Game Development Reference
In-Depth Information
If two vectors are parallel, then their cross product will be 0. This is useful when you
need to determine whether or not two vectors are indeed parallel.
The cross-product operation is distributive; however, it is not commutative:
u × v ≠ v × u
u × v = − ( v × u )
s ( u × v ) = (s)( u ) × v = u × (s)( v )
u × ( v + p ) = ( u × v ) + ( u × p )
Here's the code that takes the cross product of vectors u and v :
inline Vector operator^(Vector u, Vector v)
return Vector( u.y*v.z - u.z*v.y,
-u.x*v.z + u.z*v.x,
u.x*v.y - u.y*v.x );
Vector cross products are handy when you need to find normal (perpendicular) vectors.
For example, when performing collision detection you often need to find the vector
normal to the face of a polygon. You can construct two vectors in the plane of the polygon
using the polygon's vertices and then take the cross product of these two vectors to get
normal vector.
Vector Dot Product: The * Operator
This operator takes the vector dot product between the vectors u and v , according to
the formula:
u v = (u x * v x ) + (u y * v y ) + (u z * v z )
The dot product represents the projection of the vector u onto the vector v , as illustrated
in Figure A-8 .
Figure A-8. Vector dot product
In this figure, P is the result of the dot product, and it is a scalar. You can also calculate
the dot product if you the know the angle between the vectors:
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