Looking at the rain drop it appears it is a blended curve using two differemt radii.
So.......
I grabbed my trusty compass and scale and a scrap of paper..
I drew a 6x10 rectangle and ran a centerline long length at 3 foot
go back 3'4" and strike a radius then locate a point about 2' 9 1/2" from the front and 2' 7" from each of the sides then strike a 2' 7" radius you may need to adjust this a bit so it will blend smoothly with the larger arc.
Look at it and see if you like it.
To build it stud this curved front wall vertically. I would go 8" or 12 " on center to allow you to form the curved front from thin flat stock and keep it smooth.
Make the same exact curve profile for your roof.
When laying out a curve for on centers I have found that a cloth tape like you use for sewing is a great way to measure these points. The cloth tape lays flat and doesn't kink like a steel tape will. If you find you need a 3rd hand just put a push pin in the start end to keep it in place. You may want to start at each edge and work to the center of the nose where the odd space will be less problamatic.