Transforming vectors and points

Transforming points and vectors is done in the same way as multiplying matrices. In fact, the vector being transformed can be thought of as a matrix with 4 columns and 1 row. This means transforming vectors is a matter of multiplying a 4 x 4 and a 4 x 1 matrix together.

When a matrix transforms a vector, it affects both the orientation and scale of the vector. When a matrix transforms a point, it just translates the point in space. So, what's the difference between vectors and points? The w component of a vector is 0 and the W component of a point is 1. The following steps will guide you through implementing matrix-vector multiplication:

1. To make the matrix-vector multiplication a little easier to read, you will need to once again create a macro. This macro will take the row of a matrix and perform a dot product of that row against the provided column vector. Implement the M4VD macro in mat4.cpp:

   #define M4V4D(mRow, x, y, z, w) \
    ...