I'm learning about more quaternion conversions and I have a question regarding quaternion to spherical rotation conversion code at the following section of this website:
http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q59
What are angle and sin_angle in this code supposed to be? Angle is never used so I was guessing it's the rotation angle. Is sin_angle supposed to be sin_a?
If this was a function returning an array of float with the spherical rotation data, would [angle, latitude, longitude] be an appropriate representation of the converted quaternion?
cos_a = W;
sin_a = sqrt( 1.0 - cos_a * cos_a );
angle = acos( cos_a ) * 2;
if ( fabs( sin_angle ) < 0.0005 ) sin_a = 1;
tx = X / sin_a;
ty = Y / sin_a;
tz = Z / sin_a;
latitude = -asin( ty );
if ( tx * tx + tz * tz < 0.0005 )
longitude = 0;
else
longitude = atan2( tx, tz );
if ( longitude < 0 )
longitude += 360.0;
A quaternion is four numbers [X,Y,Z,W] that encode a rotation direction and an angle. The code extracts this information and converts the rotation axis into a latitude and longitude.
[tx,ty,tz] and angle theta is
X = tx*SIN(theta/2)Y = ty*SIN(theta/2)Z = tz*SIN(theta/2)W = COS(theta/2)This code does the reverse, since angle = 2*ACOS(W) = 2*(theta/2) = theta. So the variable angle stores the rotation angle.