How not to do it: cheap jigsaw and blunt metal blade.
I tried this on my bike's windshield (BMW R80 and I'm not tall!). I got a great curve, but when the blade warmed up the perspex melted rather than cut, and rejoined at the back after the blade passed by!
I didn't have a bandsaw at the time, but now it's my weapon of choice for cutting plastic, because the blade can't really heat up and you have good control. To be fair, the windscreen would've been hard to do because of the curve, but I'd still have got a better finish - much careful sanding was needed on the one I cut down.