How to make a fair curve?

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Better still ,french curves being short, try ships curves instead. Of course the idea of halving the distance between the length of the curve and drawing one half freehand and then flipping it and tracing the other has to be way too simple dunnit. mjh
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"Andy Dingley" < snipped-for-privacy@codesmiths.com> wrote in message
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On Sat, 14 Feb 2004 04:33:55 GMT, Michael Baglio

Speaking of "cut and paste", you will save yourself a lot of trouble by doing exactly that.
Describe the curved line in a drawing program and print it out full size.
Spray adhesive.
Bandsaur.
...and it's PURPLE !
Thomas J. Watson-Cabinetmaker (ret) Real Email is: tjwatson1ATcomcastDOTnet Website: http://home.comcast.net/~tjwatson1
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brought forth from the murky depths:

Do you pick up the mouse and speak into it like Scotty did in "Star Trek IV: The Voyage Home"? Or how does the computer program understand your description?

Poor Mikey prolly didn't "get" Art Nouveau furniture, either. 'Tis a shame, wot?

So put a bandage on it and put the Playboys away, silly savage. It'll be pink again in a week. DAMHIKT <blush>
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Impeach 'em ALL!
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On Sun, 15 Feb 2004 07:18:13 GMT, Larry Jaques

Draw it with a CAD program then print it out full scale. If one doesn't have a large format printer, you'll have to go to a place like Kinko's for that.
Then spray adhesive, then bandsaw.
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Some more comments on smooth curves and French curves.
A "smooth" curve is one that avoids corners. A "corner" is a point where there's a discontinuity in the tangent - i.e. a tangent drawn just a tiny fraction to one side of the corner wouldn't line up with a similar tangent drawn to the curve just the other side of the corner. By implication, if we can align the tangents of two curves, then we can avoid the corner.
Now the fun bit - this even works with two different curves. If we can just get those tangents to line up, then the transition between them will be smooth - no matter how much of a change in curvature is involved.
Aligning tangents is one approach. But if tangents align, then so must the perpendiculars align. Now for a simple arc, the perpendicular is a radius, which suggests a useful special case.
When joining a circular arc onto a straight line, the centre used by the compasses to strike the arc must be on a line perpendicular to the straight line, and crossing it at the point where the curves join. This sounds awkward, but it's pretty obvious in pictures. It's also the principle behind constructing the range of Gothic arches: <http://codesmiths.com/shed/workshop/techniques/arches.htm
A French curve is a curved stencil whose shape is a mathematically somewhat complex curve that changes its radius of curvature along its length. There are several sorts, and those with access to Mathematica <http://mathworld.wolfram.com/FrenchCurve.html or other drawing tools can probably generate their own. A useful source for some basic curves of this family are the Archimedian and logarithmic spirals, which can be constructed with simple paper and pencil methods.
A French curve is a curve that changes along its length. So you should be able to roughly eyeball what you need, then find a curve you already have that offers roughly the right curvature at two places roughly the right distance apart (the previous trick about making enlarged MDF duplicates by photocopying is worth it, if you need big furnituremaker's curves.)
To use a French curve, first choose the best fit you have. The place it roughly in place so that it touches the existing curve at the right places. Now slide it from side to side, keeping it aligned against those end points, until the tangents are a good fit. You're done !
If it doesn't work, then try different curves. They'll all fit and give a smooth curve, but they might not offer quite the radius you're after. _Don't_ use French curve by picking the radii you want, plonking it down and then trying to "smooth out" the corners. They just don't work that way. Each given curve will only fit at one place - if you want different combinations of radii, then you need a different curve (but photocopiers with fine enlargement control are your friend).
Avoid Bezier curves (offered by any CAD program) for freehand drawing work. Although they can be used, it's all too easy to make a spline curve look ugly in a purely aesthetic sense (and the maths of exactly _why_ is both horrible, and does actually exist). However today is Valentine's Day, and I have taken a solemn oath to forswear all aesthetics.
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