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Plotting points from a function on a unit sphere using matplotlib

I am trying to plot the following function on a unit sphere, the points should be on the sphere and fill up the whole sphere however some of the points are falling off. Any suggestions why? I believe it is because the sphere is not spanning 1,1,1 3D grid but I am not sure how to edit my code to fix this.
from itertools import product, combinations
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
def d(kx,ky):
M = 1
B = 1
vf = 1
kxx,kyy = np.meshgrid(kx,ky)
x = (vf*kxx)/(np.sqrt(((((vf**2)*(kxx**2)))+((vf**2)*(kyy**2))+(M-B*(kxx**2+(kyy**2)))**2)))
y = (vf*kxx)/(np.sqrt(((((vf**2)*(kxx**2)))+((vf**2)*(kyy**2))+(M-B*(kxx**2+(kyy**2)))**2)))
z = (M-B*(kxx**2+(kyy**2)))/(np.sqrt(((((vf**2)*(kxx**2)))+((vf**2)*(kyy**2))+(M-B*(kxx**2+(kyy**2)))**2)))
return x,y,z
kx = np.linspace(-2, 2, 10)
ky = np.linspace(-2, 2, 10)
xi, yi, zi = d(kx,ky)
phi = np.linspace(0, np.pi, 100)
theta = np.linspace(0, 2*np.pi, 100)
phi, theta = np.meshgrid(phi, theta)
x = np.sin(phi) * np.cos(theta)
y = np.sin(phi) * np.sin(theta)
z = np.cos(phi)
fig = plt.figure(figsize=plt.figaspect(1.))
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x, y, z, color="w", rstride=1, cstride=1)
ax.scatter(xi,yi,zi,color="k",s=20)
plt.show()
Thank you kindly,

How to make my surface plot appear using Axes3D?

I'm trying to create a surface plot using Python Matplotlib. I've read the documentation in an attempt to figure out where my code was wrong or if I've left anything out, but was having trouble.
The code that I've written is
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
def computeCost(X, y, theta):
m = len(y)
predictions = np.dot(X, theta)
squareErros = (predictions - y) ** 2
J = (1 / (2 * m)) * sum(squareErrors)
return J
data = np.loadtxt("./data1.txt", delimiter=',')
X = data[:, 0].reshape(-1, 1)
y = data[:, 1].reshape(-1, 1)
m = len(y)
X = np.concatenate((np.ones((m, 1)), X), axis=1)
theta0_vals = np.linspace(-10, 10, 100) # size (100,)
theta1_vals = np.linspace(-1, 4, 100) # size (100,)
J_vals = np.zeros((len(theta0_vals), len(theta1_vals)))
for i in range(len(x_values)):
for j in range(len(y_values)):
t = np.array([theta0_vals[i], theta1_vals[j]]).reshape(-1, 1)
J_vals[i][j] = computeCost(X, y, t) # size (100, 100)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
surf = ax.plot_surface(theta0_vals, theta1_vals, J_vals)
plt.show()
When I invoke plt.show() I get no output. The surface plot that I'm expecting to see is similar to this:
Would anybody be kind enough to let me know where my usage of the surface plot library went wrong? Thank you.
EDIT
I've tried to run the demo code provided here and it works fine. Here's the code for that:
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()
ax = fig.gca(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()

I think I've figured out the issue by changing a couple of the last lines of code from
ax = fig.add_subplot(111, projection='3d')
surf = ax.plot_surface(theta0_vals, theta1_vals, J_vals)
to
ax = plt.axes(projection='3d')
surf = ax.plot_surface(theta0_vals, theta1_vals, J_vals, rstride=1, cstride=1, cmap='viridis', edgecolor='none')
Making this change gives me a surface plot such that:
The link that gave me reference to this was this.

How can I visualize a function value in 3d?

Suppose I have some function, which maps 3 coordinates (x,y,z) to some real number.
How can I visualize the function values on a surface like a sphere?
Ideally, I would map the function's value to a color, and then color the sphere accordingly.
Here is my code to generate a sphere:
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_aspect("equal")
u = np.linspace(0, 2 * np.pi, 250)
v = np.linspace(0, np.pi, 250)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, color="w")
How can I edit my code to color it according to some function F(x,y,z)

