Radial Curve (work in progress)
Description
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.
History
Formula
Properties
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 .