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Geodesic radius of curvature

  1. Jun 25, 2014 #1
    I am trying to compute the geodesic (or tangent) radius of curvature of the geodesic circle by using the below formula.

    [tex]\frac{1}{\rho_c}=\frac{\partial G/\partial S}{2\sqrt{E} G}[/tex]

    where [tex]s[/tex] is the arc length parameter and [tex]E[/tex], [tex]G[/tex] are the coefficents of the first fundamental form.

    Can you please tell me how to perfrom the [tex]\partial G/\partial S[/tex]? Since [tex]G=r_v\cdot r_v[/tex] I am not sure how to derivate it with respect to arc length

  2. jcsd
  3. Jun 25, 2014 #2


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    You will first express each of your functions in terms of the arc length - re-parameterize them.
  4. Jun 25, 2014 #3
    I am dealing with non-uniform rational b-splines surface and I dont know the parametric equation of the geodesic path. I just know a set of points on the geodesic then how to re-parameterize with arc length.

    can I use [tex]\frac{d G}{d s}=G_u \frac{d u}{d s}+ G_v \frac{d v}{d s}[/tex]
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