The Funnel cooker was developed by Dr. Steven Jones.
I live in SW Western Australia and have constructed a number of solar funnels and find them the best bang for buck with regard safety, cost, portability and performance.
I don't see the point of focusing the suns energy into any smaller size than the cooking vessel and the solar funnel seems to be an optimization between the parabolic and flat reflectors - it still requires adjustment every 0.5-1.5 hours but seems to no danger of igniting anything if left lying around. It makes your hand warm - I find the best way to aim it is to put your hand in the end of the funnel and move around until optimum position is found.
They are lightweight so susceptible to wind but they fit well into another cardboard box weighed down with rocks which makes an ideal "stand".
I make mine by using white glue (PVA) to stick foil to cardboard - I know white glue isn't meant for foil but it works.
It can be used with a black pot in a Pyrex dish or inside an oven bag (cheap and ideal for hiking during fire bans).
So before you go to a large effort to create the perfect parabola take a look at the construction plans website below - there is also information about solar cooling.