an attempt at the three shears image rotation problem. Reads from first.png, outputs to out.png

threeshears.py

import math
from PIL import Image, ImageDraw

input_image = Image.open("first.png")
width,height = input_image.size
second_image = Image.new('RGB', input_image.size)
third_image = Image.new('RGB', input_image.size)
output_image = Image.new('RGB', input_image.size)
# draw = ImageDraw.Draw(output_image)

theta = math.pi/8

def apply_matrix(matrix, vector):
	return [ vector[0]*matrix[0][0] + vector[1]*matrix[0][1], vector[0]*matrix[1][0] + vector[1]*matrix[1][1] ]

a = [
	[1, -math.tan(theta/2)],
	[0, 1]
]
b = [ [1, 0], [math.sin(theta), 1] ]
c = [ [1, -math.tan(theta/2)], [0, 1] ]

for x in range(width):
	for y in range(height):
		mx = x - width/2
		my = y - height/2

		new_mx, new_my = apply_matrix(a, [mx, my])
		new_mx, new_my = round(new_mx), round(new_my)

		nx = new_mx + round(width/2)
		ny = new_my + round(height/2)

		if nx >= 0 and nx < width and ny >= 0 and ny < height:
			second_image.putpixel((nx,ny), input_image.getpixel((x,y)))

for x in range(width):
	for y in range(height):
		mx = x - width/2
		my = y - height/2

		new_mx, new_my = apply_matrix(b, [mx, my])
		new_mx, new_my = round(new_mx), round(new_my)

		nx = new_mx + round(width/2)
		ny = new_my + round(height/2)

		if nx >= 0 and nx < width and ny >= 0 and ny < height:
			third_image.putpixel((nx,ny), second_image.getpixel((x,y)))

for x in range(width):
	for y in range(height):
		mx = x - width/2
		my = y - height/2

		new_mx, new_my = apply_matrix(c, [mx, my])
		new_mx, new_my = round(new_mx), round(new_my)

		nx = new_mx + round(width/2)
		ny = new_my + round(height/2)

		if nx >= 0 and nx < width and ny >= 0 and ny < height:
			output_image.putpixel((nx,ny), third_image.getpixel((x,y)))

output_image.save('out.png')