Just so that we are clear here. I have no idea how to reverse engineer the 3rd Wave oscillator waveform in question here, especially without the recorded waveform and the fact that I do not own the synth itself. Anyway…
I was able to plot up some sine wave variations whereby I am essentially performing a Zero Order Hold (ZOH) like operation with increasing resolution/fidelity using the STAIRS function in MATLAB. Not exactly ZOH, but similar enough for the purposes we are discussing here. For example
Is this ballpark what you are looking for? Theoretically I can perform the same operations for sawtooth, reverse sawtooth, triangle, etc.,
I don’t want to get too deep here and waste cycles I don’t have if folks won’t find these sorts of waveform manipulations useful.