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}
};
A final, useful version of this is to update a vector by adding a scaled version of
another vector. This is simply a combination of vector addition and the multiplication
of a vector by a scalar:
+
a x
a y
a z
b x
b y
b z
a x
cb x
+
=
+
=
a
c b
c
a y +
cb y
a z +
cb z
We could do this in two steps with the preceding functions, but having it in one place
is convenient:
Excerpt from include/cyclone/core.h
class Vector3
{
// ... Other Vector3 code as before ...
/**
* Adds the given vector to this, scaled by the given amount.
*/
void addScaledVector(const Vector3& vector, real scale)
{
x += vector.x * scale;
y += vector.y * scale;
z += vector.z * scale;
}
};
2.1.5
M ULTIPLYING V ECTORS
Seeing how easy it is to add and subtract vectors may lull you into a false sense of
security.Whenwecometomultiplytwovectors together, life gets considerably more
complicated.
There are several ways of multiplying two vectors, and whenever we produce a
formula involving vector multiplication, we have to specify which type of multiplica-
tion to use. In algebra, for scalar values we can denote the product (multiplication)
of two values by writing them together with no intervening symbol (i.e., ab means
a
×
b ). With vectors this usually denotes one type of multiplication that we need not
cover (the vector direct product—see a good mathematical encyclopedia for infor-
mation). I will not write ab but will show the kind of product to use with a unique
operator symbol.
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