[Insight-users] quaternion integration

[Luis Ibanez]

Hi Laura,


A) The trajectory over which you are integrating this function
    of quaternions "F(q)", is it such that only the angle is changing
    and the axis remains constant ?


B)  The Quaternion Tutorials show how to compute
      differentials of quaternions.

See Part II:
http://www.itk.org/CourseWare/Training/QuaternionsII.pdf

Starting on slide 3, and continuing until slide 44.

See in particular, Slide 23.


C)  Can you tell us more about your function F(q)   ?


   Thanks


        Luis



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On Sat, May 28, 2011 at 1:37 PM, Laura Igual <lauraigual at gmail.com> wrote:
> Dear all,
>
> I am working with quaternion, and I have some questions about integration of
> a function of quaternions.
> Looking for information in the web, I have end up in itk website and I have
> read the interesting tutorials of Luis Ibañez, but I have still some doubts.
>
> I would be very gratefully if you could answer the following question:
>
> I have to compute the integral of a function of quaternions.
> A quaternion q=(w,x,y,z) can be written depending on angel of rotation alpha
> and the rotation axis u.
> w = cos(alpha/2);
> x = sin(alpha/2) *u_x;
> y = sin(alpha/2) *u_y;
> z = sin(alpha/2) *u_z;
>
>  I use spherical representation of the quaternions, where
>  t = theta = colatitude
>  t = phi = inclination angel
>  a = radius
> then:
> u_x = a *sin(theta)*cos(phi);
> u_y = a *sin(theta)*sin(phi);
> u_z = a *cos(theta);
>
> I want to solve integral between angel1 and angel2 of f(q), but I don't know
> the expression for differential of q!
> Is dq = sin(theta)?
>
> Could you give me any clue?
>
> Thank you very much in advance,
>
> Laura
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