I would like to graph a 3d plot of a sphere, which colors sections differently according to some function of the theta, phi coordinates. I could graph two separate graphs, one of each color, but I'm not sure exactly how the gridding/meshing works when plotting. Viz. I want to grid/mesh over all thetas/phis in a sphere, but then throw out certain pairs given a boolean function. Is this possible? Attached is a picture of a scatterplot that does what I'd like to do with surfaces.
Based on scatter3d_demo.py found in the matplotlib tutorial:
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')
THETA, PHI = np.ogrid[0:2*np.pi:40j, 0:np.pi:30j]
X = 10 * np.cos(THETA) * np.sin(PHI)
Y = 10 * np.sin(THETA) * np.sin(PHI)
Z = 10 * np.ones_like(THETA) * np.cos(PHI)
def func(THETA, PHI):
mask = (THETA < np.pi/2) & (np.pi/3 < PHI) & (PHI < 2 * np.pi/3)
return np.where(mask, 1, 0.5)
C = func(THETA, PHI)
x = X.ravel()
y = Y.ravel()
z = Z.ravel()
c = C.ravel()
ax.scatter(x, y, z, c=c, s=30, vmin=0, vmax=1)
ax.set_aspect('equal')
plt.show()
yields
Note you could also color patches on a sphere using plot_surface:
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
THETA, PHI = np.ogrid[0:2*np.pi:40j, 0:np.pi:30j]
X = 10 * np.cos(THETA) * np.sin(PHI)
Y = 10 * np.sin(THETA) * np.sin(PHI)
Z = 10 * np.ones_like(THETA) * np.cos(PHI)
def func(THETA, PHI):
mask = (THETA < np.pi/2) & (np.pi/3 < PHI) & (PHI < 2 * np.pi/3)
return np.where(mask, 1, 0.5)
C = func(THETA, PHI)
jet = plt.cm.jet
ax.plot_surface(X, Y, Z, rstride=2, cstride=2, facecolors=jet(C))
ax.set_aspect('equal')
plt.show()
Related
I have two formulas:
x^2 + y^2+z^2 = 6
(x-3)^2+y^2=4
So I have to draw this shapes by matplotlib on python.
My solution:
`
import math
import matplotlib.pyplot as plt
from pylab import *
import numpy as np
import matplotlib.patches as patches
from mpl_toolkits.mplot3d import Axes3D
from itertools import product, combinations
import mpl_toolkits.mplot3d.art3d as art3d
def task3():
fig = plt.figure()
ax = plt.axes(projection='3d')
coefs = (1, 1, 1) # Coefficients in a0/c x**2 + a1/c y**2 + a2/c z**2 = 1
# Radii corresponding to the coefficients:
rx, ry, rz = 1 / np.sqrt(coefs)
# Set of all spherical angles:
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
# Cartesian coordinates that correspond to the spherical angles:
# (this is the equation of an ellipsoid):
x = rx * np.outer(np.cos(u), np.sin(v))
y = ry * np.outer(np.sin(u), np.sin(v))
z = rz * np.outer(np.ones_like(u), np.cos(v))
ax.plot_surface(x, y, z, rstride=6, cstride=6,
cmap='viridis', edgecolor='none')
# ax.scatter(X, Y, Z, c=Z, cmap='viridis', label="xy")
radius = 0.3
height = 2.4
elevation = -1
resolution = 720
color = 'r'
x_center = 0.7
y_center = -0
a = np.linspace(x_center - radius, x_center + radius, resolution)
b = np.linspace(elevation, elevation + height, resolution)
X, Z = np.meshgrid(a, b)
Y = np.sqrt(radius ** 2 - (X - x_center) ** 2) + y_center # Pythagorean theorem
ax.plot_surface(X, Y, Z, rstride=6, cstride=6,
cmap='viridis', edgecolor='none')
ax.plot_surface(X, (2 * y_center - Y), Z, rstride=6, cstride=6,
cmap='viridis', edgecolor='none')
plt.show()
[![Result. I cant post images, but you can compile result and then you will see that my solution too approximate)
I want to do it correctly
I would like to make surface plot of a function which is discontinuous at certain values in parameter space. It is near these discontinuities that the plot's coloring becomes incorrect, as shown in the picture below. How can I fix this?
