December 2013
Intermediate to advanced
508 pages
16h 50m
English
Content preview from Practical Algorithms for 3D Computer Graphics, 2nd Edition
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36 2. Basic theory and mathematical results
can be expressed as a 3 × 3 matrix :
d
x
′
d
y
′
d
z
′
=
t
x
b
x
n
x
t
y
b
y
n
y
t
z
b
z
n
z
d
u
d
v
d
w
(2.15)
Equation 2.15 transforms a direction vector specified in the surface local
frame of reference to the equivalent in th e global frame, that is local to global
[d
′
] = [T
lg
][d]. However in order to determine the direction of a vector, for
example the relative location of a light to P, the transformation needed is the
one from the global to the local reference frame, that is, [T
gl
], the inverse of
[T
lg
]. It is a well known result that for rotational transformations the inverse of
its matrix representation is simply its transp ...
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