Splines, Surfaces and algorithm behind them

Not sure if this helps. Just an arcane bit of SW trivia I learned from doing API programming...

SW changes their loft algorithm from time to time. I'm sure they have their reasons.

In the API help, it once explained that it was necessary to track which version of SW was used to generate a loft feature. This was so that a loft could use its original legacy algorithm to regenerate, even if the regeneration occurred in a newer version with a new loft algorithm. e.g. A loft created in SW 2001 would continue to use the 2001 algorithm to regenerate, even in a later version of SW like SW 2007.

One result of this is that lofts created in different versions of SW with identical source features and parameters can have different results.

It's important for me to understand your question because SolidWorks end result is usually a sealed geometric Solid model... Very rare would someone climb into 3D space start plotting random Splines throw some surfaces on these splines and end result be the finished product. On the flip side; SolidWorks has its "FREEFORM" functions where you could manipulate the solid model, "project" lines (that create splines) onto this various based shape(s) then create a surface from the solid model's face. So working backwards could:

Cubische Hermitic Splines

Cardinal Splines

Catmull-Rom-Splines

Kochanek-Bartels-Splines

T-Splines

and many more

Brep

Polygon Mesh

Sub-D-Surfaces

these various algorythems and spline creations create the surface? SolidWorks seems to be real friendly to various Surface projection creators. Like the auto guys have from Clay to Surfaces etc. I am a surface (CAM) guy before I started solidmodeling. Some surfaces I could patch, repair or create better in a CAM then I could creating lots of planes and 3D sketching in Solidworks. I actually have CAMWorks too. Toolpathing actual surfaces is important for me too.

:CHIP:

I am interested in the innerworkings... But it sounds like there are tangencies that guide rockets to outerspace calculating thrust and gravity. I'm interested in the ones that keep a tool on tangent with a + or - maybe a couple half tenths... Tangency is important in toolpathing. I'll break up a spline and create arcs wherever possible.

:CHIP:

Here's an example of huge design control (where maybe the profile isn't as critical as say maybe a taillight). Lots of Splines and surface creation. As a designer you want to be able to manipulate the geometry to accomplish the finished product. As a CNC Programmer I don't want to jepordized ANY of the finished profile at all. But in many instances you have to section things up to cut it.

:CHIP: