Geodesic radius of curvature

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!
 

UltrafastPED

Science Advisor
Gold Member
1,910
214
You will first express each of your functions in terms of the arc length - re-parameterize them.
 
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]
 

Related Threads for: Geodesic radius of curvature

Replies
8
Views
10K
Replies
6
Views
3K
Replies
3
Views
1K
  • Posted
Replies
9
Views
20K
Replies
0
Views
2K
Replies
3
Views
5K
Replies
5
Views
9K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top