Game Development Reference
In-Depth Information
Glossary of Notation
a , b , c ,...
vectors, points, quaternions
0
zero vector
e i
i th vector of the standard basis
v
·
w , v
×
w
dot and cross product of vectors v and w
2
v
,
v
length and squared length of vector v
A , B , C ,...
matrices over real numers
[ α ij ]
matrix with element α ij in the i th row and j th column
[ a i ]
matrix with vector a i as i th column
A T , A 1
transpose and inverse of matrix A
det( A )
determinant of matrix A
E
identity matrix
F , τ
force and torque vector
x , x
first and second time derivatives of x (velocity and acceleration)
ω , α
angular velocity and angular acceleration
I
inertia tensor
i =1 a i
a 1 +
···
+ a n
∂f
∂x
partial derivative of multi-variable function f with respect to x
( ∂f
∂x 1 ,..., ∂f
f ( x 1 ,...,x n )
∂x n
i =1
2 f
∂x 2
i
2 f ( x 1 ,...,x n )
, Laplacian of f
q , q 1
conjugate and inverse of quaternion q
A,B,C,...
point sets (lines, planes, volumes), or predicates
{
x i }
set of elements x i
{
x : P ( x )
}
set of elements x for which predicate P ( x ) holds
empty set
A
B, A
B, A
\
B
union, intersection, and set difference of sets A and B
A
B
A is a subset of B and is possibly equal to B
A + B , A
B
Minkowski sum and CSO of objects A and B
[ a, b ]
interval of real numbers containing all x for which a
x
b
aff( A ), conv( A )
affine and convex hull of point set A
∃x : P ( x )
there exists an x such that predicate P ( x ) holds
x : P ( x )
for all x predicate P ( x ) holds
f ( n )= O ( g ( n ))
constants k and c exist such that f ( n )
cg ( n ) for all n
k