Thank you John.<br>I had found the same solution.<br>However, I see a problem here. If we use the spherical coordinates to represent quaternion rotations, the radium 'a' of the sphere has to be equal to the angel of rotation 'alpha' of the quaternion. But, the axis of rotation has to be unitary, so a has to be a=1. Is it that right?<br>
<br>I mean:<br><font><font>w = cos(alpha/2);<br>x = sin(alpha/2) *u_x;<br>y =
sin(alpha/2) *u_y;<br>z
= sin(alpha/2) *u_z;<br>and <br></font></font><font><font>u_x = sin(theta)*cos(phi);<br>u_y = sin(theta)*sin(phi);<br>u_z
= cos(theta);</font></font><br>with a=1.<br><br>I am loosing a variable here!<br>What am I doing wrong?<br><br>Laura<br><br><br><br><div class="gmail_quote">On Wed, Jun 1, 2011 at 12:28 AM, John Drozd <span dir="ltr"><<a href="mailto:john.drozd@gmail.com">john.drozd@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">Hi again,<br><br>I forgot the bottom line of partial derivatives for z in the Jacobian expression on the first page.<br>
See attached revised page 1.<br><font color="#888888"><br>John</font><div><div></div><div class="h5"><br><br><div class="gmail_quote">On Tue, May 31, 2011 at 6:19 PM, John Drozd <span dir="ltr"><<a href="mailto:john.drozd@gmail.com" target="_blank">john.drozd@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">Hi Laura,<br><br>I calculated: dq = -0.5 a^2 sin^4(alpha/2) sin(theta) d(alpha) da d(theta) d(phi)<br>
<br>See my attached derivation for dq using Jacobians.<br><br>Take care,<br><font color="#888888">John<br><br></font><div class="gmail_quote"><div><div></div><div>On Sat, May 28, 2011 at 1:37 PM, Laura Igual <span dir="ltr"><<a href="mailto:lauraigual@gmail.com" target="_blank">lauraigual@gmail.com</a>></span> wrote:<br>
</div></div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"><div><div></div><div><font><font face="Verdana,Arial,Helvetica,sans-serif">Dear all,<br>
<br>I am working with
quaternion, and I have some questions about integration of a
function of quaternions.<br>Looking for information in the web, I have
end up in itk website and I have read the interesting tutorials of Luis Ibaņez, but I have still some doubts.<br><br>I would be very gratefully if you could answer the following
question:<br><br>I have to compute the integral of a function of
quaternions.<br>A quaternion q=(w,x,y,z) can be written depending on angel of rotation alpha and the rotation axis u.<br>
w = cos(alpha/2);<br>x = sin(alpha/2) *u_x;<br>y = sin(alpha/2) *u_y;<br>z
= sin(alpha/2) *u_z;<br><br> I use spherical representation of the
quaternions, where <br> t = theta = colatitude<br> t = phi = inclination
angel<br>
a = radius<br>then:<br>u_x = a *sin(theta)*cos(phi);<br>u_y = a
*sin(theta)*sin(phi);<br>u_z = a *cos(theta);<br><br>I want to solve
integral between angel1 and angel2 of f(q), but I don't know the
expression for differential of q!<br>
Is dq = sin(theta)? <br><br>Could you give me any clue?<br><br>Thank
you very much in advance,<br><font color="#888888">
<br>Laura</font></font></font>
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<br></div></blockquote></div><div><div></div><div><br><br clear="all"><br>-- <br><div>John Drozd<br></div>
<div>Post-Doctoral Fellow, Robarts Research Institute</div>
<div>The University of Western Ontario</div>
<div>London, ON, Canada<br></div>
<br>
</div></div></blockquote></div><br><br clear="all"><br>-- <br><div>John Drozd<br></div>
<div>Post-Doctoral Fellow, Robarts Research Institute</div>
<div>The University of Western Ontario</div>
<div>London, ON, Canada<br></div>
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</div></div></blockquote></div><br>