Page 104 - Computer Graphics Handout

The problem is how to find C when we are working with representations. It turns out to be quite easy. Suppose that we are working
in some frame and we specify another frame by its representation in this frame. Thus, if in the original system we specify a frame
by the representations of three vectors, u, v, and n, and give the origin of the new frame as the point p, in homogeneous coordinates
4
all four of these entities are 4-tuples or elements of R .
Let’s consider the inverse problem. The matrix
T = C −1
converts from representations in the (u, v, n, p) frame to representations in the original frame. Thus, we must have

Likewise,

Putting these results together, we find

104