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ComponentCurve
Curve From Curvature
00000000-7fd0-a0ce-8dad-c603f1726a1d
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Create a planar curve whose curvature is determined by a given function at each point along its length. The curvature at length l as measured along the curve, equals the value of the function f(l), with positive and negative values bending the curve in opposite directions.

The curve starts at the origin of the given plane, with the initial tangent direction being parallel to the plane x-axis.

Note that the resulting curve is a sampled approximation of the mathematically exact curve, and the component does not deal well with functions that are G0 discontinuous. I.e. trying to create curves containing kinks with this component will end in tears.

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Example file CurveFromCurvature.ghz.Interactive in Grasshopper 2
Create a curve from a predefined function. Provided functions include a constant value, yielding a circular curve, a linear function, yielding an Euler spiral, and a blend function, which will smoothly alternate from one circular arc to another.
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Example file CurveFromCurvature2.ghz.Interactive in Grasshopper 2
Create a curvature controlled curve from an interpolation function based on a set of custom values. The function itself is graphed below the curve in pink.