Lines in space: Part 4: Back to the diagrams [Jim Blinn's Corner]

In this series of articles we've found that we can represent an arbitrary line in projective 3-space with six numbers. We can construct this line either from two points on it or as the intersection of two planes. If we construct the line from two points S and T, with homogeneous coordinates S=[x
_S
y
_S
z
_S
w
_S
] T=[x
_T
y
_T
z
_T
w
_T
].