Matplotlib 3D

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• Author: Diego Inácio
• GitHub: github.com/diegoinacio
• Notebook: matplotlib_3D.ipynb

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Examples of 3D visualization using Matplotlib.

[PT-BR content]

%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np

plt.rcParams['figure.figsize'] = (16, 8)

3D

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Exemplos de visualização em 3D.

• Contorno 3D: Visualização de superfície e contorno sobre os três eixo, representados pela equação:

$$ \large z=(1 - x + yx^3 + y^5)e^{-x^2-y^2} $$

• Superformula 3D: Visualização de forma complexa descrita pela equação da Superformula, em coordenadas polares:

$$ \large r(\varphi)=\left( \left\lvert \frac{\cos\left(\frac{m\varphi}{4}\right)}{a} \right\rvert^{n_2}+ \left\lvert \frac{\sin\left(\frac{m\varphi}{4}\right)}{b} \right\rvert^{n_3} \right)^{-\frac{1}{n_1}} $$

Sendo r o raio e $\varphi$ o ângulo. Os parâmetros a, b, m, $n_1$, $n_2$, $n_3$ podem ser modificados, para obter diferentes formas. As coordenadas cartesianas podem ser definidas por:

$$ \large \begin{aligned} x &= r_1(\phi)\cos(\phi)\cdot r_2(\theta)\sin(\theta) \\ y &= r_1(\phi)\sin(\phi)\cdot r_2(\theta)\sin(\theta) \\ z &= r_2(\theta)\cos(\theta) \end{aligned} $$

Sendo $\phi$ a altura e $\theta$ o azimute.

# Dados para Contorno 3D
M, N = 32j, 32j
Y, X = np.mgrid[-3:3:N*8, -3:3:M*8]
Z = (1 - X + Y*X**3 + Y**5)*np.exp(-X**2 - Y**2)

# Dados para Superformula 3D
N = 256j
# Coordenada polar
phi, theta = np.mgrid[0:2*np.pi:N, 0:np.pi:N]
a1, b1, m1, n11, n12, n13 = 1, 1, 9, 3.4, 4.5, 5.3
r1 = (np.absolute(np.cos(m1*phi/4)/a1)**n12 + np.absolute(np.sin(m1*phi/4)/b1)**n13)**(-1/n11)
a2, b2, m2, n21, n22, n23 = 1, 1, 24, 2, 4, 2
r2 = (np.absolute(np.cos(m2*theta/4)/a2)**n22 + np.absolute(np.sin(m2*theta/4)/b2)**n23)**(-1/n21)
# Coordenada cartesiana
x = r1*np.cos(phi)*r2*np.sin(theta)
y = r1*np.sin(phi)*r2*np.sin(theta)
z = r2*np.cos(theta)

# Parâmetros de visualização
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import LightSource

dist = (x**2 + y**2 + z**2)**0.5
dist = (dist - dist.min())/(dist.max() - dist.min())

light = LightSource(altdeg=45, azdeg=315)
light_surface = light.shade(dist, cmap=cm.plasma,
                            blend_mode='soft', vert_exag=10)

def defineGrid(ax, lX, lY, lZ):
    # define limites
    ax.set_xlim(lX)
    ax.set_ylim(lY)
    ax.set_zlim(lZ)
    # remove pane
    ax.w_xaxis.pane.set_alpha(0)
    ax.w_yaxis.pane.set_alpha(0)
    ax.w_zaxis.pane.set_alpha(0)
    # altera grid
    ax.w_xaxis.gridlines.set_alpha(0.5)
    ax.w_yaxis.gridlines.set_alpha(0.5)
    ax.w_zaxis.gridlines.set_alpha(0.5)
    # remove spines
    ax.w_xaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
    ax.w_yaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
    ax.w_zaxis.line.set_color((1.0, 1.0, 1.0, 0.0))

%%time
fig, (axA, axB) = plt.subplots(1, 2, subplot_kw={'projection': '3d'})

# Contorno 3D
axA.view_init(30, -30)
axA.plot_surface(X, Y, Z, lw=1, cmap='jet', rstride=2, cstride=2, alpha=0.75)
axA.contour(X, Y, Z, 8, zdir='x', cmap='jet', offset=X.min() - 1)
axA.contour(X, Y, Z, 8, zdir='y', cmap='jet', offset=Y.max() + 1)
axA.contour(X, Y, Z, 16, zdir='z', cmap='jet', offset=Z.min() - 0.1)
axA.set_title('Contorno 3D')
defineGrid(axA,
           [X.min() - 1, X.max() + 1],
           [Y.min() - 1, Y.max() + 1],
           [Z.min() - 0.1, Z.max() + 0.1])

# Superformula 3D
axB.plot_surface(x, y, z,  rstride=2, cstride=2, facecolors=light_surface)
axB.set_title('Superformula 3D')
defineGrid(axB, [-1.5, 1.5], [-1.5, 1.5], [-1.25, 1.25])

plt.show()

Wall time: 7.15 s