• Apr 11th 2010, 12:12 PM
CrashDummy11
How can I calculate the radius of curvature of a 3D curve that is parameterized in the form:
x(t), y(t), z(t)?
• Apr 11th 2010, 12:17 PM
It is the reciprocal of the curvature, whose formula can be found at Curvature - Wikipedia, the free encyclopedia

Essentially, at a point p, one takes the limiting value of the radius of the circle passing through p-dp, p, and p+dp.
• Apr 11th 2010, 12:22 PM
Plato
Quote:

Originally Posted by CrashDummy11
How can I calculate the radius of curvature of a 3D curve that is parameterized in the form:
x(t), y(t), z(t)?

If $r(t)=$ then the curvature is: $\kappa = \left\| {\frac{{dT}}
{{ds}}} \right\| = \frac{{\left\| {r' \times r''} \right\|}}
{{\left\| {r'} \right\|^3}}$
• Apr 11th 2010, 12:26 PM
CrashDummy11
Thats a really ugly formula but it was what I was looking for. Thanks!