identity matrix is a matrix with ones along the diagonal and
multiplied to a point, the identity matrix does not change the point. For this reason, the identity matrix is the
default matrix. For example, let p
[x, y, z]T.
We convert this to homogeneous coordinates by
adding a one to the vector, so p
[x, y, z, 1]T.
Notice that p = Ip
coordinates add another dimension “w” to a vector, so a point [x, y, z]T
becomes [x, y, z, w]T. Typically w = 1. Homogeneous coordinates
simplify matrix mathematics, making it possible to represent rotation,
translation, and scaling using matrices of the same size and with matrix