Quote:
Originally Posted by Dane
These are Kobenhavn curves set for shipbuilding. Very handy thing!
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Thanks for mentioning this. I'd never heard of København (Copenhagen) curves before. Could you explain how you use them for cutting?
I've attached an example of something that I couldn't get to work well with French curves or a bendable curve. This is a common graphical method of constructing a circle and putting it into perspective. It is only approximate. When projecting a circle using the perspective projection, the resulting figure will always be an ellipse. I could never get the curve through the points p7, p23, p16, p4, p17, 18, p5, p19, p20, p6, p21, p22 , p7 in the perspective drawing to look very elliptical.
In figures 1 and 2, the red curve is the path through the points. While 12 points is not many for determining a curve, the result looks pretty good. When you're doing it by hand, plotting 12 points like this can be pretty tedious.
In figures 2 and 3, the violet curve is a circle generated in the normal way, using one of the equations for a circle. Especially when magnified, it shows clearly how approximate this construction is.
The thing that bothers me about French curves is that while obviously the radius of curvature changes continuously, I could never find any information about what the radius is at any given point and according to what rule it changes.