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.
Curve relations by radial
|equiangular spiral||equiangular spiral|
|cycloid||Kampyle of Eudoxus|
Related Web Sites
Robert Yates: Curves and Their Properties.