If fit spline

So having an general discussion at work about "fit splines" and the
question of the day came up...is it the same geometry? Tolerances as
tight as can be and no sharp corners as a given, then does this become
a purly visual use, or is there more?

Take any 3 arcs, rully defined with dimensions and tangent to each
other and surface extrude. The surface is segmented. throw a fit spline
over it and it looks better, at least from out stand point. One could
argue that it is the same geometry that we are looking at, so why use
it?

Chime on in

 

Handy for some - It used to be really handy for lofting - in the old days, a
loft between sections created from tangent arcs would give segmented
surfaces, even with 'maintian tangecy' on - in 2005, we get better results.
But in 2004 and earlier, the workaround was to fit a spline so you have a
single face as a result of the loft.

Handy for everyone -
tangent mates so something could 'roll' across a series of faces (not a cam
mate, where it has to be a closed loop of tangent faces) I also had a great
trick where we could use a fit spline as a workardound for limit mates
(which often geive weird, jerky motion becasue of all the evaution as you
move a part) - unfortuately, there is a bug in 2005 that won't allow me to
mate a spline face to a flat plane. Bummer - I needed it for a torsion
spring, but fortuantley that job is still in 2004..

 

A single spline, by definition, is C2 (curvature) continuous. A string
of arcs is only C1 (tangency only) continuous. "Fit splines" needs to
make some compromises in order to make it work.

 

A single spline, by definition, is C2 (curvature) continuous. A string

Not sure that's entirely true. A spline can have fully multiple knots mid
span and be G0. Most systems either offer a tolerance or use system
tolerance (1e-08 meter?) when fitting the curve. Rhino will fit a spline
over tangent curves with almost double float precision. (Then again, I
could be wrong. <g>)

 

True. I should have been more specific. I was speaking
mathematically, though not really programmatically.

A CAD spline is actually a series of spline knitted together at knot
points. This allows for things like 3rd degree splines to fit 5 or
more points.

Most programs try to build knot points such that they are C2
continuous. It is possible for such a string to include C0 and C1
discontinuities, as they are merely a collection of patches, anyhow.

If you try to build a single surface without C2 continuity, there is
some "trouble" that needs to be handled. Different CAD programs handle
this in different ways. SW wussed out and just went with breaking the
surface at C2 discontinuities. UG, Pro/E, and CATIA are able to
assimilate C2 discontinuities as "patches", where a surface is
represented as a single entity but is still a sring of patches. Pro/E
(circa 1999) was able to create surfacee with patches, but would break
them up if they were imported from neutral formats (IGES, STP, or "PTC
Neutral").

 

appreciated the mathematical comment. I always find the juxtaposition
between the math of graphics and the actual graphics frustrating, being
a mathematician at heart.

 

Also, I would have to say that from a strictly graphics point of view,
it is possible that the distinction between a fit spline and tangent
curves really is only visual.

 

Lofted bends in sheet metal - fit spline allows you to create continous
curves from a set of intersection curves and produce a continous sheet metal
part - just spent two days doing this to create stringers in a boat hull -
very handy!

 

I guess that is my biggest questions overall is, it strictly visual or
is it more. ie go to RP systems that "create what it sees" and that is
really where you would want 1:1 results.

 

I guess that is my biggest questions overall is, it strictly visual or

From the perspective of a surface modeler; edges are either useful tools or
your enemy. The ability to fit a single curve over several curves (or to
split a single edge) gives you additional control. For most peoples'
"mechanical" modeling they are irrelevant but become more important for
more "organic" shapes.