poly.set_alpha(0.7)
ax.add_collection3d(poly, zs=zs, zdir='y')

ax.set_xlabel('X')
ax.set_xlim3d(0, 10)
ax.set_ylabel('Y')
ax.set_ylim3d(-1, 4)
ax.set_zlabel('Z')
ax.set_zlim3d(0, 1)

plt.show()

"""
========================================
Create 2D bar graphs in different planes
========================================

Demonstrates making a 3D plot which has 2D bar graphs projected onto
planes y=0, y=1, etc.
"""

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')
for c, z in zip(['r', 'g', 'b', 'y'], [30, 20, 10, 0]):
    xs = np.arange(20)
    ys = np.random.rand(20)

    # You can provide either a single color or an array. To demonstrate this,
    # the first bar of each set will be colored cyan.
    cs = [c] * len(xs)
    cs[0] = 'c'
    ax.bar(xs, ys, zs=z, zdir='y', color=cs, alpha=0.8)

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')

plt.show()

'''
==============
3D quiver plot
==============

Demonstrates plotting directional arrows at points on a 3d meshgrid.
'''

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111, projection='3d')

# Make the grid
x, y, z = np.meshgrid(np.arange(-0.8, 1, 0.2),
                      np.arange(-0.8, 1, 0.2),
                      np.arange(-0.8, 1, 0.8))

# Make the direction data for the arrows
u = np.sin(np.pi * x) * np.cos(np.pi * y) * np.cos(np.pi * z)
v = -np.cos(np.pi * x) * np.sin(np.pi * y) * np.cos(np.pi * z)
w = (np.sqrt(2.0 / 3.0) * np.cos(np.pi * x) * np.cos(np.pi * y) *
     np.sin(np.pi * z))

ax.quiver(x, y, z, u, v, w, length=0.1, normalize=True)

plt.show()