I think you might be doing something wrong if the texture isn't applied correctly... But we don't have quads now because some hardware doesn't support them (some entire platforms don't support them)... I don't see any need. Maybe you could post your code?

Sorry, I don't know what OpenLayer's Bitmap::BlitDistorted() does. Can you explain? Sometimes when you need a 3d effect, you need to use 3d?

Ok.. I'm not even sure how you would do that without shaders or making a bunch of triangles. I wouldn't add it to Allegro, I think it's too specialized but wait for the smart people to speak.

It's not clear to me what that function does, or why you couldn't do the same thing by splitting the thing up into two triangles (as long as you order your vertices correctly and set the texture coordinates properly), however it seems to me you could just use a textured polygon?

Here's what it looks like when I use triangles:

{"name":"Screenshot-EOF%20Audition-1.png","src":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/4\/4\/44024acc4a3d7d543c3c9d1231bb858b.png","w":640,"h":480,"tn":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/4\/4\/44024acc4a3d7d543c3c9d1231bb858b"}

Here's the original texture:

{"name":"neck.png","src":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/b\/c\/bc919f4302dab4e56a4de6097e031646.png","w":512,"h":1024,"tn":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/b\/c\/bc919f4302dab4e56a4de6097e031646"}

It can be done with triangles, but as the posted example shows, you can't do it with just two (four will work: chop off the slanted sides, then split the remaining rectangle in two).
I would still say that a textured polygon should work, but that may have the same issue (not sure).

I would've guessed that since the original function was using QUADs the texture's mapping would be fixed... but why does the mapping in your example look like it was done with 2 triangles?

Because it is done like that internally. GL_QUADS is just a convenience type. Internally, OpenGL tesselates the quad into two triangles. For Todd Cope to get what he wants he needs to either:

1. Use perspective (primitives addon in principle supports this in hardware mode)

2. Approximate the effect using more triangles (e.g. in the way Evert suggested)

Note that without the third dimension you can never get the proper mapping (unless your vertices are arranged in a particular way) because the generic quad to quad mapping is non-affine... and without 3D, only affine mappings can be done. You can get a good approximation by throwing more triangles at it, but it won't be exact in the general case.

Assuming that the projection matrix is set up as an orthogonal projection, you can get the effect with just 2 triangles and playing with the z coordinate. A bit of trigonometry should give you what z values you need to use.

Well if the output he expects is what I think (the horizontal lines won't be equidistant).

Now I'm starting to not be sure about what OpenGL would output doing that. I would think that the z coordinate would be used to perform the perspective correction and you could get the desired output that way (it's a bit of a hack/trick actually). But I haven't used OpenGL in a lot of time and now I'm unsure about that.

Can't we just investigate on OpenLayer's setup and see how it setups the projections?

AFAIK, OpenLayer sets up an ortographic projection like this:

    glMatrixMode( GL_PROJECTION );
    glPushMatrix();
    glLoadIdentity();
    glOrtho( 0, w, 0, h, -1, 1000 );
    glScalef( 1, -1, 1 );
    glTranslatef( 0, -h, 0 );

    glMatrixMode( GL_MODELVIEW );
    glLoadIdentity();
    glDisable( GL_DEPTH_TEST );

There must be something else though, but I'm looking for any clues. If you want, I'll attach OpenLayer's source here.

EDIT: Ok, here it is. I took away the demos, but I just 7-zipped the old package I had. Download.