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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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Q: What are governing equations of french curve shapes?
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