I need to combine two images in C# ( 4.7.2 ), and have the top image transformed putting each of the four corners at specific coordinates in the image.
Is that possible? Preferably with a solution that doesn't require spending a ton of money. As far as I can tell i can't do it with the Bitmap/Graphics classes.
Shear (or skew), which is what an affine transform such as used in GDI+ or WPF, is unlikely to do what you want, if I understand the question correctly. With shear/skew the transformed coordinate space is still a parallelogram, whereas in your image, the original rectangle is squeezed or stretched arbitrarily.
Assuming that's correct, I would recommend using the features in the WPF Media3D namespace (WPF, simply because it's the most accessible 3D API in the .NET context). In particular, you will want to define a texture that is your original bitmap. Then you will want to define a quadrilateral 2D surface in 3D coordinate space with sufficient resolution (i.e. triangles) for your purposes (see below), and where the triangles in that surface are constructed by tessellating the shape that you want as your final image, and where you've interpolated the texture (UV) coordinates for that shape across the vertexes that result from the tessllation.
How many triangles you actually want depends on the desired quality. In theory, you could use just two. This is the simplest approach, and determining the UV coordinates is trivial, because you only have your original four corners. But there will be a visual discontinuity along the diagonal where the two triangles meet, where the interpolation of the texture pixels changes direction due to the triangles not being square to each other.
For better results, you'll need to use more triangles. But then this complicates the assignment of the UV coordinates. For each inner vertex of this surface, you'll need to interpolate across the surface. This is probably easier to do if you generate the tessellation in the first place by subdividing the quadrilateral with lines connecting opposite sides (which will form smaller interior quadrilaterals bounded by intersecting lines) and then just divide each of those quadrilaterals into pairs of triangles. If you do it this way, then you can use the distance along each line to determine the appropriate U or V coordinate at each vertex that line goes through.
Having created the appropriate texture and geometry, it's a simple matter to render the result into a RenderTargetBitmap via the Viewport3DVisual class, and then do whatever you want with that bitmap.
Now, all that said…
If it turns out that your problem can be simplified such that shear/skew is sufficient for your needs, you can look at De-skew characters in binary image for help with that. In that particular example, they are trying to undo skew caused by optical effects, but skewing is skewing; the same exact principle works in either direction.
Even if your problem is not amenable to shear/skew approaches, before you implement your own solution (e.g. based on my outline above), you may want to look at other available tools. Information about some options can be found in, for example, Image Modification (cropping and de-skewing) in C# and Image comparison - rotation, alignment and scaling.
