Graphics Reference
In-Depth Information
P
m
p
Y
λ
Q
q
Z
ε
θ
D
n
d
j
θ
k
O
l
i
X
Figure 9.2.
We begin by declaring the following conditions:
i
·
l
=
cos
m
=
j n
·
k
=
cos
=
−
OD
=
−
OQ
=
−
OP
d
=
d
k q
p
n
·
d
=
d cos
The relationship between the rotated axial system
lmn
and
ijk
can be represented as
⎡
⎤
⎡
⎤
⎡
⎤
l
m
n
cos 0
sin
010
sin 0
−
i
j
k
⎣
⎦
=
⎣
⎦
·
⎣
⎦
(9.2)
cos
and represents the transform relating coordinates in
ijk
to
lmn
. Q is the point on the
projection plane intersected by
p
, and once more, our task is to find the scalars and .
From Fig. 9.2 we see that
+
−
DQ
q
=
d
but
−
DQ
=
l
+
m
Therefore,
q
=
d
+
l
+
m
or
l
+
m
=
q
−
d
(9.3)
We now define
q
in terms of
p
,sowelet
q
=
p
