[R] French Curve

[Marc Schwartz]

On Fri, 2005-04-01 at 22:56 +0100, Ted.Harding at nessie.mcc.ac.uk wrote:
> 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.

Ted,

Thanks for the clarification. I think that I have a better mind's eye
view of the differences, combining your additional comments with your
initial explanation. The mention of laminated wood clicked and took my
mind back to some physics experiments with bi-metals...

Regards,

Marc