How does PIL.Image.PERSPECTIVE work?

Question

Python

Good afternoon.
I started to study Pillow and the following question arose:
How does PIL.Image.PERSPECTIVE mode work in img.transform?

img = Image.new("RGB", (100, 100), (155, 155, 155))
draw = ImageDraw.Draw(img)
draw.text((0, 90), "LOLOLOLOLOLOLOL!", font=font)
draw.text((0, 80), "LOLOLOLOLOLOLOL!", font=font)
draw.text((0, 70), "LOLOLOLOLOLOLOL!", font=font)
draw.text((0, 60), "LOLOLOLOLOLOLOL!", font=font)
draw.text((0, 50), "LOLOLOLOLOLOLOL!", font=font)
img.transform((100, 100), Image.PERSPECTIVE, (25, 25, 25, 75, 75, 75, 75, 25))

I thought that it "moves" the corners of the image to the appropriate coordinates, but apparently it doesn't...

Answer 1

No, the coordinates are not indicated there, but the coefficients of the equation (ax + by + c) / (gx + hy + 1), (dx + ey + f) / (gx + hy + 1), calculates the coordinates, where to get the value for each pixel (x, y).

From the package documentation:

Data is a 8-tuple (a, b, c, d, e, f, g, h) which contains the coefficients for a perspective transform. For each pixel (x, y) in the output image, the new value is taken from a position (a x + b y + c)/(g x + h y + 1), (d x + e y + f)/(g x + h y + 1) in the input image, rounded to nearest pixel.

Based on this, you can make simple examples:
(1, 0, 0, 0, 1, 0, 0, 0) - will not change the picture
(1, 0, 0, 0, 2, 0, 0, 0) - "flatten "picture 2 times vertically, etc.
To find these coefficients, you can use an auxiliary function, for example, from here https://stackoverflow.com/a/14178717