The french curve is a set of segments of Euler spirals, also known as clothoids. The curvature of a clothoid varies linearly along its length. If you start at the least curved end of one of the segments (curvature closest to zero) there will be a declining radius of curvature as you go until you reach the end of that segment. The french curve set has several segments with different rates of curvature change.
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There are infinitely many equations for each - and they are of different form, depending on the shape of the curve etc.
Ludwig Burmester, a German geometer, invented the Burmester curve also known as the French curve.
french curve is used to connect arce and semi-circles, such as the neckline, armholes , and collar. it is either made of flat metal or wood.
This starts with the collocation circle to go through the three points on the curve. First write the equation of a circle. Then write three equations that force the collocation circle to go through the three points on the curve. Last, solve the equations for a, b, and r.
Kirvenlineale von Gebrüder