The point on the positive ray of the normal vector at a distance 
, where 
is the radius of curvature.
It is given by
where 
is the normal vector and 
is the tangent vector. It
can be written in terms of 
explicitly as
 |
(3)
|
For a curve represented parametrically by 
,
(Lawrence 1972, p. 25).
See also
Curvature,
Osculating
Circle
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References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, 1997.Lawrence, J. D. A
Catalog of Special Plane Curves. New York: Dover, 1972.Referenced
on Wolfram|Alpha
Curvature Center
Cite this as:
Weisstein, Eric W. "Curvature Center."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CurvatureCenter.html
Subject classifications