My code is given below:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
def phase(mu_a, mu_b, t, gamma):
theta = 0.5*np.arctan2(2*gamma, mu_b-mu_a)
epsilon = 2*gamma**2/np.sqrt((mu_a-mu_b)**2+4*gamma**2)
y1 = np.arccos(0.5/t*(-mu_a*np.sin(theta)**2 -mu_b*np.cos(theta)**2 - epsilon))
y2 = np.arccos(0.5/t*(-mu_a*np.cos(theta)**2 -mu_b*np.sin(theta)**2 + epsilon))
return y1+y2
fig = plt.figure()
ax = fig.gca(projection='3d')
# Make data.
X = np.arange(-2.5, 2.5, 0.01)
Y = np.arange(-2.5, 2.5, 0.01)
X, Y = np.meshgrid(X, Y)
Z = phase(X, Y, 1, 0.6)
# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm, linewidth=0, antialiased=False)
surf.set_clim(1, 5)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
An idea is to make all the arrays 1D, filter out the NaN values and then call ax.plot_trisurf:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
def phase(mu_a, mu_b, t, gamma):
theta = 0.5 * np.arctan2(2 * gamma, mu_b - mu_a)
epsilon = 2 * gamma ** 2 / np.sqrt((mu_a - mu_b) ** 2 + 4 * gamma ** 2)
with np.errstate(divide='ignore', invalid='ignore'):
y1 = np.arccos(0.5 / t * (-mu_a * np.sin(theta) ** 2 - mu_b * np.cos(theta) ** 2 - epsilon))
y2 = np.arccos(0.5 / t * (-mu_a * np.cos(theta) ** 2 - mu_b * np.sin(theta) ** 2 + epsilon))
return y1 + y2
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
# Make data.
X = np.linspace(-2.5, 2.5, 200)
Y = np.linspace(-2.5, 2.5, 200)
X, Y = np.meshgrid(X, Y)
X = X.ravel() # make the array 1D
Y = Y.ravel()
Z = phase(X, Y, 1, 0.6)
mask = ~np.isnan(Z) # select the indices of the valid values
# Plot the surface.
surf = ax.plot_trisurf(X[mask], Y[mask], Z[mask], cmap=cm.coolwarm, linewidth=0, antialiased=False)
surf.set_clim(1, 5)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
Some remarks:
plot_trisurf will join the XY-values via triangles; this only works well if the domain is convex
to make things draw quicker, less points could be used (the original used 500x500 points, the code here reduces that to 200x200
calling fig.gca(projection='3d') has been deprecated; instead, you could call fig.add_subplot(projection='3d')
the warnings for dividing by zero or using arccos out of range can be temporarily suppressed; that way the warning will still be visible for situations when such isn't expected behavior
I'm making multiple density plots in 3D with a circle shape, using contourf.
What I want to do is similar to a clip_path for a pcolormesh plot.
How can I clip the plot in 3D in particular for a contourf plot?
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.path import Path
import matplotlib.patches as patches
fig = plt.figure()
ax = fig.gca(projection='3d')
x = np.linspace(0, 1, 100)
X, Y = np.meshgrid(x, x)
levels = np.linspace(-0.1, 0.4, 100) #(z_min,z_max,number of contour),
a=0
b=1
c=2
Z1 = a+.1*np.sin(2*X)*np.sin(4*Y)
Z2 = b+.1*np.sin(3*X)*np.sin(4*Y)
Z3 = c+.1*np.sin(4*X)*np.sin(5*Y)
plt.contourf(X, Y,Z1, levels=a+levels,cmap=plt.get_cmap('rainbow'))
plt.contourf(X, Y,Z2, levels=b+levels,cmap=plt.get_cmap('rainbow'))
plt.contourf(X, Y,Z3, levels=c+levels,cmap=plt.get_cmap('rainbow'))
ax.set_xlim3d(0, 1)
ax.set_ylim3d(0, 1)
ax.set_zlim3d(0, 2)
plt.show()
Are you sure your code generated that output image with the given parameters? I only got some blue squares. Tweaking a bit, it starts looking like yours.
