French Curve

On 01-Apr-05 Marc Schwartz wrote:

On Fri, 2005-04-01 at 20:07 +0100, Ted.Harding at nessie.mcc.ac.uk wrote:

<snip>

[...]
Splines, in the drawing-office sense, were long narrow
(about 1/4 inch wide) strips of thin springy metal with,
along their length, little flanges at right-angles to the
plane of the strip. Each little flange had a hole in it.

The principle was that you would pinthe flanges to the
drawing-board at chosen points by pushing drawing-pins
through the holes. The metal strip then stood up at a
right-angle to the paper.

The flanges were attached in such a way that you could
slide them along the metal strip. (Or you could use a
strip without flanges, and special pins which raised
little pillars up from the paper, against which the
spline would press.)

The end result was that the metal strip then defined
a curve on the paper, and you could run a pencil along
it and draw a curve on the paper (taking care not to
press too hard against the metal, to avoid deforming
the curve).

By virtue of the laws of elasticity, the curve delineated
by the metal strip had a continuous second derivative, i.e.
what modern kids call a second-derivative-continuous
piecewise cubic spline.

We have not moved on.

Happy whatever it is to all,
Ted.

Ted,

That sounds like the flexible curves that I found earlier, while
Googling for an example of a French Curve and found the Mathworld link:

http://www.artsupply.com/alvin/curves.htm

and

http://www.reuels.com/reuels/product21021.html

Marc

Not quite, I think, Marc. The principle of the spline as I
described it meant that the shape of the curve between the
fixed points was the static-equilibrium shape determined
by the elasticity of the metal (though some kinds were also
made of thin strips of laminated wood, but worked on the
same principle). They were therefore typically used for
interpolating "mathematically" between given points.

The curves shown on those web-site operate differently:
they are simply flexible, and can be bent by hand to any
shape, rather like modelling clay, which they then hold
by virtue of how they are constructed (see especially
the description on the 'artsupply' website: the lead core
gives the mouldability and was not springy, and the outer
plastic covering makes them smoother to use). (I've used
these too, once upon a time).

Best wishes,
Ted.