Frecce in matplotlib utilizzando mplot3d

Question

Sto cercando di utilizzare matplotlib per ricreare lo schema in questa pagina: http://books.google.co.uk/books?id=sf9Qn9MS0ykC&pg=PA18

Ecco quello che ho finora:

import numpy as np 
from matplotlib import pyplot as plt 
from mpl_toolkits.mplot3d import Axes3D 
from matplotlib.patches import FancyArrowPatch 
from mpl_toolkits.mplot3d import proj3d 

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) 

def Rx(phi): 
    return np.array([[1, 0, 0], 
        [0, np.cos(phi), -np.sin(phi)], 
        [0, np.sin(phi), np.cos(phi)]]) 

def Ry(theta): 
    return np.array([[np.cos(theta), 0, np.sin(theta)], 
        [0, 1, 0], 
        [-np.sin(theta), 0, np.cos(theta)]]) 

def Rz(psi): 
    return np.array([[np.cos(psi), -np.sin(psi), 0], 
        [np.sin(psi), np.cos(psi), 0], 
        [0, 0, 1]]) 

# define origin 
o = np.array([0,0,0]) 

# define ox0y0z0 axes 
x0 = np.array([1,0,0]) 
y0 = np.array([0,1,0]) 
z0 = np.array([0,0,1]) 

# define ox1y1z1 axes 
psi = 20 * np.pi/180 
x1 = Rz(psi).dot(x0) 
y1 = Rz(psi).dot(y0) 
z1 = Rz(psi).dot(z0) 

# define ox2y2z2 axes 
theta = 10 * np.pi/180 
x2 = Rz(psi).dot(Ry(theta)).dot(x0) 
y2 = Rz(psi).dot(Ry(theta)).dot(y0) 
z2 = Rz(psi).dot(Ry(theta)).dot(z0) 

# define ox3y3z3 axes 
phi = 30 * np.pi/180 
x3 = Rz(psi).dot(Ry(theta)).dot(Rx(phi)).dot(x0) 
y3 = Rz(psi).dot(Ry(theta)).dot(Rx(phi)).dot(y0) 
z3 = Rz(psi).dot(Ry(theta)).dot(Rx(phi)).dot(z0) 

# produce figure 
fig = plt.figure() 
ax = fig.add_subplot(111, projection='3d') 

# plot ox0y0z0 axes 
a = Arrow3D([o[0], x0[0]], [o[1], x0[1]], [o[2], x0[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], y0[0]], [o[1], y0[1]], [o[2], y0[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], z0[0]], [o[1], z0[1]], [o[2], z0[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 

# plot ox1y1z1 axes 
a = Arrow3D([o[0], x1[0]], [o[1], x1[1]], [o[2], x1[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], y1[0]], [o[1], y1[1]], [o[2], y1[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], z1[0]], [o[1], z1[1]], [o[2], z1[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 

# draw dotted arc in x0y0 plane 
arc = np.arange(-5,116) * np.pi/180 
p = np.array([np.cos(arc),np.sin(arc),arc * 0]) 
ax.plot(p[0,:],p[1,:],p[2,:],'k--') 

# mark z0 rotation angles (psi) 
arc = np.linspace(0,psi) 
p = np.array([np.cos(arc),np.sin(arc),arc * 0]) * 0.6 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 
p = np.array([-np.sin(arc),np.cos(arc),arc * 0]) * 0.6 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 

# plot ox2y2z2 axes 
a = Arrow3D([o[0], x2[0]], [o[1], x2[1]], [o[2], x2[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], y2[0]], [o[1], y2[1]], [o[2], y2[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], z2[0]], [o[1], z2[1]], [o[2], z2[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 

# draw dotted arc in x1z1 plane 
arc = np.arange(-5,105) * np.pi/180 
p = np.array([np.sin(arc),arc * 0,np.cos(arc)]) 
p = Rz(psi).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k--') 

