How does "spline" mean "curved"?
I am learning about "splined leaders" in CAD drawings:
The cryptic words "spline" & "leader" seem to indicate curved arrows:
To me, neither "spline" nor "leader" indicate a curved arrow
but that's what they call them in the text books:
I can see how a "leader" might "lead" you to somewhere; but how does
"spline" mean curved?
In mathematics a splines form a special class of functions used to fit a
curve to a series of points. I've used them to create calibration curves
from experimental data, although eventually I decided that cubics,
fitted to four adjacent points, to be more useful than splines.
Any good drawing software will have a way to fit splines to produce a
smooth-looking curve from a set of points. In that situation you're
probably not fitting to experimentally obtained points, but rather
moving the points around until you get a suitably attractive curve.
In the days before computers, draughtsmen created splines with the aid
of a flexible ruler.
I've never heard "spline" used to mean an arrow, but I suppose you can
always tack an arrowhead onto the end of a curved line.
"Leader" is presumably a term of art that I haven't met.
In woodworking, a spline is a long (and perforce rigid) bar of
material used to join two grooved work pieces (essentially acting as a
two-sided "tongue"), running cross-grain and providing greater
strength than a simple butt joint by greatly increasing glue surface
area. I suspect the same sense exists in metalworking as well.
Garrett A. Wollman | What intellectual phenomenon can be older, or more oft
firstname.lastname@example.org| repeated, than the story of a large research program
Garrett Wollman wrote, on Mon, 06 Oct 2014 04:50:01 +0000:
With that as a starting point, I find the woodworking use of "spline" here.
I wonder if the woodworkers know that a "spline" means a curved line?
That might explain why the woodworker's "spline" is straight, while the
draftsman's spline is decidedly curved!
I wonder how a woodworking draftsman handles the confusion when he has
to draw a draftsman's splined leader to a woodworking spline?
If this a problem for him, then he should sort nails: The nails to use
on the east side of the house in one pile, and those for the west side
of his house in another pile.
The latter was the sort of the punch line to a joke that went around
last week or so.
A spline, in caning chairs, etal., is a "reed" used to hold cane in place,
as with pressed in cane. It's flexible, so it can be installed in/on strai
ght and curved grooves/runs. A caning spline is usually seen, once install
ed, so it is part of the "decor" of the caned application.
"David Howard" wrote in message
Garrett Wollman wrote, on Mon, 06 Oct 2014 04:50:01 +0000:
In the boat-building craft, a spline is a long thin strip of wood with very
uniform bending characteristics. It's used in a process called lofting.
In the days before computers did all this, the designer produced a table
called a table of offsets, and the builder laid out the lines of the boat
full-size on a large flat surface (often in the loft of the boat shop, hence
the term lofting). The boat builder laid out the coordinates of points on
the surface from the table of offsets, and then used the spline to fair the
lines of the boat into fair curves. The builder would try to locate the
spline so that it ran through all the points, holding it down in place with
weights called ducks (hence the phrase "get your ducks in a row"). Because
the table of offsets contained coordinates to no better than a sixteenth of
an inch, and also because there were sometimes errors in the table, the
builder would nudge the spline a bit here and there to end up with a fair
curve that went through the points as closely as possible. Only from a fair
curve could you bend a plank to match the lines of the boat.
The original definition of spline (according to the OED) was
simply a long thin strip of wood - used to keep two boards
aligned and flat (the cross-grain application Garrett
describes is more modern - and depends on modern glues,
A later definition is a spline was a rigid bar used to lock
two pieces together - typically a wheel on an axle or something
similar. Today we'd usually call that a key.
Because spline stock tended to be long and relatively thin, the
name transferred to the lath used in lofting for shipbuilding,
as David says. By extension the same name came to be used for
small lead strips which would hold a curved shape - today we
call these flexible curves (and they're usually plastic-covered).
Curves laid out with a spline (i.e. a flexible curve) were
logically called "spline curves", and in the early days of
computers mathematicians trying to analyse such curves by computers
came up with math functions to represent the curve as a series of
short segments; those functions in turn came to be called splines.
By a further extension, the particular curve created by a spline
function is also called a spline.
Probably more than anyone cares to know :-)
On Monday, October 6, 2014 5:33:06 PM UTC-5, John McCoy wrote:
Getting off subject, a little, but similar....
Long ago, I saw a carpenter use a metal Venetian blind slat to draw a strai
ght line, 90 degrees to the front edge, across and up a counter top, with c
ontinuous (curved corner) back splash. I thought that was a neat trick to
get that accurate curved layout/alignment line. Since then, I'd gotten a
Venetian blind slat for when I need to sketch a similar curved line.
Maybe it does, or maybe it comes from ducklings following their mother,
as Snidely said. It seems unlikely to come from the name of weights
used with splines, though. According to Michael Quinion at World Wide
Words, the oldest known example of "getting your ducks in a row" is from
1889, in a newspaper.
But at Google Books I can't find any uses of "ducks" for spline weights
before 1939. Instead they were called "weights" in print. No doubt
drafters called them ducks earlier than 1939, but I can hardly imagine
that the term was sufficiently widely known in 1889 to be used
metaphorically in a newspaper.
(Of course, "I can hardly imagine" isn't proof.)
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