Evolute of a curve
Let be a smooth planar curve, space curve, or more generally, a smooth curve in a Riemannian manifold. The evolute of is defined as the locus of the center of curvature for each point on , with respect to .
For a planar curve
- The length of the evolute between any two points is the total variation in the radius of curvature between those points.
- The radial line to a point on the curve from its center of curvature, is tangent to the evolute at the center of curvature.