# mark y1 rotation angles (theta) 
arc = np.linspace(0,theta) 
p = np.array([np.cos(arc),arc * 0,-np.sin(arc)]) * 0.6 
p = Rz(psi).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 
p = np.array([np.sin(arc),arc * 0,np.cos(arc)]) * 0.6 
p = Rz(psi).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 

# plot ox3y3z3 axes 
a = Arrow3D([o[0], x3[0]], [o[1], x3[1]], [o[2], x3[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], y3[0]], [o[1], y3[1]], [o[2], y3[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 
a = Arrow3D([o[0], z3[0]], [o[1], z3[1]], [o[2], z3[2]], mutation_scale=20, arrowstyle='-|>', color='k') 
ax.add_artist(a) 

# draw dotted arc in y2z2 plane 
arc = np.arange(-5,125) * np.pi/180 
p = np.array([arc * 0,np.cos(arc),np.sin(arc)]) 
p = Rz(psi).dot(Ry(theta)).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k--') 

# mark x2 rotation angles (phi) 
arc = np.linspace(0,phi) 
p = np.array([arc * 0,np.cos(arc),np.sin(arc)]) * 0.6 
p = Rz(psi).dot(Ry(theta)).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 
p = np.array([arc * 0,-np.sin(arc),np.cos(arc)]) * 0.6 
p = Rz(psi).dot(Ry(theta)).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 

text_options = {'horizontalalignment': 'center', 
       'verticalalignment': 'center', 
       'fontsize': 14} 

# add label for origin 
ax.text(0.0,0.0,-0.05,r'$o$', **text_options) 

# add labels for x axes 
ax.text(1.1*x0[0],1.1*x0[1],1.1*x0[2],r'$x_0$', **text_options) 
ax.text(1.1*x1[0],1.1*x1[1],1.1*x1[2],r'$x_1$', **text_options) 
ax.text(1.1*x2[0],1.1*x2[1],1.1*x2[2],r'$x_2, x_3$', **text_options) 

# add lables for y axes 
ax.text(1.1*y0[0],1.1*y0[1],1.1*y0[2],r'$y_0$', **text_options) 
ax.text(1.1*y1[0],1.1*y1[1],1.1*y1[2],r'$y_1, y_2$', **text_options) 
ax.text(1.1*y3[0],1.1*y3[1],1.1*y3[2],r'$y_3$', **text_options) 

# add lables for z axes 
ax.text(1.1*z0[0],1.1*z0[1],1.1*z0[2],r'$z_0, z_1$', **text_options) 
ax.text(1.1*z2[0],1.1*z2[1],1.1*z2[2],r'$z_2$', **text_options) 
ax.text(1.1*z3[0],1.1*z3[1],1.1*z3[2],r'$z_3$', **text_options) 

# add psi angle labels 
m = 0.55 * ((x0 + x1)/2.0) 
ax.text(m[0], m[1], m[2], r'$\psi$', **text_options) 
m = 0.55 * ((y0 + y1)/2.0) 
ax.text(m[0], m[1], m[2], r'$\psi$', **text_options) 

# add theta angle lables 
m = 0.55 * ((x1 + x2)/2.0) 
ax.text(m[0], m[1], m[2], r'$\theta$', **text_options) 
m = 0.55 * ((z1 + z2)/2.0) 
ax.text(m[0], m[1], m[2], r'$\theta$', **text_options) 

# add phi angle lables 
m = 0.55 * ((y2 + y3)/2.0) 
ax.text(m[0], m[1], m[2], r'$\phi$', **text_options) 
m = 0.55 * ((z2 + z3)/2.0) 
ax.text(m[0], m[1], m[2], r'$\phi$', **text_options) 

# show figure 
ax.view_init(elev=-150, azim=60) 
ax.set_axis_off() 
plt.show() 

che produce la seguente immagine:

Le frecce sembrano leggermente troppo corte; non si incontrano nel mezzo e non toccano nemmeno le linee tratteggiate. C'è un modo per risolvere questo problema?

