Connect points in a three dimensional plot

Question

I have an algorithm that can be controlled by two parameters so now I want to plot the runtime of the algorithm depending on these parameters.

My Code:

from matplotlib import pyplot
import pylab
from mpl_toolkits.mplot3d import Axes3D

fig = pylab.figure()
ax = Axes3D(fig)

sequence_containing_x_vals = [5,5,5,5,10,10,10,10,15,15,15,15,20,20,20,20]
sequence_containing_y_vals = [1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4]
sequence_containing_z_vals = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]

ax.scatter(sequence_containing_x_vals, sequence_containing_y_vals, sequence_containing_z_vals)

pyplot.show()

This will plot all the points in the space but I want them connected and have something like this:

(The coloring would be nice but not necessary)

Answer 1

To plot the surface you need to use plot_surface, and have the data as a regular 2D array (that reflects the 2D geometry of the x-y plane). Usually meshgrid is used for this, but since your data already has the x and y values repeated appropriately, you just need to reshape them. I did this with numpy reshape.

from matplotlib import pyplot, cm
from mpl_toolkits.mplot3d import Axes3D
import numpy as np

fig = pyplot.figure()
ax = Axes3D(fig)

sequence_containing_x_vals = np.array([5,5,5,5,10,10,10,10,15,15,15,15,20,20,20,20])
X = sequence_containing_x_vals.reshape((4,4))

sequence_containing_y_vals = np.array([1,2,3,4,1,2,3,4,1,2,3,4,1,2,3,4])
Y = sequence_containing_y_vals.reshape((4,4))

sequence_containing_z_vals = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16])
Z = sequence_containing_z_vals.reshape((4,4))

ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.hot)

pyplot.show()

Note that X, Y = np.meshgrid([1,2,3,4], [5, 10, 15, 20]) will give the same X and Y as above but more easily.

Of course, the surface shown here is just a plane since your data is consistent with z = x + y - -5, but this method will work with generic surfaces, as can be seen in the many matplotlib surface examples.