📘

Batch Affine Transform with PyTorch

Implement batch affine transformations on 2D points using PyTorch tensors.

Given a batch of 2D points and a 2×3 affine transformation matrix, apply the transformation to all points efficiently using matrix operations.

An affine transformation combines linear transformation (rotation, scaling, shearing) with translation:

$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} a & b & t_x \\ c & d & t_y \end{pmatrix} \begin{pmatrix} x \\ y \\ 1 \end{pmatrix}$

Or equivalently: $x' = ax + by + t_x$ , $y' = cx + dy + t_y$

Key insight: For N points, convert to homogeneous coordinates (add column of 1s) and multiply with the transformation matrix transposed: $P' = P_h \cdot M^T$

where $P_h$ is (N, 3) and $M^T$ is (3, 2), giving $P'$ as (N, 2).

Example:

Input:

points = [[1, 0], [0, 1], [1, 1]]
transform = [[1, 0, 10], [0, 1, 20]]  # Translation by (10, 20)

Output:

[[11.0, 20.0], [10.0, 21.0], [11.0, 21.0]]

Reasoning:

Affine matrix (translation only): $M = \begin{pmatrix} 1 & 0 & 10 \\ 0 & 1 & 20 \end{pmatrix}$

For each point [x, y], compute: $x' = 1 \cdot x + 0 \cdot y + 10 = x + 10$ $y' = 0 \cdot x + 1 \cdot y + 20 = y + 20$

Results:

[1, 0] → [1+10, 0+20] = [11, 20]
[0, 1] → [0+10, 1+20] = [10, 21]
[1, 1] → [1+10, 1+20] = [11, 21]

Constraints:

points: Tensor of shape (N, 2) containing 2D points
transform: Tensor of shape (2, 3) - affine transformation matrix
Return: Transformed points as tensor of shape (N, 2)
Round to 4 decimal places

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.