As in the two-dimensional case, the last row of each vector (i.e., coordinate location) is always one and the last row of the matrix (i.e., transformation) always consists of zeroes except for a one in the last column. These fixed elements serve as placeholders to ensure that the matrices can be inverted or multiplied to obtain appropriate results. A complete specification of the parameterization of the model requires explicit designation of the sequence in which these transformations are applied. As with the two-dimensional model, different results will be obtained depending on whether rotations precede or follow translations. However, a new sequence issue also arises because the order in which the three rotations are applied alters the result. All of the following orders are reasonable:
pitch * roll * yaw pitch * yaw * roll roll * pitch * yaw roll * yaw * pitch yaw * pitch * roll yaw * roll * pitch
Combined with the possibility of performing translations before or after rotations, a total of 12 different orders are
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