design mathematics for 3d hull design

Actually there is a lot of mathematical info available about hull design. However, most of it is just curve fitting of standard series or far field "peanut butter" solutions. There is no "mathematically perfect" hull, so therefore software cannot find an optimum; the best you can hope for is a local maximum based upon your algorithm's errors. As George Box said, "Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." (Empirical Model-Building and Response Surfaces , 1987)

 

Development of similar tool was my Diploma work 35 years ago. In before NURBS era. It is quite easy now scale or somehow transform existing NURBS model and get well faired and satisfied you requirements hull. Most interesting is not get quick hull lines estimation, but lines, satisfied all design parameters. I am just afraid it will be not enough to have parameters for that.

 

Actually mathematical definition of ship hull shapes has long history began from Chapmen parabola.

 

This is something similar.