To clip the contours, consider masking the Z arrays. As in:
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
import numpy.ma as ma
fig = plt.figure()
ax = fig.gca(projection='3d')
x = np.linspace(0, 1, 100)
X, Y = np.meshgrid(x, x)
levels = np.linspace(-0.1, 0.4, 100) #(z_min,z_max,number of contour),
a = 0
b = 1
c = 2
Z1 = a + .3 * np.sin(2 * X) * np.sin(4 * Y)
Z2 = b + .3 * np.sin(3 * X) * np.sin(4 * Y)
Z3 = c + .3 * np.sin(4 * X) * np.sin(5 * Y)
mask_cond = (X - .5) ** 2 + (Y - .5) ** 2 > .25
Z1 = ma.masked_where(mask_cond, Z1)
Z2 = ma.masked_where(mask_cond, Z2)
Z3 = ma.masked_where(mask_cond, Z3)
plt.contourf(X, Y, Z1, levels=a + levels, cmap='rainbow')
plt.contourf(X, Y, Z2, levels=b + levels, cmap='rainbow')
plt.contourf(X, Y, Z3, levels=c + levels, cmap='rainbow')
ax.set_xlim3d(0, 1)
ax.set_ylim3d(0, 1)
ax.set_zlim3d(0, 3)
plt.show()
The idea is to plot the following vector field:
I have two main issue with it:
1) I do not know how to make sure that the arrows are not too long (I know I have to use length, but how?).
2) I am told to use Numpyto draw the vector field but again, how?
This is what I have tried:
# The components of the vector field
F_x = y*e**x
F_y = x**2 + e**x
F_z = z**2*e**z
# The grid
xf = np.linspace(-0.15, 2.25, 8)
yf = np.linspace(-0.15, 2.25, 8)
zf = np.linspace(-0.75, 2.50, 8)
X_grid, Y_grid, Z_grid = np.meshgrid(xf, yf, zf)
# The arrows; how to deal with them?
dx = 1
#dy = ...
#dz = ...
# Standardize the arrows; In this way all arrows have the same length.
length = np.sqrt(dx**2 + dy**2 + dz**2)
dx_N = dx/length
dy_N = dy/length
dz_N = dz/length
#how to involve numpy in the process??
# Drawing the figure
fig, ax = plt.subplots(1, 1)
ax.quiver(X_grid, Y_grid, Z_grid, dx_N, dy_N, dz_N, dy, dz, cmap=plt.get_cmap('gnuplot2'))
plt.show()
Thanks
EDIT
Based on the provided link I tried:
from sympy import *
x,y,z = sp.symbols('x y z', real = True)
import matplotlib.pyplot as plt
x, y, z = np.meshgrid(np.arange(0, 2 * np.pi, .2), np.arange(0, 2 * np.pi, .2), np.arange(0, 2 * np.pi, .2))
F_x = y * exp(x)
F_y = x**2 + exp(x)
F_z = z**2 * exp(z)
# Normalize the arrows:
F_x = F_x / np.sqrt(F_x**2 + F_y**2 + F_z**2)
F_y = F_y / np.sqrt(F_x**2 + F_y**2 + F_z**2)
F_z = F_z / np.sqrt(F_x**2 + F_y**2 + F_z**2)
plt.figure()
plt.title('Vector field')
Q = plt.quiver(x, y, z, F_x, F_y, F_z, units='width')
qk = plt.quiverkey(Q, 0.9, 0.9, 2, r'$2 \frac{m}{s}$', labelpos='E',
coordinates='figure')#I don't understand this line
The TypeError: Shape should contain integers only comes up.
The problem is that I don't understand this part of the code:
qk = plt.quiverkey(Q, 0.9, 0.9, 2, r'$2 \frac{m}{s}$', labelpos='E',
coordinates='figure')
I am still stuck on how to plot this vector field
Assume that you want a 3D quiver, you can check out the matplotlib tutorial on quiver3D. And to control the arrow size, check out the Axes3d.quiver library doc, especially the parameters.
A quick snippet:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
x, y, z = np.meshgrid(np.arange(0, 2*np.pi, .5), np.arange(0, 2*np.pi, .5), np.arange(0, 2*np.pi, .5))
F_x = y * np.exp(x)
F_y = x**2 + np.exp(x)
F_z = z**2 * np.exp(z)
fig = plt.figure()
ax = fig.gca(projection='3d')
Q = ax.quiver(x, y, z, F_x, F_y, F_z, length=0.3, normalize=True)
But 3d quiver plot can be very crowded! : )
The quiver() method is a great tool to render vector fields. Since Matplotlib is a two-dimensional plotting library, we need to import the mplot3d toolkit to generate a three-dimensional plot.
