Limit/mask matplotlib contour to data area

Question

I have a pandas DataFrame with non-uniformly spaced data points given by an x, y and z column, where x and y are pairs of variables and z is the dependent variable. For example:

import matplotlib.pyplot as plt
from matploblib.mlab import griddata
import numpy as np
import pandas as pd

df = pd.DataFrame({'x':[0, 0, 1, 1, 3, 3, 3, 4, 4, 4], 
                   'y':[0, 1, 0, 1, 0.2, 0.7, 1.4, 0.2, 1.4, 2], 
                   'z':[50, 40, 40, 30, 30, 30, 20, 20, 20, 10]})

x = df['x']
y = df['y']
z = df['z']

I want to do a contour plot of the dependent variable z over x and y. For this, I create a new grid to interpolate the data on using matplotlib.mlab's griddata function.

xi = np.linspace(x.min(), x.max(), 100)
yi = np.linspace(y.min(), y.max(), 100)
z_grid = griddata(x, y, z, xi, yi, interp='linear')
plt.contourf(xi, yi, z_grid, 15)
plt.scatter(x, y, color='k') # The original data points
plt.show()

While this works, the output is not what I want. I do not want griddata to interpolate outside of the boundaries given by the min and max values of the x and y data. The following plots are what shows up after calling plt.show(), and then highlighted in purple what area of the data I want to have interpolated and contoured. The contour outside the purple line is supposed to be blank. How could I go about masking the outlying data?

The linked question does unfortunately not answer my question, as I don't have a clear mathematical way to define the conditions on which to do a triangulation. Is it possible to define a condition to mask the data based on the data alone, taking the above Dataframe as an example?

user_1033074 · Answer

Ernest's answer is a great solution, but very slow for lots of contours. Instead of clipping every one of them, I built a mask by constructing the complement polygon of the desired clipping mask.

Here is the code based on Ernest's accepted answer:

import numpy as np
import pandas as pd
import matplotlib.tri as tri
import matplotlib.pyplot as plt
from descartes import PolygonPatch
from shapely.geometry import Polygon

df = pd.DataFrame({'x':[0, 0, 1, 1, 3, 3, 3, 4, 4, 4], 
                   'y':[0, 1, 0, 1, 0.2, 0.7, 1.4, 0.2, 1.4, 2], 
                   'z':[50, 40, 40, 30, 30, 30, 20, 20, 20, 10]})

points = df[['x', 'y']]
values = df[['z']]

xi = np.linspace(points.x.min(), points.x.max(), 100)
yi = np.linspace(points.y.min(), points.y.max(), 100)

triang = tri.Triangulation(points.x, points.y)
interpolator = tri.LinearTriInterpolator(triang, values.z)
Xi, Yi = np.meshgrid(xi, yi)
zi = interpolator(Xi, Yi)

clipindex = [ [0,2,4,7,8,9,6,3,1,0],
              [0,2,4,7,5,8,9,6,3,1,0],
              [0,2,4,7,8,9,6,5,3,1,0]]

fig, axes = plt.subplots(ncols=3, sharey=True, figsize=(10,4))

for i, ax in enumerate(axes):

    ax.set_xlim(-0.5, 4.5)
    ax.set_ylim(-0.2, 2.2)
    xlim = ax.get_xlim()
    ylim = ax.get_ylim()    

    cont = ax.contourf(Xi, Yi, zi, 15)
    ax.scatter(points.x, points.y, color='k', zorder=2) # The original data points
    ax.plot(points.x[clipindex[i]], points.y[clipindex[i]], color="crimson", zorder=1)

    #### 'Universe polygon': 
    ext_bound = Polygon([(xlim[0], ylim[0]), (xlim[0], ylim[1]), (xlim[1], ylim[1]), (xlim[1], ylim[0]), (xlim[0], ylim[0])])
    #### Clipping mask as polygon:
    inner_bound = Polygon([ (row.x, row.y) for idx, row in points.iloc[clipindex[i]].iterrows() ])
    #### Mask as the symmetric difference of both polygons:
    mask = ext_bound.symmetric_difference(inner_bound)

   ax.add_patch(PolygonPatch(mask, facecolor='white', zorder=1, edgecolor='white'))

plt.show()

Limit/mask matplotlib contour to data area

2 Answers