Derivating Curvature

Hi everybody,

My aim is to derivate vectors in GH.

I wan't to test it with the help of curvature as it is given by Rhino.

The formula for curvature is:

Kn = dt/ds

where

t is the tangent vector

n the normal vector

K the curvature

which I approximate by

Kn(s) ~= (t(s+ds/2) - t(s-ds/2)) / ds

where ds is very small.

I find a vector with the right direction (youpi!), but its way too long (see picture).

Obviously something is wrong, but I can't figure out what..

I would really appreciate any help

thanks

Attachments:

derivate.ghx, 220 KB
untitled.png, 10 KB

Replies to This Discussion

Permalink Reply by Sebastien Turcaud on August 24, 2011 at 6:39am

Nobody knows?

I'm kind of stuck there. What is troubling me, is that the difference in length between the curvature vector I calculate, and the one given by rhino is not constant along the curve.. However, both vectors stay colinear...

Am I missing something obvious? Is this not the way to derivate vectors?

Permalink Reply by Chris Tietjen on August 24, 2011 at 7:51am

I suspect that the vector in Rhino has been unitized. Divide your vector by its length and see what you get.

Chris

Permalink Reply by Chris Tietjen on August 24, 2011 at 8:48am

No, that's not it.

Chris

Permalink Reply by Chris Tietjen on August 24, 2011 at 11:20am

In your formula above s is curve length not parameter space. Rev1 is still using parameter space in locating the tangent points but is using curve length for division by s but because of this mixing it is still not correct in it's logic. Rev2 is using curve length for both tangent points and division by s and is correct in it's logic...or so I believe.

Chris

Attachments:

derivateRev1.gh, 9 KB
derivateRev2.gh, 11 KB

Permalink Reply by Sebastien Turcaud on August 25, 2011 at 1:50am

oua
thanks alot man!
I suspected something hidden, but couldn't put my finger on it.
You made my day!
I guess both approaches are right in finding the curvature, but you're right saying the 2nd is more coherent.
From now on I'll pay attention to parameter space vs. arc-length^^

Permalink Reply by Pieter Segeren on August 24, 2011 at 7:25am