The lines of the Fano plane may also be given homogeneous coordinates, again using non-zero triples of binary digits.
42.
The advantage of using homogeneous coordinates is that one can combine any number of affine transformations into one by multiplying the respective matrices.
43.
Homogeneous coordinates identify the plane " E " with the " z " = 1 plane in three dimensional space.
44.
Since the homogeneous coordinates given by the minors are 6 in number, this means that the latter are not independent of each other.
45.
Applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation.
46.
Switching to homogeneous coordinates using the embedding, the extension to the real projective plane is obtained by permitting the last coordinate to be 0.
47.
Therefore, the components of are homogeneous coordinates for the 3-space through the origin of "'R "'4.
48.
All coordinates may then be divided by the w component ( the fourth component in homogeneous coordinates ) in what is called the perspective division.
49.
Geometric objects, such as points, lines, or planes, can be given a representation as elements in projective spaces based on homogeneous coordinates.
50.
Specifically, in the projective plane,, with a field, we have the correlation given by : points in homogeneous coordinates lines with equations.
