Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Thanks!
     
  2. jcsd
  3. Jun 25, 2014 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook