Interpolating a 3D surface known by its corner nodes and coloring it with a colormap

Question

I want to construct a 3D representation of experimental data to track the deformation of a membrane. Experimentally, only the corner nodes are known. However I want to plot

Answer 1

Indeed it seems plot_trisurf should be perfect for this task! Additionally, you can make use of tri.UniformTriRefiner to get a Triangulation with smaller triangles:

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

x = numpy.array([0, 0, 1, 1])
y = numpy.array([0.5, 0.75, 1, 0.5])
z = numpy.array([0, 0.5, 1, 0])

triang = tri.Triangulation(x, y)
refiner = tri.UniformTriRefiner(triang)
new, new_z = refiner.refine_field(z, subdiv=4)

norm = plt.Normalize(vmax=abs(y).max(), vmin=-abs(y).max())
kwargs = dict(triangles=new.triangles, cmap=cm.jet, norm=norm, linewidth=0.2)

fig = plt.figure()
ax = Axes3D(fig)
pt = ax.plot_trisurf(new.x, new.y, new_z, **kwargs)
plt.show()

Resulting in the following image:

Triangular grid refinement was only recently added to matplotlib so you will need version 1.3 to use it. Though if you would be stuck with version 1.2 you should also be able to use the source from Github directly, if you comment out the line import matplotlib.tri.triinterpolate and all of the refine_field method. Then you need to use the refine_triangulation method and use griddata to interpolate the new corresponding Z-values.

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Edit: The above code uses cubic interpolation to determine the Z-values for the new triangles, but for linear interpolation you could substitute / add these lines:

interpolator = tri.LinearTriInterpolator(triang, z)
new, new_z = refiner.refine_field(z, interpolator, subdiv=4)

Alternatively, to do the interpolation with scipy.interpolate.griddata:

from scipy.interpolate import griddata

new = refiner.refine_triangulation(subdiv = 4)
new_z = griddata((x,y),z, (new.x, new.y), method='linear')