Game Development Reference
In-Depth Information
Figure 9 - Cross product between u and v yields a perpendicular vector w.
The direction of the resulting vector
w
is given by the
right hand rule
, this means that by
usingyourrighthand,ifyouaimyourforefingerinthedirectionof
u
andthemiddlefinger
in the direction of
v
, the vector formed by extending your thumb will be the direction of
w
.
Thecrossproducthasthepropertyofbeinganticommutative, thismeansthatswappingthe
position of any of the two arguments will negate the result.
This will yield a negated
w'
vector, which will have the opposite direction as
w
. We can
confirm this by applying the right hand rule in the same way we did before.
1.2.2 Matrices
Matrices are a tool used to solve systems of linear equations, and in our case, transform
geometric objects, among many other uses. A matrix is represented by a grid, or array of
numbers arranged in rows and columns.
Arraysmayhavedifferentnumbersofrowsandcolumns,differentsizesofmatricescanbe
used to solve problems either in two dimensional space or three dimensional space, at least
these are the uses we are interested in. The size of a matrix is usually described by
m
x
n
,
where
m
is the number of rows and
n
the number of columns.
