A Dot Product is a product of 2 vectors, used to determine the direction an object is facing relative to another object. NPC vision in games is a good example of this, especially in stealth games since they need to know if the player is right in front of them so they can begin pursuit.
Many game engines allow you to use libraries to determine a dot product which contain functions like the one below.
In Unity, the `.forward` is a normalized vector that only considers the objects rotation.
(self = npc, target = player)
Vector3 dotTarget = (targetPosition - selfPosition).normalized;
Vector3.Dot(dotTarget, selfObject.forward);
An important thing to remember is that this doesn't account for the objects position, so if the rotation is `Vector3(0, 30, 0)`, then
the `.forward` property will always output the same `Vector3(0.50, 0.00, 0.87)` regardless of it's position in world space. Therefore if you
do need to check that the target is in range first you will need to do something like:
float magnitude = (targetPosition - selfPosition).magnitude;
return magnitude < radius;
Both formulas below can be used to attain the Dot Product (a·b), remember that a vector between 2 lines
(|a|) means the magnitude of that vector
a·b = |a| * |b| * cos(θ)
a·b = (ax * bx) + (ay * by) + (az * bz)
If you recall, our `dotTarget` and `selfObject.forwards` properties are normalized, so we will get a value between -1 and 1. To make this useful we want to find out the degree of the angle and then use it to act as peripheral vision for the NPC.
Let's say for example that our NPC is a monster with huge eyes granting it a large field of view, in Unity we'll first use Acos(f)
which returns the value in radians, and then transform our Radians to Degrees:
float angle = Mathf.Acos(dotProduct) * Mathf.Rad2Deg;
if (angle < peripheralVisionDegrees)
{
// attack player!
}
Dot Products are useful for more than just NPC vision, you may want to check the angle of a plane and give it more friction if ascending higher into the air because - well gravity. Another example being a drifting mechanic that begins once your car stops facing the way that it's moving towards, or even using it to measure how much damage a vehicles should receive during a head-on collision.
Finding use-cases for Dot products can be fun so I suggest coming up with something and try to build it for yourself. If you would like to see a full working example of how I implemented this technique for NPC vision then I've left a link to the repo below, good luck!
See example:
https://github.com/Pang/NpcLogic/blob/master/HelperMethods.cs