Answer 1

Questo codice potrebbe essere ben servito da alcuni per-loop, ma lascio che come come esercizio per il lettore;)

Il cambiamento chiave è la shirnkA e shrinkB paramaters in

arrow_prop_dict = dict(mutation_scale=20, arrowstyle='-|>', color='k', shrinkA=0, shrinkB=0) 

Il codice completo è qui sotto:

import numpy as np 
from matplotlib import pyplot as plt 
from mpl_toolkits.mplot3d import Axes3D 
from matplotlib.patches import FancyArrowPatch 
from mpl_toolkits.mplot3d import proj3d 

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) 

def Rx(phi): 
    return np.array([[1, 0, 0], 
        [0, np.cos(phi), -np.sin(phi)], 
        [0, np.sin(phi), np.cos(phi)]]) 

def Ry(theta): 
    return np.array([[np.cos(theta), 0, np.sin(theta)], 
        [0, 1, 0], 
        [-np.sin(theta), 0, np.cos(theta)]]) 

def Rz(psi): 
    return np.array([[np.cos(psi), -np.sin(psi), 0], 
        [np.sin(psi), np.cos(psi), 0], 
        [0, 0, 1]]) 

# define origin 
o = np.array([0,0,0]) 

# define ox0y0z0 axes 
x0 = np.array([1,0,0]) 
y0 = np.array([0,1,0]) 
z0 = np.array([0,0,1]) 

# define ox1y1z1 axes 
psi = 20 * np.pi/180 
x1 = Rz(psi).dot(x0) 
y1 = Rz(psi).dot(y0) 
z1 = Rz(psi).dot(z0) 

# define ox2y2z2 axes 
theta = 10 * np.pi/180 
x2 = Rz(psi).dot(Ry(theta)).dot(x0) 
y2 = Rz(psi).dot(Ry(theta)).dot(y0) 
z2 = Rz(psi).dot(Ry(theta)).dot(z0) 

# define ox3y3z3 axes 
phi = 30 * np.pi/180 
x3 = Rz(psi).dot(Ry(theta)).dot(Rx(phi)).dot(x0) 
y3 = Rz(psi).dot(Ry(theta)).dot(Rx(phi)).dot(y0) 
z3 = Rz(psi).dot(Ry(theta)).dot(Rx(phi)).dot(z0) 

# produce figure 
fig = plt.figure() 
ax = fig.add_subplot(111, projection='3d') 
arrow_prop_dict = dict(mutation_scale=20, arrowstyle='-|>', color='k', shrinkA=0, shrinkB=0) 
# plot ox0y0z0 axes 
a = Arrow3D([o[0], x0[0]], [o[1], x0[1]], [o[2], x0[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], y0[0]], [o[1], y0[1]], [o[2], y0[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], z0[0]], [o[1], z0[1]], [o[2], z0[2]], **arrow_prop_dict) 
ax.add_artist(a) 

# plot ox1y1z1 axes 
a = Arrow3D([o[0], x1[0]], [o[1], x1[1]], [o[2], x1[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], y1[0]], [o[1], y1[1]], [o[2], y1[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], z1[0]], [o[1], z1[1]], [o[2], z1[2]], **arrow_prop_dict) 
ax.add_artist(a) 

# draw dotted arc in x0y0 plane 
arc = np.arange(-5,116) * np.pi/180 
p = np.array([np.cos(arc),np.sin(arc),arc * 0]) 
ax.plot(p[0,:],p[1,:],p[2,:],'k--') 

# mark z0 rotation angles (psi) 
arc = np.linspace(0,psi) 
p = np.array([np.cos(arc),np.sin(arc),arc * 0]) * 0.6 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 
p = np.array([-np.sin(arc),np.cos(arc),arc * 0]) * 0.6 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 

# plot ox2y2z2 axes 
a = Arrow3D([o[0], x2[0]], [o[1], x2[1]], [o[2], x2[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], y2[0]], [o[1], y2[1]], [o[2], y2[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], z2[0]], [o[1], z2[1]], [o[2], z2[2]], **arrow_prop_dict) 
ax.add_artist(a) 

