The demos have been relying on the firmware to setup the HDMI display pipeline and to provide them with a frame buffer to draw on.
The program found here attempts to take the control of the pipeline from the firmware, and run it on its own.
Because of the lack of documentation, the Linux vc4 driver was consulted
to determine the registers to setup and the sequence of steps necessary, to
disable and enable the pipeline.
The program can successfully setup the pipeline to display at resolutions 640x480@60Hz, 800x600@60Hz, and 1920x1080@60Hz.
One of the problems faced during this programming was the problem where the monitor would display a horizontal resolution of +2 pixels. That is, if the desired resolution were 640x480@60Hz, the monitor would instead run with 642x480@60Hz. The left-most two columns of the pixels were purple/violet in colour. The first column of the frame buffer was thus at column #2 on the screen.
A similar problem is described within a bug, here. The bug also describes the root cause - monitor not being sent the appropriate infoframe packets.
Following that hint, the program sends a properly configured AVI InfoFrame corresponding to the resolution being set. It does so by writing into the appropriate HDMI Packet RAM registers, and asking the HDMI encoder to pull the infoframe by reading them. With these two steps, the monitor displays the expected resolutions exactly.