Probably in order to ease the whole job the drawer sides are not wavy inside, and they are only the fronts that match the sides of the frame. Caro'l suggestion is right, and you would need to make some jigs and shape molds to achieve such curvatures.
A rather time consuming and difficult project IMHO as no one single piece is equal to other, but that's the price one has to pay if you want to step out of the treaded way... The whole picture has very clear reminiscences of Alice in wonderland tale.