TikZ trapezoid transformation (vanishing point)

Question

Within a TikZ drawing, I want to distort a 2D rasterimage (from \includegraphics) so that it appears to be rotated by 90° around the vertical axis in 3D (it should look perpendicular to the sheet of paper). I've managed to achieve a transformation with yslant and xscale, like the following.

\begin{tikzpicture}
  \node (term) at (0,0) [yslant=-0.7,xscale=0.3] 
        {\includegraphics[width=40mm]{image.png}};
\end{tikzpicture}

which distorts an image like this

                            a    
                            |\             
a---------b                 | \  
|         |                 |  \ 
|         |      -->        c   b
|         |                  \  |
c---------d                   \ |
                               \|
                                d

I'm not really happy with this: The distance |a-c| should be smaller than |b-d|. How can I achieve this?

There is an example of a cuboid which looks pretty nice, but it seems useless to distort an imported raster image.

Welcome to TeX.sx! No need to add signature, your username is included in the lower right of your Q. — Peter Jansson, Jan 28 '13 at 23:42
The transformation you achieved would be the result of a parallel projection. You actually want to simulate a perspective projection? I don’t think this is doable with vanilla TikZ options. You probably need to calculate these transformations. — Qrrbrbirlbel, Jan 28 '13 at 23:46
This is not doable via PDF transformation (TikZ and PGF use PDF transformations). You need to transform your rasterimage via Gimp (or Photoshop). — Paul Gaborit, Jan 29 '13 at 00:13
Maybe a duplicate : http://tex.stackexchange.com/questions/52578/perspective-transform ? Nope you have an image, nevermind — percusse, Jan 29 '13 at 00:32
Maybe you could draw your rectangle in perspective using the 3D capabilities of Tikz? See http://tex.stackexchange.com/q/59406/19156 — Lionel MANSUY, Jan 29 '13 at 08:58
I think this is best done with ImageMagick’s convert tool. Using example-image.png from the mwe package one can do convert example-image.png -distort Perspective "0,0,0,40 0,300,0,260 400,0,400,0 400,300,400,300" example-image-distorted.png. Though, I couldn’t get the now black background color to be either white or transparent. I’m sure, it is somehow possible. — Qrrbrbirlbel, Apr 09 '13 at 17:02

TikZ trapezoid transformation (vanishing point)

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