Transforming Canvas Images: Resizing, Skewing, and Dragging with Ease

I have a vision for an application that allows users to upload images and manipulate them by dragging the corners to distort the image. However, I am at a loss on where to begin and can't seem to find any examples to guide me.

In the meantime, here is an example in flash that showcases similar functionality:
- Click "Cando Stijlkamer"
- Choose one of the six backgrounds
- Select step 2 "Kies uw deur" at the top
- Double click on the door and repeat at the bottom
- Now you can drag the corners of the image

Here is an example image:

If anyone has insight on how to bring this idea to life, please share your knowledge!

UPDATE
I have started using ThreeJS for webGL and currently have a cube with capabilities to adjust perspective, scale, and skew. However, the corners are still not flexible as desired.

UPDATE 2
I have successfully created a custom geometry with draggable corners for further experimentation.

javascriptcanvasthree.jswebgl

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