I think you can do this without the math. Take a look at the attached drawing. I basically did this like it was a piece of sheet metal (without bend deductions). I just laid it out in 2D and projected points and transferred measurements to the flat layouts of each part. It would probably be best to make the sides first then just lay the front on, trace your curves and cut the front, (or even cut the front after it's attached). Please note I just picked the overall size and curves at random. Also, I divided the curved segments by 4 for simplicity. Obviously you can divide it into more segments to smooth the curve.