Here's a good example:
Dependencies:
Axes3D for 3D rendering
Pyplot to get a MATLAB-like plotting framework
Numpy for numeric-array manipulation
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
x, y, z = np.meshgrid(np.arange(-0.8, 1, 0.25),
np.arange(-0.8, 1, 0.25),
np.arange(-0.8, 1, 0.8))
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))
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.quiver(x, y, z, u, v, w,
length=0.15,
color='Purple'
)
ax.view_init(elev=10, azim=30)
ax.dist=8
plt.show()
I have the following code which produces a cylinder-like object using matplotlib:
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
nphi,nz=7,20
r=1 # radius of cylinder
phi = np.linspace(0,360, nphi)/180.0*np.pi
z= np.linspace(0,1.0,nz)
print z
cols=[]
verts2 = []
for i in range(len(phi)-1):
cp0= r*np.cos(phi[i])
cp1= r*np.cos(phi[i+1])
sp0= r*np.sin(phi[i])
sp1= r*np.sin(phi[i+1])
for j in range(len(z)-1):
z0=z[j]
z1=z[j+1]
verts=[]
verts.append((cp0, sp0, z0))
verts.append((cp1, sp1, z0))
verts.append((cp1, sp1, z1))
verts.append((cp0, sp0, z1))
verts2.append(verts)
value=np.random.rand()
#print value
col=plt.cm.rainbow(0.9)
#print col
cols.append(col)
poly3= Poly3DCollection(verts2, facecolor=cols,edgecolor = "none" )
poly3.set_alpha(0.8)
ax.add_collection3d(poly3)
ax.set_xlabel('X')
ax.set_xlim3d(-1, 1)
ax.set_ylabel('Y')
ax.set_ylim3d(-1, 1)
ax.set_zlabel('Z')
ax.set_zlim3d(0, 1)
plt.show()
This code produces the following image:
However as you can see the are sharp corners in the figure. Is there anyway to make these edges rounder so that the figure looks like a proper cylinder with a circular cross-section as opposed to a hexagonal cross-section?
The third argument to
np.linspace
controls how many values you want it to generate. Thus, nphi controls the
number of values in phi, and nz controls the number of values in z:
phi = np.linspace(0,360, nphi)/180.0*np.pi
z = np.linspace(0,1.0,nz)
So if you increase nphi, then you'll get more points along the circle:
cp0 = r*np.cos(phi[i])
sp0 = r*np.sin(phi[i])
For example, try changing nphi, nz = 7,20 to nphi, nz = 70, 2.
Note that there is no need for nz to be greater than 2 since the sides of the
cylinder are flat in the z direction.
By the way, the double for-loop can be replaced by:
PHI, Z = np.meshgrid(phi, z)
CP = r * np.cos(PHI)
SP = r * np.sin(PHI)
XYZ = np.dstack([CP, SP, Z])
verts = np.stack(
[XYZ[:-1, :-1], XYZ[:-1, 1:], XYZ[1:, 1:], XYZ[1:, :-1]], axis=-2).reshape(-1, 4, 3)
So, for example,
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
nphi, nz = 70, 2
r = 1 # radius of cylinder
phi = np.linspace(0, 360, nphi) / 180.0 * np.pi
z = np.linspace(0, 1.0, nz)
PHI, Z = np.meshgrid(phi, z)
CP = r * np.cos(PHI)
SP = r * np.sin(PHI)
XYZ = np.dstack([CP, SP, Z])
verts = np.stack(
[XYZ[:-1, :-1], XYZ[:-1, 1:], XYZ[1:, 1:], XYZ[1:, :-1]], axis=-2).reshape(-1, 4, 3)
cmap = plt.cm.rainbow
cols = cmap(np.random.random())
poly3 = Poly3DCollection(verts, facecolor=cols, edgecolor="none")
poly3.set_alpha(0.8)
ax.add_collection3d(poly3)
ax.set_xlabel('X')
ax.set_xlim3d(-1, 1)
ax.set_ylabel('Y')
ax.set_ylim3d(-1, 1)
ax.set_zlabel('Z')
ax.set_zlim3d(0, 1)
plt.show()
yields