Graphics Reference
In-Depth Information
I = I
n
= n ¥ n identity matrix which consists of 1s along the diagonal and
0s elsewhere
A
T
= transpose of the matrix A
GL
(n,k)
= the linear group of nonsingular n ¥ n matrices over k =
R
or
C
O
(n)
= the group of real orthogonal n ¥ n matrices
SO
(n)
= the group of real special orthogonal n ¥ n matrices
R
(f,g) = R
X
(f,g) = the resultant of polynomials f(X) and g(X)
= the complex conjugate of the complex number or quaternion
z
z
T (
A
,
B
,...) = (
A
¢,
B
¢, . . .): This means that T (
A
) =
A
¢, T (
B
) =
B
¢,...
1
X
= the identity map on the set
X
c
A
= the characteristic function of a set
A
as a subset of a given larger
set
X
(X
A
(x) = 1 if xŒA and 0 otherwise.)
f
-1
(y)
= {x | f(x) = y}
= L
p
norm
|| ||
p
= the inner product of f and g in L
2
([a,b])
<f,g>
a | b
= a divides b
Sign (x)
=+1 if x ≥ 0 and -1 otherwise (returns an
integer
)
Sign (s)
= sign of permutation s
=+1 if s is an even permutation, -1 if s is an odd permutation
Trunc (x)
= greatest integer £x (returns a
real
value)
Floor (x)
= greatest integer £x (returns an
integer
value)
= e
x
exp (x)
k (s)
= curvature function
t (s)
= torsion function
Let p(u) be a parametrized curve:
ppcpp
dp
du
()
u
u
=
()
=
,
=¢=
,
ppc
c
Let p(u,v) be a parametrized surface:
ppabp
p
u
∂
∂
∂
∂
p
u
∂
∂
p
v
∂
∂
p
v
(
)
u
a
u
(
)
v
a
v
(
)
=
,,
=
,
p
=
ab
,,
p
=
,
p
=
ab
,
ab
2
2
∂
∂∂
p
uv
∂
∂∂
p
uv
ab
uv
uv
(
)
p
=
,
p
=
,
ab
