Game Development Reference
In-Depth Information
* This matrix is not padding to produce an aligned structure, since
* it is most commonly used with a mass (single real) and two
* damping coefficients to make the 12-element characteristics array
* of a rigid body.
*/
class Matrix3
// ... Other Matrix3 code as before ...
};
Matrices as Transformations
Earlier in this chapter I talked about using matrices to represent orientations. In fact
matrices can represent rotations, scaling, sheering, and any number of other trans-
formations.
The elements of the matrix control the transformation being performed, and it is
worth getting to know how they do it. We can think of the matrix
abc
def
ghi
as being made up of three vectors:
a
d
g
b
e
h
c
f
i
,
,
and
These three vectors represent where each of the three main axes—X, Y, and Z—will
end up pointing after the transformation. For example, if we have a vector pointing
along the positive X axis,
1
0
0
it will be transformed into the vector
a
d
g
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