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4.1.6 Transformation matrices

Some objects incorporate 4x4 real matrices for homogeneous object transformations. These matrices act by multiplication on the right of vectors. Thus, if p is a 4-element row vector representing homogeneous coordinates of a point in the OOGL object, and A is the 4x4 matrix, then the transformed point is p' = p A. This matrix convention is common in computer graphics; it's the transpose of that often used in mathematics, where points are column vectors multiplied on the right of matrices.

Thus for Euclidean transformations, the translation components appear in the fourth row (last four elements) of A. A's last column (4th, 8th, 12th and 16th elements) are typically 0, 0, 0, and 1 respectively.