Image Rotation Coding

HardPython

Problem

Tesla Tecnologia e Comunicação's computer vision pipeline receives grayscale images that must be rotated before downstream processing. Implement a function that rotates an image counterclockwise by an arbitrary angle and returns the smallest rectangular output canvas containing the rotated image.

Use inverse mapping with nearest-neighbor sampling. Treat each pixel as a unit square centered at integer coordinates. Pixels in the output whose mapped source coordinate falls outside the input image must be filled with 0.

Formal Specification

The input image is a non-empty rectangular 2D list of integers, where image[y][x] is the pixel at column x and row y. The input angle is measured in degrees and may be positive, negative, or greater than 360. Return a new 2D list of integers.

Rotate around the center of the input image. The output dimensions are:

ceil(width * |cos(angle)| + height * |sin(angle)|) columns
ceil(width * |sin(angle)| + height * |cos(angle)|) rows

For every output pixel, map its center backward through the inverse rotation. Round each source coordinate to the nearest integer, and copy that pixel when it is in bounds.

Constraints

1 <= height, width <= 500
Pixel values are integers from 0 through 255
-10^5 <= angle <= 10^5
The input image is rectangular and non-empty
Use nearest-neighbor sampling
Out-of-bounds output pixels must contain 0

Function Signature

def rotate_image(image, angle):

Formal Specification

Rotate around the center of the input image. The output dimensions are:

ceil(width * |cos(angle)| + height * |sin(angle)|) columns
ceil(width * |sin(angle)| + height * |cos(angle)|) rows

For every output pixel, map its center backward through the inverse rotation. Round each source coordinate to the nearest integer, and copy that pixel when it is in bounds.