What do you think this roof construction is?
There are several ways to do this but given that the building is small, not in the Far East, and obviously not an expensive architecture demonstration, the builder probably simulated carved rafters by adding carved wedges or stacked wedges to standard rafter beams. 



Given the apparent age of the building, the roof cladding is probably 1" boards fastened horizontally, which would naturally follow the curvature of the modified beams. The builder could have chosen from 1" x 8" to 1" x 4" with the narrower boards being more work but giving a smoother curve. 

If you were building this today you would probably want to use plywood cladding, so you would put it all together with strong fasteners like deck screws and just force the plywood into the desired shape.