Odd indentation near origin of graph (sometimes)

[MathewsMD]

from mpl_toolkits.mplot3d
import Axes3D
import matplotlib
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
import numpy as np
import matplotlib.pylab as plt
import math
import random from scipy
import integrate

step = 0.1
maxval = 1.0
fig = plt.figure()
ax = Axes3D(fig)
R1 = 4.
R2 = 7.
r = np.linspace(0,20,100)
p = np.linspace(0,2*np.pi,100)
R,P = np.meshgrid(r,p)
X,Y = R*np.cos(P),R*np.sin(P)
sigma0 = random.randint(4000., 7000.)/1000.
r0 = random.randint(0, R1*1000.)/1000. #random centroid
theta0 = random.uniform(0, np.pi*2)

Z = (np.e**((-(R**2 + r0**2- 2*R*r0*(np.cos(P)*np.cos(theta0) +  np.sin(P)*np.sin(theta0)))/(2*sigma0**2))))

ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=cm.jet)
ax.set_zlim3d(0,1)
ax.set_zlabel('Intensity')
plt.show()

When I run this code, it works. But due to the random number generator, sometimes the input values have the graph centred near the origin (e.g. set r0 = 5), and when this occurs, there seems to be an odd indentation in the graph itself. Maybe I'm missing something, but if I'm trying to display a 2D Gaussian, this shouldn't be there, right? If anyone has any thoughts on why this is occurring and any ideas to approach this problem, that would be greatly appreciated!

 

[gsal]

I don't understand what you mean.

If you set r0 first and THEN determine r and p around it...would that center it as you desired? or would that defeat the purpose of what you are trying to do?

 

[D H]

Maybe I'm missing something, but if I'm trying to display a 2D Gaussian, this shouldn't be there, right?

It's an artifact of your mesh. I've modified your code a bit so I can choose between a polar mesh or a cartesian mesh, and so I can optionally specify the centroid and variance:

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
from scipy import random
import argparse

parser = argparse.ArgumentParser(description='Plot a 2D Gaussian.')
parser.add_argument(
    '-p', '--polar',
    help = 'plot with polar X,Y mesh (default: cartesian mesh)',
    action = 'store_true')
parser.add_argument(
    '-c', '--centroid',
    help = 'centroid coordinates (default: random)',
    type = float,
    nargs = 2)
parser.add_argument(
    '-s', '--sigma',
    help = 'variance (sigma) (default: random)',
    type = float,
    nargs = 1)
args = parser.parse_args()

if args.polar :
    r = np.linspace(0.0,20.0,100.0)
    p = np.linspace(0.0,2*np.pi,100.0)
    R,P = np.meshgrid(r,p)
    X,Y = R*np.cos(P),R*np.sin(P)
else :
    x = np.linspace(-20.0,20.0,101.0)
    y = np.linspace(-20.0,20.0,101.0)
    X,Y = np.meshgrid(x,y)

if args.centroid is not None :
    x0,y0 = args.centroid
else :
    x0,y0 = random.uniform(-4.0,4.0), random.uniform(-4.0,4.0)

if args.sigma is not None :
    sigma0 = args.sigma[0]
else :
    sigma0 = random.uniform(4.0, 7.0)

Z = np.e**(-((X-x0)**2 + (Y-y0)**2)/(2*sigma0**2))

fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=cm.jet)
ax.set_zlim3d(0,1)
ax.set_zlabel('Intensity')
plt.show()

I get the following plot when I run this via python plot.py --centroid -5 5:

Using a polar mesh (python plot.py --centroid -5 5 --polar) yields the following:

 

[MathewsMD]

It's an artifact of your mesh. I've modified your code a bit so I can choose between a polar mesh or a cartesian mesh, and so I can optionally specify the centroid and variance:

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from matplotlib import cm
from matplotlib import pyplot as plt
from scipy import random
import argparse

parser = argparse.ArgumentParser(description='Plot a 2D Gaussian.')
parser.add_argument(
    '-p', '--polar',
    help = 'plot with polar X,Y mesh (default: cartesian mesh)',
    action = 'store_true')
parser.add_argument(
    '-c', '--centroid',
    help = 'centroid coordinates (default: random)',
    type = float,
    nargs = 2)
parser.add_argument(
    '-s', '--sigma',
    help = 'variance (sigma) (default: random)',
    type = float,
    nargs = 1)
args = parser.parse_args()

if args.polar :
    r = np.linspace(0.0,20.0,100.0)
    p = np.linspace(0.0,2*np.pi,100.0)
    R,P = np.meshgrid(r,p)
    X,Y = R*np.cos(P),R*np.sin(P)
else :
    x = np.linspace(-20.0,20.0,101.0)
    y = np.linspace(-20.0,20.0,101.0)
    X,Y = np.meshgrid(x,y)

if args.centroid is not None :
    x0,y0 = args.centroid
else :
    x0,y0 = random.uniform(-4.0,4.0), random.uniform(-4.0,4.0)

if args.sigma is not None :
    sigma0 = args.sigma[0]
else :
    sigma0 = random.uniform(4.0, 7.0)

Z = np.e**(-((X-x0)**2 + (Y-y0)**2)/(2*sigma0**2))

fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(X, Y, Z, rstride=2, cstride=2, cmap=cm.jet)
ax.set_zlim3d(0,1)
ax.set_zlabel('Intensity')
plt.show()

I get the following plot when I run this via python plot.py --centroid -5 5:View attachment 83929Using a polar mesh (python plot.py --centroid -5 5 --polar) yields the following:
View attachment 83930

Thank you so much for the help!