How to do a 3D plot of gaussian using numpy? - python

I'm trying to plot a gaussian function using numpy.
the funtion is z=exp(-(x2+y2)/10) but I only get a 2D function
import numpy as np
from matplotlib import pyplot as plt
x=np.linspace(-10,10, num=100)
y=np.linspace(-10,10, num=100)
z=np.exp(-0.1*x**2-0.1*y**2)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(x,y,z)
I obtain:
but I want to obtain:
I'm using numpy becouse I need the set of data.

You need to obtain the correct dimensions. This can be done using meshgrid. Also, your desired plot is a surface plot, not a wireframe (though you can do that too).
# import for colormaps
from matplotlib import cm
x=np.linspace(-10,10, num=100)
y=np.linspace(-10,10, num=100)
x, y = np.meshgrid(x, y)
z = np.exp(-0.1*x**2-0.1*y**2)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(x,y,z, cmap=cm.jet)
plt.show()

given the original formula of a gaussian distribution I wrote the following code:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D # <--- This is important for 3d plotting
A = 1
x0 = 0
y0 = 0
sigma_X = 2
sigma_Y = 2
xg = np.linspace(-5,5,num=100)
yg = np.linspace(-5,5,num=100)
theta= np.pi
X, Y = np.meshgrid(xg,yg)
a = np.cos(theta)**2/(2*sigma_X**2) + np.sin(theta)**2/(2*sigma_Y**2);
b = -np.sin(2*theta)/(4*sigma_X**2) + np.sin(2*theta)/(4*sigma_Y**2);
c = np.sin(theta)**2/(2*sigma_X**2) + np.cos(theta)**2/(2*sigma_Y**2);
aXXdet = np.array([a*(Xi-x0)**2 for Xi in X],float)
bbXYdet = np.array([2*b*(Xi-x0)*(Y[ii]-y0) for ii,Xi in enumerate(X)],float)
cYYdet = np.array([c*(Yi-y0)**2 for Yi in Y],float)
Z = np.array([A*np.exp( - (ai + bbXYdet[i] + cYYdet[i])) for i,ai in enumerate(aXXdet)],float);
# plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap=cm.coolwarm)
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.show()
which also plots the distribution. So you could play around with the parameters and see their effect!

Related

Curve overlay on a Surface Matplotlib

I am interested in plotting curves on surfaces of revolution and have done so, but the surface is over-layed over the curve, does anyone know how to do the opposite?
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
def surface_of_rev(u,v):
f = v
x = f*np.cos(u)
y = f*np.sin(u)
z = np.exp(-v**2)
return x,y,z
U = np.linspace(0,2*pi,n)
V = np.linspace(0.,3,n)
U,V = np.meshgrid(U,V)
x,y,z = surface_of_rev(U,V)
# curve
a = 3
b = 1
T = np.linspace(0,3,100)
xx,yy,zz = surface_of_rev(a*T+b,2*T)
# plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
curve = ax.plot(xx, yy, zz, 'o-', lw=2)
surface = ax.plot_surface(x, y, z,color= 'g')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.view_init(50, 10)
plt.show()
Thank you

How to get the slice of a plot3d object?

I have some points and I plot the surface of them using the code below:
import matplotlib.pyplot as plt
from matplotlib import cm, colors
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
# Create a sphere
r = 1
pi = np.pi
cos = np.cos
sin = np.sin
phi, theta = np.mgrid[0.0:pi:20j, 0.0:2.0*pi:20j]
radis=np.random.normal(1,0.2,(20,20))
x = radis*sin(phi)*cos(theta)
y = radis*sin(phi)*sin(theta)
z = radis*cos(phi)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(
x, y, z, rstride=1, cstride=1, color='c', alpha=0.3, linewidth=0)
ax.scatter3D(x,y,z, c='r')
ax.set_xlim([-1,1])
ax.set_ylim([-1,1])
ax.set_zlim([-1,1])
# ax.set_aspect("equal")
plt.tight_layout()
plt.show()
Then I get the 3d plot result:
The thing I want to do is that get the image of any plane, like z=0.
Is there any method or library can cover this problem?

