Re: [pygame] Perspective Transform Quad

[Alex Holkner <aholkner@xxxxxxxxxxxxxx>]

Kamilche wrote:

> I have a need to tile a bitmap across an arbitrary quadrilateral, and
> apply perspective to it.
> The Python Imaging Library (PIL) has an undocumented function that
> might work, but I can't figure out how to make it work. You're
> supposed to pass it 8 parameters, a b c d e f g h .

My version of PIL doesn't have this function (the Image.PERSPECTIVE 
constant exists, but it raises an exception), but most likely the 8 
parameters correspond to all but one of the elements for a 2D 
transformation matrix:

[x']   [a b c][x]
[y'] = [d e f][y]
[w']   [g h 1][1]

The AFFINE transform method allows you to supply 6 of these:

[x'] = [a b c][x]
[y'] = [d e f][y]
[w'] = [0 0 1][1]

Typically projection occurs from 3D to 2D, and the Z coordinate is used 
as the perspective divide:

[x'] = [1 0 0 0][x]
[y'] = [0 1 0 0][y]
[z'] = [0 0 1 0][z]
[w'] = [0 0 1 0][1]

The resulting 4-tuple (x,y,z,w) is divided through by w to project into 
3D: (x/w, y/w, z/w).

In your application you don't have 3D data, but you can achieve the same 
result using Y as the perspective divide (higher values of Y mean higher 
values of W, so pixels near the top of the image will be have have their 
X coordinate divided more):

[x'] = [1 0 0][x]
[y'] = [0 y 0][y]
[w'] = [0 1 0][1]

However, it appears that the function you describe will not accept "y" 
as a matrix parameter, or any value besides 0 for the bottom-left 
element.  So this function won't solve your problem.

There is a QUAD transform in PIL which you could use to map a trapezium 
to a rectangle.  The result will not look correct though, as it will not 
apply perspective-correct interpolation.  The result may be "good 
enough" (the current generation of mobile devices with 3D chipsets do 
not employ perspective correction, but all PC chips have done so since 
texture mapping was introduced).

Any 3D imaging library will be able to apply the perspective you need.

Cheers
Alex.