Irregular shape 3D solid: some useful book on theory behind 3D direct modelling. I'm a senior mechanical engineer that design pressure vessels for petrochemical use. 
Very often I have to check mass and centroids of irregural shape objects since my drafters are not skill enough to use 3D geometry, we do not use 3D cad software and my Company ( we prefer to use 2D cad to generate drawing to pass to my workshop for the fabrication activities) and this mass/centroid check is a boring but necessary activity to be performed for each vessel, activity than nobody want to perform.
I am affascinated to the amazing software routines behind generation and modification of 3D objects in commercial 3D cads. Hard to write general pourpose routine (high skill professional activity), but the theory is allways the same! Analitical gemetry! Quaterions, 2D/3D Algebra, Linear Algebra, Vectors and Matrix Operations, multiple variable integration, jacobians, ...
So, Can some one suggest me some books that deal with the generation of 3D solids? More specific in DIRECT MODELLING. I have god skill in math.
I do not want to duplicate a commercial 3D cad .... I wan to to know theory behind and try to write some semplified software or XLS file to get data of simple irregular shape solid to turn easy this check (nozzles, tubesheets, formed heads, transitions with flare and knuckles, support saddles/brackets, trunnions, ....)
Thanks in advance.
EDIT: Examples
Nozzle 1 Nozzle1
Nozzle 2 Nozzle2
 A: There are good books about solid modeling written by Chris Hoffman and Martti Mäntylä. I can't remember whether they cover the specific topic of calculating volumes. Here are the references:
Introduction to Solid Modeling -- Martti Mäntylä
Geometric and Solid Modeling -- Christoph Hoffman
You could also read the code of an open source solid modeler, like OpenCascade. 
To compute mass properties, you will probably need to construct a 3D model.  You may as well do this in a 3D CAD system, and then you can use the CAD system's functions to do the computations.
If you really want to do the computations yourself, you could start by reading some of the following:


*

*Y. T. Lee and A. A. G. Requicha. Algorithms for computing the volume
and other integral properties of solids. I. Known methods and
open issues. Communications of the ACM, 25(9):635–641, 1982.

*Y. T. Lee and A. A. G. Requicha. Algorithms for computing the volume
and other integral properties of solids. II. A family of algorithms
based on representation conversion and cellular approximation. Communications
of the ACM, 25(9):642–650, 1982.

*B. Mirtich. Fast and accurate computation of polyhedral mass properties.
Journal of Graphics Tools, 1(2):31–50, 1996.

*O. Soldea, G. Elber, and E. Rivlin. Exact and efficient computation
of moments of free-form surface and trivariate based geometry.
Computer-Aided Design, 34(7):529–539, 2002.

*H. Timmer and J. Stern. Computation of global geometric properties
of solid objects. Computer-Aided Design, 12(6):301–304, 1980.
