Let me show you how I made this curved cabinet...
Step 1: Plans & materials
I made this cabinet 900mm high, because of the standard sizes for MDF that I can easily buy here. You can change all the dimensions to your liking, these are just used as an example.
The curve is consistent, so all the arcs have the same curve and size. If you print out (or draw) 1 part of the arc to scale (4th image below) you can trace all the curved lines onto the wood, by rotating and mirroring the piece.
I made the cabinet from 9mm thick MDF and a thin 0,4mm 'MDF cardboard' (this is how we call it). You can also use a thicker MDF or wood for the main structure, and perhaps a thin, bendable triplex for the curved shape.
Draw the curved shape onto the MDF/wood and mark which pieces you want to cut out.