How do I create a colormap plot that can make a sphere in matplotlib 3d look like half i bright (look like the earth is illuminated on one side)

I am trying to create a 3D sphere in matplotlib and have it color like one side of the sphere is illuminated by the sun.
I have tried using matplotlib colormaps.
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_axis_off()
phi = np.linspace(0,2*np.pi, 50)
theta = np.linspace(0, np.pi, 25)
x=np.outer(np.cos(phi), np.sin(theta))
y=np.outer(np.sin(phi), np.sin(theta))
z=np.outer(np.ones(np.size(phi)), np.cos(theta))
PHI=np.outer(phi,np.ones(np.size(theta)))
THETA=np.outer(np.ones(np.size(phi)),theta)
data = PHI/np.pi
norm = plt.Normalize(vmin=data.min(), vmax=data.max())
surface=ax.plot_surface(x, y, z, cstride=1, rstride=1,
facecolors=cm.jet(norm(data)))
surface=ax.plot_surface(x, y, z, cstride=1, rstride=1,
facecolors=cm.binary(norm(data)),cmap=plt.get_cmap('jet'))
plt.show()
I am expecting a sphere that looks something like this:
Or basically something that looks like the earth with the day side and the night side
But instead my results are something like this:
current plot from the above code
You need to use LightSource package:
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.colors import LightSource
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_axis_off()
phi = np.linspace(0,2*np.pi, 100)
theta = np.linspace(0, np.pi, 50)
x=np.outer(np.cos(phi), np.sin(theta))
y=np.outer(np.sin(phi), np.sin(theta))
z=np.outer(np.ones(np.size(phi)), np.cos(theta))
PHI=np.outer(phi,np.ones(np.size(theta)))
THETA=np.outer(np.ones(np.size(phi)),theta)
data = PHI/np.pi
norm = plt.Normalize(vmin=data.min(), vmax=data.max())
# use Light Source
ls = LightSource(0, 0)
# create rgb shade
rgb = ls.shade(x, cmap=cm.Wistia, vert_exag=0.1, blend_mode='soft')
# blend shade
bsl = ls.blend_hsv(rgb, np.expand_dims(x*0.8, 2))
# plot surface
surface = ax.plot_surface(x, y, z, cstride=1, rstride=1, facecolors=bsl,
linewidth=0, antialiased=False, shade=False)
plt.show()
Output:

Way of plotting data into boxes instead of pyramids using mplot3d

So I have an array of values that I am trying to plot using the plot_surface command. Specifically I have a 30x30 array with one in the middle and zeros elsewhere. When I plot it this is what I obtain:
I would like however for the value to be represented as a cuboid. Is that possible?
Thank you
edit: Code that shows the figure
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
N=30
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(0, N)
z = np.zeros((N,N))
z[15,15] = 1
X, Y = np.meshgrid(x, y)
ax.plot_surface(X, Y, z, cmap='YlOrBr')
plt.show(block=False)
I think a 3D bar plot will give what you're looking for.
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
N=30
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = y = np.arange(0, N)
z_bottom = np.zeros((N,N))
z_top = z_bottom.copy()
z_top[15,15] = 1
X, Y = np.meshgrid(x, y)
ax.bar3d(X.ravel(), Y.ravel(), z_bottom.ravel(), 1, 1, z_top.ravel())
plt.show(block=False)
The full documentation is here if you want to play with the colors and so forth.

matplotlib surface plot extends past axis limits

How do I make a nice paraboloid in Matplotlib that looks like
All I can get is this,
where the top is not "cut off". I've tried just dropping all values of the Z array outside of the radius of the parabola at the top, but that gives very jagged edges. Can someone help me?
Here is my code:
from matplotlib import *
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from pylab import *
import math
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
X = np.arange(-5, 5, 0.1)
Y = np.arange(-5, 5, 0.1)
X, Y = np.meshgrid(X, Y)
Z = (X**2 + Y**2)
ax.set_zlim(-10, 20)
ax.plot_surface(X, Y, Z, alpha=0.9, rstride=4, cstride=4, linewidth=0.5, cmap=cm.summer)
plt.show()
For future reference, I had a thought to parametrize the surface in cylindrical coordinates, and it looks exactly how I want it:
from matplotlib import *
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from pylab import *
import math
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
r = T = np.arange(0, 2*pi, 0.01)
r, T = np.meshgrid(r, T)
#Parametrise it
X = r*np.cos(T)
Y = r*np.sin(T)
Z = r**2
ax.plot_surface(X, Y, Z, alpha=0.9, rstride=10, cstride=10, linewidth=0.5, cmap=cm.summer)
plt.show()
I guess it makes sense: when working with a cylindrical object, use cylindrical coordinates!
Manual data clipping
One approach I've seen that works is to manually clip the data; e.g. your example would be updated to
from matplotlib import *
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from pylab import *
import math
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
X = np.arange(-5, 5, 0.1)
Y = np.arange(-5, 5, 0.1)
X, Y = np.meshgrid(X, Y)
Z = (X**2 + Y**2)
ax.set_zlim(-10, 20)
for i in range(len(X)):
for j in range(len(Y)):
if (Z[j,i] < -10) or (Z[j,i] > 20):
Z[j,i] = NaN
ax.plot_surface(X, Y, Z, alpha=0.9, rstride=4, cstride=4, linewidth=0.5, cmap=cm.summer)
plt.show()
Note
This can be done concisely for this case using
Z[Z>20] = NaN
Resulting in

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