
42 Chapter 2 The Graphics System
1
(x
1
, mx
1
)
(x
2
, 0)
(1/m, 1)
(x
0
, mx
0
)
w
Figure 2.14 All homogeneous points along a line of slope m, excluding the origin, are equivalent
to the homogeneous point (1/m,1). The points with a w-component of zero are
vectors and are said to be equivalent to the point at infinity.
The division is not a matrix operation, because it involves a quantity dependent on
the input X. The use of the symbol ∼ in
Y
1
∼
Y
w
indicates that the 4-tuples are not equal but equivalent in the sense that the division
by w does produce two equal 4-tuples. This equivalence is the basis for projective
geometry.
To understand the equivalence in two