Very quickly:

1) vline~ stores a linked list of events with start times and target times (the end point of the linear movement) using the t_vseg struct; events are scheduled in the vline_tilde_float routine.

2) vline_tilde_new sets all of the relevant struct members. You'll want to see how the x_referencetime member works because it's used to measure time everywhere else. There are lots of 

3) As vline_tilde_perform runs, it checks every sample to see if the start time of the next event(s) have elapsed (it's possible to have two events at the same logical time, where one leaps to a value and the other ramps from that value). It calculates the increment based on a linear interpolation from the start time to the target time, and from there it can increment until the target time has elapsed. The interpolation is how it gets subsample accuracy. Checking every sample to see if a new event should start is more expensive than checking every block (obviously).

4) A lot of the clock objects and functions are in m_sched.c; there are others in the system interface file s_inter.c

Hopefully this is all correct. If not, someone else please chime in.