Homogeneous Transformations pace Biomedical Engineerin Life Support G oa a coordinate transformation that includes both translational and rotational transformations Define 4x1 vectors and the 4x4 matrix R v Recall homogeneous X=x +Rx X=AX transformationHomogeneous Transformations Goal: • A coordinate transformation that includes both translational and rotational transformations • Define 4x1 vectors: and the 4x4 matrix: ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 1 z y x X ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 1 w v u b X ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 0 1 xR A o b o += Rxxx • Recall thus b = AXX homogeneous transformation