Lets look at this in pieces. You have a ray, say in direction (rx, ry, rz). In effect, you would like to rotate your z axis so that it points toward the ray. That is simple enough. Here''s a partial rotation matrix that will do this:

    [? ? rx]R = |? ? ry|    [? ? rz] 

You can test that this does properly transform your z axis (or the effect''s axis) by applying R to the z axis vector:


Effect_axis = R * z_axis_vector

or,

                        [? ? rx]   [0]Effect_z_axis_rotated = |? ? ry| * |0|                        [? ? rz]   [1]which yields:                        [rx]Effect_z_axis_rotated = |ry|                        [rz] 

which is what you wanted. So the R matrix is correct as we''ve written it so far.

The problem is that you really need to transform the complete coordinate system of the effect, e.g., the effect''s x and y axes not just z axis. So you need to fill in the rest of that rotation matrix. I won''t try to advise you on how to determine the rotated x and y axes, except that you need to create some rules. You could for example find a rule that says the effect''s x axis always points toward some object. A constraint is that it is perpendicular to the effect''s z axis. Then the effect''s y axis is found by y = z cross x.

I will tell you that once you determine that the effect should act along (rx,ry,rz) and also that its x axis should be (exx, exy, exz) and y axis should be (eyx, eyy, eyz), the complete rotation matrix is:

    [exx eyx rx]R = |exy eyy ry|    [exz eyz rz] 

Hope that helps.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Yes, of course, quaternions.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.