Loft command background


#1

Hi!
I am using the loft command quite a lot and want to know if anyone knows of a technical or research paper written that shows the math behind lofts.


(Brian James) #2

Hi Lance,

I think @dale or @dalelear (yes two Dales!) may know where to point you on this one.


(Dale Lear) #3

There are thousands of places that discuss “lofting” for NURBS curves and surfaces. The first thing to understand is non-rational cubic NURBS curve lofting. Search the internet for “Cubic NURBS interpolation” to get a list of books and papers you could read.

In my view, the gold standard for all basic NURBS calculations, including interpolation (lofting) is de Boor’s A Practical Guide To Splines (1978) and Bohm’s paper A survey of curve and surface methods in CAGD (CAGD 1984).


#4

Thank you! I will start there. Let me know if you find other papers!

Side question:
I am interpolating survey cross-section point clouds (.xyz) using 3rd degree and sq rt chord method. Basically, after interpolating, I use a “normal” loft that I rebuild with 500 control points. Then I go and rebuild the mesh again using 400 (U) and 300 (V) that way I can get the loft to fit the cross-section curves tightly. So, my question is…are these interpolated cross-sections considered NURBS curves? Is the loft considered a NURBS surface?