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Math Help - Radius of Curvature

  1. #1
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    Radius of Curvature

    How can I calculate the radius of curvature of a 3D curve that is parameterized in the form:
    x(t), y(t), z(t)?
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by CrashDummy11 View Post
    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)=<x(t),y(t),z(t)> then the curvature is: \kappa  = \left\| {\frac{{dT}}<br />
{{ds}}} \right\| = \frac{{\left\| {r' \times r''} \right\|}}<br />
{{\left\| {r'} \right\|^3}}
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  4. #4
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    Thats a really ugly formula but it was what I was looking for. Thanks!
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