Radial Curve (work in progress)


Let P be a point on a curve. Let C be the center of osculating circle at P. Now, the locus of the vector C-P is the radial of the curve C.

The idea of a radial curve is analogous to the Gauss Map for surfaces.

The radial curve is very much related to curvature of a curve, in that it gives a visual map of a curve's curvature change.

See also: evolute, Curvature.




Curve relations by radial

Base Curve Radial
deltoid trifolium
epicycloid rose
astroid quadrifolium
equiangular spiral equiangular spiral
cycloid Kampyle of Eudoxus
tractrix Kappa curve

Related Web Sites

See: Websites on Plane Curves, Plane Curves Books.

Robert Yates: Curves and Their Properties.


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