I'm not certain I understand your request. Do you want to know the voltage at two descreet points in time, or do you want to generate the waveform given V1 and V2 and their times?
What accuracy & precision do you require? Using an MCU (microcontroller) can be a very easy (ok, relatively easy) way to achieve this. Many MCU's have analog to digital converters (ADC) already built in, ranging from 8-bit to 20-bit resolution. The timing can be in the nSec range. The output can be a serial stream (COM port) or even USB without too much effort. Is using an MCU a viable option?