calculating dual quaternion from two vectors

hi, i have two points (vectors) and i would like to calculate the rotation between them using quaternions. as i understand quaternion only give me the rotation, there fore if there is a translation between the two points as well the results i would get for the rotation angles are not good. i have read that to represent a rotation and translation using quaternion i need to uses the dual quaternion. i know how to calculate a quaternion between two points and then extract the rotation angles:

    p1 = [1,0,0]; p2 = [0,1,0];
    u = cross(p1,p2)/norm(cross(p1,p2));
    alpha = acos(dot(p1,p2)/(norm(p1)*norm(p2)));
    q = [cos(alpha/2), sin(alpha/2)*u(1), sin(alpha/2)*u(2), sin(alpha/2)*u(3)]
    [roll, pitch, yaw] = quat2angle(q,'XYZ')

the question is how do i calculate a dual quaternion between two points?

thank you for your help.

Answer 1

[Matt J]

I think you've under-posed your problem. There is no unique rotation and translation relating just two points. Given only 2 points p1 and p2, you can always just say that they are related by translation p2-p1 and zero rotation.

On the other hand, if you have 2 groups of points each group with 3 or more non-colinear points, then a quaternion-based solver for the roto-translation between them is here,

http://www.mathworks.com/matlabcentral/fileexchange/26186-absolute-orientation-horn-s-method

[Matt J]

Dany commented:

you are right. i do have several points in each data set, there fore i could use the solver in the link you provided. thank you