Actually what you have there is pretty much a dimmer circuit, and where you show a diode it is likely a diac. Here nor there, but if you look at what you have and then
take a look at this you will see the similarity. A Google of Dimmer Circuits will bring up a dozen similar circuits.
So what you want to do is use an AO (Analog Output) from a pic to control the voltage out of a dimmer as in 0 to some voltage DC like 0 to 5 volts gets you 0 to 240 VAC correct. Take a look at the circuiit found in
this data sheet as I believe that is what you are after. The downside is it uses 0 to 10 VDC so you would need to amplify your PIC AO X2.
The kit is available here. or you can choose to roll your own.
To answer your initial question I don't know of any way to go about what you want to do other than the method presented in the link(s).
A Google of DC Controlled Dimmer should yield more results.
Ron