Design your own waveform synths?

[Rob & Heather Williams]

This may be a topic more appropriate for DH, but haven't
there been some music machines built that allow you to
design your own waveform right on a monitor screen?  I've
often been interested in what the tonal properties would be
like for a waveform, say, sine on the upramp, and square on
the return to zero.  Or maybe an ascending sawtooth on the
first 50% with a descending sine on the last half.  Since
analogs are limited in this area, I've never been able to
experiment to find out for myself.

Anyway, how come the idea isn't more popular with
synthesists?  Is this something that would HAVE to be
digitally controlled?  Couldn't an analog be built that
could do it with precision voltage control?

Robert