Curve over Time envelope

I'm creating a custom slide envelope via a Sine FM osc running through an A to E trig and then into an accumulator. Say I have the "resolution" of the envelope at 1000 via the F input of the Sine FM. I'd then have the A input of the A to E at 0.001, so that the output is essentially a line from 0 to 1 over the course of one exact second. I can change how long that takes by multiplying the 0.001 input by anywhere between 0 to 1 for slower than one second, greater than 1 for faster than a second, etc. Now, however, I'd like to be able to make this line curved and still have it reach the 1 value after exactly 1 second (or however long I have it set to). Either highly convex-ly or concave-ly curved, and anywhere in between so that say if I were routing this "envelope" into the F of an oscillator (x 1000 or so) it'd make a kind of liquidy bbloooOIIP sound instead of straight rise or fall in frequency (you get what I mean). I've been really wracking my brain here, no results. (I have the "resolution" of the envelope set to 11016.8, bout a fourth of the sample rate). In case you ask, I have my reasons for not simply using an ADSR. Any help would be greatly appreciated.

 

Have you looked at the triggered envelope in Cyan?
You can adjust the ramp time in mid-flight, so that's a curve right?
In the structure it's called D/W Automatization

Sorry if I misunderstand, haven't had any tea yet..