If you are given three orthogonal unit vectors, or two from which the third
would be their cross product, describing the orientation of the rotated
object, those vectors *are* the columns (or rows?) of the rotation matrix
you want.  If i understand the question correctly, this is what you're
looking for.

Suppose you start with <1,0,0>,  <0,1,0>, and <0,0,1> vectors glued onto
your object, and your object rotates so that now you have vectors U,V,W.
then the matrix to perform that rotation would be
  matrix< U[0], U[1], U[2],
          V[0], V[1], V[2],
          W[0], W[1], W[2],
          0, 0, 0>

(or maybe the transpose; i just had a Mike's Hard Lemonade, got tipsy. i'm
never sure of anything anyway...)

Note that you need at least two unit vectors stuck to your object. Only one
would lead to ambiguity, allowing an axis of rotation about which the
object isn't nailed down.

Does this answer the question?

DSW

Post a reply to this message