Math for Artists | Live from HQ | Inside Unreal

To add two vectors together, place the tail of vector B at the tip point of vector A. This creates a new vector that is the combination of A and B. It begins at the common point between vectors A and B and intersects with the tail of A + B.

There are two ways to view subtraction. (1) Subtraction is the same as addition of the negative of B. (2) Draw a vector from the tip of B to the tip of A. Then move that vector to the common point (origin) of vectors B and A. Shown above is method (2), shown below is method (1).

Reflection Vectors

Dot Product will give us a comparison between vectors.

Normally, the length of the arrow symbolizes how fast it is moving. The red arrow represents the normal surface.

Vectors are simply components. The combination of X, Y, and Z gives us direction in 3 dimensional space. Shown above is a limitation to 2 dimensional space.

A reflection is the inverse of direction along an axis using the normal (vector) of the surface as the comparison. The Dot Product tells you when you hit that plane and some other criteria as well.

Using Normals: Dot Product Trick

If you are given a direction, we can compare how much of my vector is in that direction. V represents the vector of a wall. N represents are arbitrary vector.

Here the normal vector has been scaled up to be as long as V. Now we can do interesting things like "What happens to my vector, V, if I subtract that normalized vector N?

To take a component and flip it, you must subtract it twice. Thus, you end up with a reflection vector. Dot Product is ONE OF THE THREE BIG THINGS.

Using a trace (vector for X units) yields a hit position, which can be used to create a new trace at a reflection vector, so long as material == mirror material.