Transpose

To transpose a matrix, flip every element of the matrix across its main diagonal. For example, the 2, 1 element would become the 1, 2 element. Elements where both subscripts are the same, such as 1, 1, will remain the same:

1. Implement the transpose function in mat4.cpp. Don't forget to add the function declaration to mat4.h:

   #define M4SWAP(x, y) \

       {float t = x; x = y; y = t; }

   void transpose(mat4 &m) {

       M4SWAP(m.yx, m.xy);

       M4SWAP(m.zx, m.xz);

       M4SWAP(m.tx, m.xw);

       M4SWAP(m.zy, m.yz);

       M4SWAP(m.ty, m.yw);

       M4SWAP(m.tz, m.zw);

   }

2. Create a transposed function in mat4.cpp. The transposed function modifies a matrix that is passed into it. Don't forget to add the function declaration to mat4.h:

   mat4 transposed(const mat4 &m) {

       return mat4(

           m.xx, m.yx, m.zx, m.tx,

           m.xy, m.yy, m.zy, m.ty,

           m.xz, m.yz, m.zz, m.tz,

           m.xw, m.yw, m.zw, m.tw

       );

   }

Transposing a matrix is useful if you need to convert a matrix from row-major to column-major or the other way around. In the next section, you will learn how to calculate the determinant of a square matrix.