[Insight-users] quaternion integration

[Laura Igual]

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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