Graphics Reference
In-Depth Information
or
N
N
F
u
P
v
F
v
P
u
×
−
×
N
=
N
+
(10.9)
N
Blinn proposed two ways to interpret Eq. (10.9): the first interpretation, and probably the most
obvious one, is to see
N
as the sum of two vectors:
N
=
N
+
D
where
N
N
F
u
P
v
F
v
P
u
×
−
×
=
D
(10.10)
N
Figure 10.8(a) shows this vector addition, and Fig. 10.8(b) shows the vector cross product
associated with
D
.
N
N
N
′
∂
P
∂u
⎯
×
θ
N
∂
F
∂u
D
D
∂
F
−
∂v
∂
P
⎯
×
N
∂v
(
a
)
(
b
)
Figure 10.8.
P
v
must lie in the tangent plane of the surface. When these vectors are scaled by the partial
derivatives of the bump map F, they are summed to produce
D
, which is subsequently used to
perturb
N
.
P
u and
N
Figure 10.8(b) shows us that with
N
as the surface normal vector,
N
×
×
The height field F was originally used to scale the unit normal vector
N
, which is
eventually used to perturb
N
by
D
. However, we can save ourselves a lot of work if the bump
map takes the form of an offset vector function
D
uv, then all we have to do is add it to
N
uv. Such a technique is called an
offset map
.
Blinn's second interpretation of Eq. (10.9) is to imagine that
N
is rotated about some axis to
N
. The axis will lie in the tangent plane and is computed using
N
N
×
N
. But as
N
=
N
+
D