Plot line of constant x[0] for vector function

Question

Hi, I have a surface described by a vector function, and I'd like to plot a line of constant x[0]. Here's a minimal example of the code.

from dolfin import *
import numpy as np
mesh = CircleMesh(Point(0.0,0.0),1.0,0.1)
space = VectorFunctionSpace(mesh,"CG",2,dim=3)
X = Function(space)
X.interpolate(Expression(("x[0]","x[1]","x[0]*x[0]+x[1]*x[1]")))
x_coords = []
y_coords = []
z_coords = []
for x in np.linspace(-0.9,0.9,10):
    p=Point(x,0.0)
    x_coords.append(X(p)[0])
    y_coords.append(X(p)[1])
    z_coords.append(X(p)[2])

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x_coords,y_coords,z_coords)
plt.show()

I am obviously doing something wrong, as this produces complete nonsense.

Any help would be appreciated.

Answer 1

Hi, since your y values are all of order 1E-16 or so, matplotlib adjusted the y-axis accordingly and on that scale the curve is not smooth because e.g. points with y equal to 1E-16 and 9E-16 (which is 0) take you from one end of axis to another. So the fix is

plt.ylim([-1, 1])

Btw, why is it necessary represent the surface as vector map: x, y --> x, y, z? You know what x, y are so a scalar map: x, y --> z seems to be a more appropriate choice. The code would then look as follows (note that it does not need ylim adjustment)

from dolfin import *
import numpy as np

mesh = CircleMesh(Point(0.0,0.0), 1.0, 0.1)
space = FunctionSpace(mesh, "CG", 2)
X = Function(space)
X.interpolate(Expression("x[0]*x[0]+x[1]*x[1]"))

plot(X, interactive=True)

x_coords = np.linspace(-0.9, 0.9, 10)
y_coords = np.zeros(len(x_coords))
z_coords = np.zeros(len(x_coords))

for i, (x, y) in enumerate(zip(x_coords, y_coords)):
  z_coords[i] = X(x, y)

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x_coords, y_coords, z_coords)
plt.show() 

Comments

Ah, well that is embarrassing. Thank you for your response.

Btw, why is it necessary represent the surface as vector map: x, y -->
x, y, z? You know what x, y are so a scalar map: x, y --> z seems to
be a more appropriate choice.

The actual equation I will be solving is an embedding of a Riemannian manifold, so that X is a map from an open subset of R^2 into R^3 :-)

---

Okay, thanks for clarification.