Graphics Reference
In-Depth Information
imaginary
component
P
(1 + i2)
i2
Q(
−
2 + i1)
i1
−
2
−
1
1
2
real
component
−
i1
S
(2
−
i1)
R
(
−
1
−
i2)
i2
−
Fig. 2.3.
The graphical representation of complex numbers.
Finally,
S
(2
−
i1) can be rotated 90
◦
to
P
by multiplying it by i:
i(2
−
i1) = i2
ii1
=i2+1
=1+i2
−
Although we rarely use complex numbers in computer graphics, we can
see that they are intimately related to Cartesian coordinates, and that the
ordered pair (
x, y
)
x
+i
y
.
Before concluding this chapter, I cannot fail to include the famous equation
discovered by Euler:
≡
e
i
π
+ 1 = 0
(2.1)
which integrates 0, 1, e,
π
and i in a simple and beautiful arrangement, and
is on a par with Einstein's
e
=
mc
2
.
2.9 Summary
This short chapter made sure that the terminology of numbers was under-
stood, and now provides a good link into the basics of algebra.
