The
Dot Product is useful for
comparing the direction of two vectors. If you turn on "Normalize
Output", the Dot Product is actually the cosine of the angle
between the two vectors. A value of 1.0 means the vectors point the
same way. A value of 0 means that they are at right angles to each
other. And a value of -1 means that the vectors point in opposite
directions. Dot Product is defined as follows:
Dot Product = (a*d) + (b*e) + (c*f)
A dot product is a single value, so all three output values x, y
and z will be set to the same thing. The
Cross Product of
two vectors gives you a new vector. This new vector is guaranteed
to be perpendicular (
i.e. at right angles to) both of the
input vectors. Cross Product is defined as follows:
x = (b*f)-(c*e)
y = (c*d)-(a*f)
z = (a*e)-(b*d)
Note: If you just want to do simple component-by-component
combinations of your vectors (
i.e., x = a*d, y=b*e, z=c*f)
then you should use the Multiply Divide utility node instead of the
Vector Product utility node. The
Vector Matrix Product is
useful for taking a vector in one coordinate space and moving it to
another. For example, if you have a vector in camera coordinate
space, you can multiply it by the Xform Matrix attribute of the
camera. That will give you a new vector in world coordinate space.
Similarly, the
Point Matrix Product is useful for taking a
point in one coordinate space and moving it to another. For
example, if you have a point in camera coordinate space, you can
multiply it by the Xform Matrix attribute of the camera. That will
give you a new point in world coordinate space. Given an input
vector (a, b, c) and an input matrix:
A B C D
E F G H
I J K L
M N O P
Then Vector Matrix Product is defined as follows:
x = (a*A) + (b*B) + (c*C)
y = (a*E) + (b*F) + (c*G)
z = (a*I) + (b*J) + (c*K)
And the Point Matrix Product is defined as follows:
x = (a*A) + (b*B) + (c*C) + D
y = (a*E) + (b*F) + (c*G) + H
z = (a*I) + (b*J) + (c*K) + L