Matplotlib allows to use the facecolor argument to plot_surface to set the color of each polygon in the surface. The argument needs to have the same shape as the input arrays and must consist of valid colors. A way to obtain those colors is a colormap.
Also see this question for details.
Below is a working example code.
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
u = np.linspace(0, 2 * np.pi, 180)
v = np.linspace(0, np.pi, 90)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
F = np.sin(x)*y + z
F = (F-F.min())/(F-F.min()).max()
#Set colours and render
fig = plt.figure(figsize=(8, 8))
fig.subplots_adjust(top=1, bottom=0, left=0, right=1)
ax = fig.add_subplot(111, projection='3d')
#use facecolors argument, provide array of same shape as z
# cm.<cmapname>() allows to get rgba color from array.
# array must be normalized between 0 and 1
ax.plot_surface(
x,y,z, rstride=1, cstride=1, facecolors=cm.jet(F), alpha=0.9, linewidth=0.9)
ax.set_xlim([-1,1])
ax.set_ylim([-1,1])
ax.set_zlim([-1,1])
ax.set_aspect("equal")
plt.savefig(__file__+".png")
plt.show()

The documentation for surface_plot lists the option facecolors. There is a example that alternates between two colors but you can pass any matplotlib color, including and array of RGB values.
You need to do the mapping yourself from x, y, z to F(x, y, z) to "color", then convert F to a RGB value.
facecolors = plt.cm.Red(F(x,y,z))
should do.
See: http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html#surface-plots

Converting a 2D figure into a cylinder in Python

At the moment I have a figure that looks like this,
Generated by the code:
import matplotlib.pyplot as plt
import numpy as np
data = np.random.rand(20,5)
rows,cols = data.shape
plt.imshow(data, interpolation='nearest', extent=[0.5, 0.5+cols, 0.5, 0.5+cols], cmap='bwr')
plt.show()
However I would like to 'fold' this up into a 3D cylinder, joining the left and right edges (as one would do with a sheet of paper). In other words the left edge and the right edges are actually the same edge and so I would like to join them together to form a cylinder.
How would I go about doing this?

The Poly3DCollection is the method of choice for arbitrary 3D polygons in mplot3d.
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=12,20
r=1 # radius of cylinder
phi = np.linspace(0,360, nphi)/180.0*np.pi
z= np.linspace(0,1.0,nz)
print z
facecolors=['r','g','b','y']
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.bwr(value)
print col
cols.append(col)
poly3= Poly3DCollection(verts2, facecolor=cols )
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()

You could use plot_surface:
import numpy as np
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d.axes3d as axes3d
np.random.seed(2016)
data = np.random.rand(12, 20)
h, w = data.shape
theta, z = np.linspace(0, 2 * np.pi, w), np.linspace(0, 1, h)
THETA, Z = np.meshgrid(theta, z)
X = np.cos(THETA)
Y = np.sin(THETA)
fig = plt.figure()
ax = fig.add_subplot(1,1,1, projection='3d')
cmap = plt.get_cmap('bwr')
plot = ax.plot_surface(
X, Y, Z, rstride=1, cstride=1, facecolors=cmap(data),
linewidth=0, antialiased=False, alpha=0.75)
plt.show()
yields

Fixing jagged edges of 3D plot, selecting an appropriate mask

So I have some 3D data that I am able to plot just fine except the edges look jagged.
The relevant code:
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
x = np.arange(-1, 1, 0.01)
y = np.arange(-1, 1, 0.01)
x, y = np.meshgrid(x, y)
rho = np.sqrt(x**2 + y**2)
# Attempts at masking shown here
# My Mask
row=0
while row<np.shape(x)[0]:
col=0
while col<np.shape(x)[1]:
if rho[row][col] > 1:
rho[row][col] = None
col=col+1
row=row+1
# Calculate & Plot
z = rho**2
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x, y, z, rstride=8, cstride=8, cmap=cm.bone, alpha=0.15, linewidth=0.25)
plt.show()
Produces:
This is so close to what I want except the edges are jagged.
If I disable my mask in the code above & replace it with rho = np.ma.masked_where(rho > 1, rho) it gives:
It isn't jagged but not want I want in the corners.
Any suggestions on different masking or plotting methods to get rid of this jaggedness?

Did you consider using polar coordinates (like in this example) ?
Something like:
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# create supporting points in polar coordinates
r = np.linspace(0,1.25,50)
p = np.linspace(0,2*np.pi,50)
R,P = np.meshgrid(r,p)
# transform them to cartesian system
x, y = R * np.cos(P), R * np.sin(P)
rho = np.sqrt(x**2 + y**2)
# Calculate & Plot
z = rho**2
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap=cm.bone, alpha=0.15, linewidth=0.25)
plt.show()