French Curve

On Fri, 2005-04-01 at 09:30 +0200, Martin Maechler wrote:

"dream" == dream home <dreamhouse at gmail.com>
    on Wed, 30 Mar 2005 12:27:08 -0800 writes:

    dream> Dear R experts, Did someone implemented French Curve
    dream> yet?  Or can anyone point me some papers that I can
    dream> follow to implement it?

Are you talking about "splines" ?

I vaguely remember having read that in the distant past,
splines were sometimes called "French curves".

I found this:

G. Wahba and S. Wold, "A completely automatic french curve:
Fitting splines by cross validation," Commun. Statist.,
vol. 4, no. 1, pp. 1-17, 1975.

I remember that my father had a French curve: it was a plastic
template used for drawing which had several smooth edges of
varying curvature.
You could use it to draw a wide variety of curved shapes.
 No doubt the French called it something else. 

I still have some, from the 1950s ... The curves in the edges
are supposed to be segments of logarithmic spirals (which
ensures a kind of self-similarity on different scales).
A nice picture is at

http://missourifamilies.org/learningopps/
learnmaterial/tools/frenchcurves.htm

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.


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Date: 01-Apr-05                                       Time: 20:07:59
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