How can I rotate a graph that contains an imshow in matplotlib?

Question

I have some microscopic scan data in a rectangular grid that was scanned by an X/Y scanner. The object I'm scanning contains markers in a nice, rectangular, orthogonal pattern on its surface.

Due to practicalities, we can only align the object to the X/Y scanner to within a few degrees when fixing it to the X/Y scanner table. We compensate for this by some calibration measurement, and then performing scans that are nicely aligned with the object we're trying to scan (by moving the X and Y axes simultaneously).

This works well, but now I want to display this data in a coordinate system that corresponds to the X/Y scanner's axes. So the scanned, rectangular dataset will be rotated a bit in that coordinate system. (See the second image below for what I mean).

For presentation purposes however, I would prefer to have the scanned image nicely horizontal, and the axes rotated. I am trying to accomplish this in Matplotlib but I'm failing miserably.

I can get a rotated Axes (see the third image), but I am unable to figure out what kind of transforms I should do to get the ax3.imshow() to show its data at its intended position.

Here's where I am so far:

The program to generate the test data and the image I have so far is shown below.

I'd appreciate any help I can get. I'm afraid to say the documentation of matplotlib leaves a lot to be desired, so I hope somebody who knows matplotlib inside out may chime in.

#! /usr/bin/env python3

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.transforms import Affine2D
import mpl_toolkits.axisartist.floating_axes as floating_axes

import random

angle_deg = 5.0 # degrees CCW.

# Test data

NX = 5
NY = 3

x = np.zeros(shape=(NY, NX))
y = np.zeros(shape=(NY, NX))
c = np.zeros(shape=(NY, NX))

angle_rad = np.deg2rad(angle_deg)

for iy in range(NY):
    for ix in range(NX):

        icx = 0.5 * (NX - 1)
        icy = 0.5 * (NY - 1)

        # To centered coordinates, in physical units
        xcp = (ix - icx) * 0.1
        ycp = (iy - icy) * 0.1

        # Rotate
        xcpr = xcp * np.cos(angle_rad) - ycp * np.sin(angle_rad)
        ycpr = xcp * np.sin(angle_rad) + ycp * np.cos(angle_rad)

        # Rotate, and translated to the physical center
        x[iy, ix] = xcpr + 40.0
        y[iy, ix] = ycpr + 30.0

        c[iy, ix] = 100 + ix + iy

fig = plt.figure()
fig.set_size_inches(15, 9)

# Add axis #1.

ax1 = fig.add_subplot(131)
ax1.set_title("imshow()")
ax1.imshow(c, origin='lower')
ax1.grid()

# Add axis #2.

ax2 = fig.add_subplot(132)
ax2.set_title("pcolormesh()")
ax2.pcolormesh(x, y, c, shading='nearest')
ax2.axis('equal')
ax2.grid()

# Add axis #3.

min_x = x.min()
max_x = x.max()
min_y = y.min()
max_y = y.max()

cx = 0.5 * (min_x + max_x)
cy = 0.5 * (min_y + max_y)

transform = Affine2D().rotate_deg(-angle_deg)

grid_helper = floating_axes.GridHelperCurveLinear(transform, extremes=(min_x, max_x, min_y, max_y))

ax3 = floating_axes.FloatingSubplot(fig, 133, grid_helper=grid_helper)
ax3.grid()
ax3.set_title("rotate the entire graph.
How do I do get the data to show up here,
horizontally like in the leftmost image!?
")

ax3.imshow(c, origin='lower')

fig.add_subplot(ax3)

plt.show()

How can I rotate a graph that contains an imshow in matplotlib?

0 Answers