design mathematics for 3d hull design

already read a lot of reference books about yacht/sailboat design. Find a lot of beautiful designs and very high level explanation of the drawings on paper.
but failed to get design mathematics expained for 3d design. Seems to be forgotten, only reference to spline, nurbs, polynominals,....
Where to find practical info?
Without reference to NA since i would like to learn !

 

What type of mathematics are you referring to? I'm not a designer and have only a small amount of experience with 3d CAD, so I'm having trouble imagining what would be different about the math from 2d or pencil drawn design work.

Are you talking about the math for rendering 3d shapes or naval architecture and engineering specific formulae?

-Will (Dragonfly)

 

As Will said....Are you talking about how to shape a hull or how to describe the hull in 3d numerical form. Very different topics!

 

look for papers by John Letcher

Eight Bells: John Letcher - Professional BoatBuilder Magazine https://www.proboat.com/2018/09/eight-bells-john-letcher/
Or buy the book
https://www.amnautical.com/products/principles-of-naval-architecture-series-the-geometry-of-ships#.XyzN3oEiehA

 

Want to transform the imagination into 3d mathematical based outcome !

 

want to go from imagination to a mathematical based 3d outcome (numerical form).

 

Thanks for the reference to the author and his books !
will certainly start to read geometry of ships !

 

John Letcher's book, The Geometry of Ships, contains a good though not comprehensive overview of the methods used to represent hull geometry. It is light on equations which is good for anyone seeking a general understanding but insufficient for to use as a reference when creating software. The Nurbs Book is an excellent reference on the details of B-Splines and NURBS.

A reader of The Geometry of Ships should be aware that Letcher included descriptions of and references to his proprietary "Relational Geometry" system and associated terminology in several sections of the book, in particular sub-sections 1.3.4, 2.5, 2.6, 3.12, 3.13, 4.13, 4.15, 4.18 and section 6. Terms such as "snakes", "beads" and "magnets" are words with specific meaning in the "Relational Geometry" system but are not generally used in computational geometry. Much of these sections could be read as promotion of the Relational Geometry system by the creator of the system.

 

Consider getting a basic book on Linear Algebra. A lot of geometric functions in 3D computer graphics use Linear Algebra to describe curved space. An introduction to non-Euclidean Geometry would also be helpful. Mostly for the conceptual thinking.

Masters in Math-Education drop-out here.


I also have an associate's and a bachelor's in computer science, but now I raise chickens and make art by burning wood, so that should tell you something.

By the way, you are likely reinventing the wheel by getting heavily into this. Not that I want to discourage you, quite the contrary, but I don't want you to look at the enormous pile of work you are carving out for yourself and become discouraged by that, either.

This is fascinating stuff that, for the right person, can really pull you in. It is also the kind of stuff that makes some people cover their eyes from the pain and run screaming in terror.
WARNING, Beyond this point, HERE BE MONSTERS!

-Will (Dragonfly)

 

Actually, you are missing all the hard stuff in the middle, like design and engineering. Even if you are looking to develop a program for "Series" vessels, those hulls are only going to be compromises based on the input data.
See my discussion here.... Lines Plan https://www.boatdesign.net/threads/lines-plan.29882/#post-310553
And this paper.... https://scholarworks.uno.edu/cgi/viewcontent.cgi?article=3698&context=td

 

Along similar lines to the above - https://apps.dtic.mil/dtic/tr/fulltext/u2/066689.pdf

 

thanks, can start elaborating !

 

My contribution here attached : the formulations used for the hull geometry within the new "Gene-Hull Sailboat 3.0" application that I have just posted.

The approach is based on fit for purpose analytical functions defined directly in the usual cartesian coordinates x,y,z (not B-splines or Nurbs, neither elementary polynomes) , with adimensional parameters dedicated for each purpose, in order to cover the widest possible variety of hull shapes for a sailboat. That allows to directly draw the traditional 3 views 2D with its waterlines and its buttock lines, an isometric perspective, and to compute the hull contribution to the usual ouput about hydrostatics, loading influence, stability, righting moment, ....an approach that can match with a standard spreadsheet like Open Office Calc.

The needed input includes exactly (for the hull shaping alone) :
13 geometrical data in metric
2 geometrical data in %
1 angle (for the so-called alfa transformation)
21 adimensional parameters
, so in total : 37 input data

From a given set of input data, we can either :

• change only the geometrical data in metric : you build another project with a similar shape for the hull
• change only the adimensional parameters : you build another hull shape within the same geometrical constraints.
• change all the data, then for a new project with a new shape of hull

​

I pay attention to use combination of functions which keep a smooth evolution of the curvatures, which does not generate curvature max or min other than the ones necessary to shape the hull and to comply with the input geometrical constraints. It is a concern about the so-called « fairing » issue.

 

Why do you want to do that? Is it your curiosity how the 3d programs render? I was working for years in the automotive sector in 3d CAD design and worked with several 3d programs and you have to understand how you to use the program, but it is not necessary to know how the program renders the design. Or do you want to dive in in the more mathematical/theoretical aspects? It's surely interesting but will not give you more power in the real designing process.

 

I am wondering why there is no mathematical info available about hull design. From 3D CAD point of view it is very expensive part of SW + unsure the methodology behind it, its IMHO a black box.
Very nice rendering but I doubt the added value ! Starting from a template and starting stretching doesn't IMHO look very professional.
How does 3D CAD support the hull characteristics of e.g. less drag I am wondering.
From math point of view You understand better the pro's and con's of the mandatory design parameters - 3D CAD can't manage that based on public available low cost solution.
Already looked around for a good piece of SW tool - or it is very expensive - or it is limited to template that I have to admid are nice to see - but IMHO are clones or better stating results that are "imported" from very professional Tools.