How can I render a square bitmap to an arbitrary four-sided polygon using GDI?

Question

I need to paint a square image, mapped or transformed to an unknown-at-compile-time four-sided polygon. How can I do this?

Longer explanation

The specific

Answer 1

Take a look at 3D Lab Vector graphics. (Specially "Football field" in the demo).

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Another cool resource is AggPas with full source included (download)

AggPas is Open Source and free of charge 2D vector graphics library. It is an Object Pascal native port of the Anti-Grain Geometry library - AGG, originally written by Maxim Shemanarev in C++. AggPas doesn't depend on any graphic API or technology. Basically, you can think of AggPas as of a rendering engine that produces pixel images in memory from some vectorial data.

Here is how the perspective demo looks like:

After transformation: