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2D Scaling Matrix

Implement a 3×3 homogeneous transformation matrix for 2D scaling, a fundamental concept in 2D/3D Transformations. This transformation is crucial in Computer Vision as it allows images to be resized while maintaining their aspect ratio.

In 2D space, scaling is a linear transformation that enlarges or reduces objects by a certain factor. The scaling factors $s_x$ and $s_y$ determine how much an object is stretched or shrunk along the $x$ and $y$ axes. To represent this transformation mathematically, we use a matrix equation.

To create the scaling matrix, follow these steps:

Define the scaling factors $s_x$ and $s_y$ .
Construct a 3×3 matrix with $s_x$ and $s_y$ on the diagonal.

\begin{pmatrix} s_x & 0 & 0 \\ 0 & s_y & 0 \\ 0 & 0 & 1 \end{pmatrix}

This technique is widely used in image processing applications.

Example:

Input:

scaling_matrix(2, 3)

Output:

[[2,0,0],[0,3,0],[0,0,1]]

Reasoning:

The function is called with scaling factors $s_x = 2$ and $s_y = 3$ : scaling_matrix(2, 3).
For 2D homogeneous scaling, we place $s_x$ and $s_y$ on the main diagonal of a $3 \times 3$ matrix, with $1$ in the bottom-right:
$S = \begin{pmatrix} s_x & 0 & 0 \\ 0 & s_y & 0 \\ 0 & 0 & 1 \end{pmatrix}$ .
Substituting $s_x = 2$ , $s_y = 3$ gives
$S = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 1 \end{pmatrix}$ ,
which corresponds to [[2,0,0],[0,3,0],[0,0,1]].

Constraints:

sx and sy are positive floating-point numbers

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.

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