C.8.8.5.2 Frame of Reference Transformation Matrix

In a rigid body system, two coordinate systems can be related using a single 4 x 4 transformation matrix to describe any rotations and/or translations necessary to transform coordinates from the related coordinate system (frame of reference) to the primary system. The equation performing the transform from a point (X’,Y’,Z’) in the related coordinate system to a point (X,Y,Z) in the current coordinate system can be shown as follows, where for homogeneous transforms M 41 = M 42 = M 43 = 0 and M 44 = 1:

X M 11 M 12 M 13 M 14 X’

Y = M 21 M 22 M 23 M 24 x Y’

Z M 31 M 32 M 33 M 34 Z’

1 M 41 M 42 M 43 M 44 1