Custom Grid Transformation with Matplotlib

Introduction

This lab provides a step-by-step guide on how to use GridHelperCurveLinear to define custom grids and ticklines by applying a transformation on the grid. We will use Python's Matplotlib library to create custom grids and ticklines.

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Import Required Libraries

The first step is to import the required libraries, including matplotlib.pyplot, numpy, ExtremeFinderSimple, MaxNLocator, and GridHelperCurveLinear.

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.axisartist.axislines import Axes
from mpl_toolkits.axisartist.grid_finder import (ExtremeFinderSimple, MaxNLocator)
from mpl_toolkits.axisartist.grid_helper_curvelinear import GridHelperCurveLinear

Define Transformation Functions

The second step is to define the transformation functions. In this example, we will use the tr function to transform the x-axis values and leave the y-axis values unchanged. The inv_tr function will be used to invert the transformation.

def tr(x, y):
    return np.sign(x)*abs(x)**.5, y

def inv_tr(x, y):
    return np.sign(x)*x**2, y

Define GridHelperCurveLinear

The third step is to define the GridHelperCurveLinear instance. We will use the transformation functions defined in Step 2 to transform the grid. We will also set the grid_locator1 and grid_locator2 to MaxNLocator(nbins=6) to increase the tick density.

grid_helper = GridHelperCurveLinear(
    (tr, inv_tr),
    extreme_finder=ExtremeFinderSimple(20, 20),
    grid_locator1=MaxNLocator(nbins=6), grid_locator2=MaxNLocator(nbins=6))

Define Axes and Display Image

The fourth step is to define the axes using the grid_helper instance created in Step 3. We will also display an image using the imshow function.

ax1 = fig.add_subplot(axes_class=Axes, grid_helper=grid_helper)
ax1.imshow(np.arange(25).reshape(5, 5), vmax=50, cmap=plt.cm.gray_r, origin="lower")

Create the Figure

The final step is to create the figure using the plt.figure function. We will set the figure size to (7, 4) and call the curvelinear_test1 function created in Steps 2-4.

if __name__ == "__main__":
    fig = plt.figure(figsize=(7, 4))
    curvelinear_test1(fig)
    plt.show()

Summary

In this lab, we learned how to use GridHelperCurveLinear to define custom grids and ticklines by applying a transformation on the grid. We used Python's Matplotlib library to create a custom grid and ticklines for a 5x5 matrix displayed on the axes.