Operating principles of a sawtooth wave generator bootstrap circuit
Hmm that looks quite a clever circuit - it largely forces a constant current into C1 by keeping the DC voltage across R1 fairly constant between discharge events. I may be wrong but, if you have a simulator you could try it out. 


  but what I don't understand is what is the role of Vcc, capacitor C2
  and the Op-Amp.


 \$\color{red}{\text{(the diode is important too)}}\$

Once the discharge event has finished, C1 starts to charge and the bootstrap capacitor C2 lifts the cathode voltage of the diode and reverse biases it. Now, the diode doesn't have any role and a constant voltage is applied across R1 thus, it feeds a constant current into C1 and you get a linear charging voltage.

For this to be fairly linear, C2 needs to be many times bigger in value than C1.

Take a bow on presenting me a circuit I've never seen before.