Constant current uses a switch to control charging the capacitor. For the ideal switch, no matter when it turns off/on, the voltage is kept increasing.
Follow the same way as you would do with voltage pulses.
(for voltage pulse charging and discharging)
1. From 0V, raise voltage to V (you need to introduce some resistance so that a time constant may be defined)
2. The capacitor charges exponentially to voltage V
3. After time t, reset the voltage to 0V
4. The capacitor discharges exponentially to 0V
(for const current charging)
1. Apply a const current to the capacitor (through a resistor, of course)
2. The cap charges up linearly to infinite voltage
3. After time t, reverse the current (may not be same value)
4. The capacitor discharges to minus infinity (goes via zero)
Now you can see the reasons for the slopes and offsets in your simulations...