Matplotlib - Transforms

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Transform in general is a way to change something from one form to another. It is like taking an input and turning it into a different output. Transforms are used in various fields, such as mathematics, physics, and computer science.

For example, in mathematics, a transform can be a mathematical operation that changes a set of numbers or functions into a different representation. The Fourier transform, for instance, converts a function in the time domain (like a sound wave) into its frequency components.

Transforms in Matplotlib

In Matplotlib, transforms refer to the conversion process from data coordinates to pixel coordinates, allowing to place the graphical elements such as points, lines, and text within a plot accurately.

You can use various types of transformations in matplotlib, such as linear transformations, logarithmic transformations, and more. To handle these transformations, Matplotlib provides the "transform" parameter.

The "transform" parameter can take various values, such as instances of the "matplotlib.transforms.Transform" class or strings representing common transformations like 'ax.transData' for data coordinates or 'ax.transAxes' for axes coordinates. By using the transform parameter, you can customize the coordinate system and apply different transformations to enhance the visualization of their data on the Matplotlib plots.

Data to Axes Transform

In Matplotlib, the data to axes transform refers to the process of converting your actual data points into coordinates within the axes of your plot. When you plot data, you use specific "x" and "y" values. The transformation ensures that these data points are correctly positioned within the axes of your plot, taking into account the scaling and limits of the "x" and "y" axes.

Example

In the following example, we are creating a simple line plot using data coordinates (x, y). We then use the ax.text() function to add text to the plot, specifying the position (2, 25) in data coordinates. The "transform=ax.transData" parameter ensures that the text is positioned using data coordinates −

import matplotlib.pyplot as plt
# Data
x = [1, 2, 3, 4]
y = [10, 20, 25, 30]

# Creating a plot
fig, ax = plt.subplots()
ax.plot(x, y, marker='o', linestyle='-', label='Data points')
ax.legend()

# Transforming data coordinates to axes coordinates
ax.text(2, 25,'Text in Data Coordinates' , transform=ax.transData)

# Setting plot title and labels
ax.set_title('Data to Axes Transform')
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')

plt.show()

Output

Following is the output of the above code −

Axes to Data Transform

The axes to data transform in Matplotlib is the reverse of the "data to axes transform". While the "data to axes transform" converts your actual data points into coordinates within the axes of your plot, the "axes to data transform" does the opposite. It takes coordinates specified in terms of the axes of your plot and converts them into the corresponding data values.

Example

In here, we are creating a plot with axis limits set between "0" and "1" for both "x" and "y" axes. We use the ax.text() function to add text to the plot, specifying the position "(0.5, 0.5)" in axes coordinates. The "transform=ax.transAxes" parameter ensures that the text position is interpreted as relative to the axes rather than the data −

import matplotlib.pyplot as plt

# Creating a plot with normalized axes
fig, ax = plt.subplots()
ax.set_xlim(0, 1)
ax.set_ylim(0, 1)

# Transforming axes coordinates to data coordinates
ax.text(0.5, 0.5, 'Text in Axes Coordinates', transform=ax.transAxes, ha='center', va='center')

# Setting plot title and labels
ax.set_title('Axes to Data Transform Example')
ax.set_xlabel('X-axis (normalized)')
ax.set_ylabel('Y-axis (normalized)')

plt.show()

Output

On executing the above code we will get the following output −

Blended Transform

In Matplotlib, a blended transform is a way to combine or blend different coordinate systems when placing elements on a plot. It allows you to create a custom transformation that contains aspects of both data coordinates and axes coordinates.

Example

In the example below, we are creating a plot and using the blended_transform_factory() function to create a blended transformation. The resulting "trans" object is a blend of both data and axes coordinates. The ax.text() function then uses this blended transformation to position text at (0.8, 0.2), effectively combining data and axes coordinates −

import matplotlib.pyplot as plt
from matplotlib.transforms import blended_transform_factory

# Creating a plot
fig, ax = plt.subplots()

# Creating a blended transformation
trans = blended_transform_factory(ax.transData, ax.transAxes)

# Adding text using the blended transformation
ax.text(0.8, 0.2, 'Blended Transform', transform=trans, ha='center', va='center')

# Setting plot title and labels
ax.set_title('Blended Transform')
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')

plt.show()

Output

After executing the above code, we get the following output −

Offset Transform

In Matplotlib, an offset transform is a way to add a precise offset to the position of elements on a plot. It involves shifting or translating the coordinates of the elements by a specified amount. This type of transformation is useful when you want to fine-tune the placement of text, markers, or other graphical elements.

For example, if you have a data point at (2, 10) and you want to display a label slightly to the right and above this point, you can use an Offset Transform to apply a specific offset to the original coordinates. This allows you to control the exact positioning of elements relative to their original locations in the data.

Example

Now, we are creating a plot, and using the "ScaledTranslation" class to create an offset transformation. The "trans" object is a combination of the original data transformation (ax.transData) and a scaled translation of (0.1, 0.2) in data coordinates. The ax.text() function then uses this transformed coordinate to position text at (2, 25) with the specified offset −

import matplotlib.pyplot as plt
from matplotlib.transforms import ScaledTranslation

# Creating a plot
fig, ax = plt.subplots()

# Creating an offset transformation
trans = ax.transData + ScaledTranslation(0.1, 0.2, ax.transData)

# Adding text with the offset transformation
ax.text(0.4, 0.2, 'Text with Offset', transform=trans)

# Setting plot title and labels
ax.set_title('Offset Transform Example')
ax.set_xlabel('X-axis')
ax.set_ylabel('Y-axis')

plt.show()

Output

On executing the above code we will get the following output −