Graphics Reference
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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
 
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