Matrix majors

When we talk about a 4 X 4 matrix containing translation, rotation, and scale, it's important to realize that all of that information lives somewhere in the matrix. The following figure demonstrates how data is packed into the components of a 4 X 4 matrix:

The preceding figure demonstrates how data is packed into a Row Major matrix. This is called a Row Major Matrix because all three of the rotation basis vectors, as well as the translation vecto, are stored in the rows of the matrix. There is another notation to store the same data in a 4 X 4 matrix: Column Major notation. The following figure demonstrates how the same data is stored in a Column Major matrix:

It is important to note that the indexing of the matrix did not change between the row and column major notations. This is because the major of a matrix does not affect the definition of what a matrix is! The only thing the major of a matrix describes is in which elements the rotation, translation, and scaling data are stored. With a Row Major matrix the data is stored in rows; with a Column Major matrix the data is stored in columns.

We have to choose a major for our matrix class, it's important to define whether we are working with Row Major or Column Major matrices. For me, this choice comes down to memory layout. The rotation basis vectors: X-Rotation Axis, Y-Rotation Axis, and Z-Rotation Axis should be laid out linearly in memory. The easiest way to do this is to use a Row Major Matrix. This decision means our matrix will conceptually look like this:

The matrix will be laid out in a linear array of memory, like so:

float linear[] = { 11, 12, 13, 14, 21, 22, 23, 24, 
                   31, 32, 33, 34, 41, 42, 43, 44 };

You may have noticed that converting between a row and column major matrix is a matter of transposing the matrix.