# draw dotted arc in x1z1 plane 
arc = np.arange(-5,105) * np.pi/180 
p = np.array([np.sin(arc),arc * 0,np.cos(arc)]) 
p = Rz(psi).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k--') 

# mark y1 rotation angles (theta) 
arc = np.linspace(0,theta) 
p = np.array([np.cos(arc),arc * 0,-np.sin(arc)]) * 0.6 
p = Rz(psi).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 
p = np.array([np.sin(arc),arc * 0,np.cos(arc)]) * 0.6 
p = Rz(psi).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 

# plot ox3y3z3 axes 
a = Arrow3D([o[0], x3[0]], [o[1], x3[1]], [o[2], x3[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], y3[0]], [o[1], y3[1]], [o[2], y3[2]], **arrow_prop_dict) 
ax.add_artist(a) 
a = Arrow3D([o[0], z3[0]], [o[1], z3[1]], [o[2], z3[2]], **arrow_prop_dict) 
ax.add_artist(a) 

# draw dotted arc in y2z2 plane 
arc = np.arange(-5,125) * np.pi/180 
p = np.array([arc * 0,np.cos(arc),np.sin(arc)]) 
p = Rz(psi).dot(Ry(theta)).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k--') 

# mark x2 rotation angles (phi) 
arc = np.linspace(0,phi) 
p = np.array([arc * 0,np.cos(arc),np.sin(arc)]) * 0.6 
p = Rz(psi).dot(Ry(theta)).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 
p = np.array([arc * 0,-np.sin(arc),np.cos(arc)]) * 0.6 
p = Rz(psi).dot(Ry(theta)).dot(p) 
ax.plot(p[0,:],p[1,:],p[2,:],'k') 

text_options = {'horizontalalignment': 'center', 
       'verticalalignment': 'center', 
       'fontsize': 14} 

# add label for origin 
ax.text(0.0,0.0,-0.05,r'$o$', **text_options) 

# add labels for x axes 
ax.text(1.1*x0[0],1.1*x0[1],1.1*x0[2],r'$x_0$', **text_options) 
ax.text(1.1*x1[0],1.1*x1[1],1.1*x1[2],r'$x_1$', **text_options) 
ax.text(1.1*x2[0],1.1*x2[1],1.1*x2[2],r'$x_2, x_3$', **text_options) 

# add lables for y axes 
ax.text(1.1*y0[0],1.1*y0[1],1.1*y0[2],r'$y_0$', **text_options) 
ax.text(1.1*y1[0],1.1*y1[1],1.1*y1[2],r'$y_1, y_2$', **text_options) 
ax.text(1.1*y3[0],1.1*y3[1],1.1*y3[2],r'$y_3$', **text_options) 

# add lables for z axes 
ax.text(1.1*z0[0],1.1*z0[1],1.1*z0[2],r'$z_0, z_1$', **text_options) 
ax.text(1.1*z2[0],1.1*z2[1],1.1*z2[2],r'$z_2$', **text_options) 
ax.text(1.1*z3[0],1.1*z3[1],1.1*z3[2],r'$z_3$', **text_options) 

# add psi angle labels 
m = 0.55 * ((x0 + x1)/2.0) 
ax.text(m[0], m[1], m[2], r'$\psi$', **text_options) 
m = 0.55 * ((y0 + y1)/2.0) 
ax.text(m[0], m[1], m[2], r'$\psi$', **text_options) 

# add theta angle lables 
m = 0.55 * ((x1 + x2)/2.0) 
ax.text(m[0], m[1], m[2], r'$\theta$', **text_options) 
m = 0.55 * ((z1 + z2)/2.0) 
ax.text(m[0], m[1], m[2], r'$\theta$', **text_options) 

# add phi angle lables 
m = 0.55 * ((y2 + y3)/2.0) 
ax.text(m[0], m[1], m[2], r'$\phi$', **text_options) 
m = 0.55 * ((z2 + z3)/2.0) 
ax.text(m[0], m[1], m[2], r'$\phi$', **text_options) 

# show figure 
ax.view_init(elev=-150, azim=60) 
ax.set_axis_off() 
plt.show()