I’ll need a simple circuit to mix my video signals together. The Arduino TV Out library shows how to do this, but that works with 5V IOs, but the STM32L Discovery (and all ARM chips AFAIK) uses 3.3V.

So which resistors will I need?  To produce a white signal, the sync and video lines will be high.  The equivalent circuit looks like this:

(The 75Ω resistor is the resistance inside the TV).

To show a black signal, the sync line will be high, and the video line will be low, which looks like this:

Wikipedia gives the formula for a voltage divider, so the resistors in the first diagram can be calculated with this formula:

FIXME

and in the second:

FIXME

I tried solving these, but that’s well beyond my mathematical ability.  Instead I found some online site that could plot the two formulas (edit: I could have used Wolfram Alpha).  The lines crossed at about RV=250Ω and RS=580Ω. These resistor values don’t exist, so RV=270Ω and RS=560Ω is close enough.  They seem to work fine in the circuit.