Question

Given two 2D vectors, how can you tell whether the second is to the right (clockwise) of the first, or to the left (counter-clockwise)?

For instance, in these diagram B is to the right (counter-clockwise) of A

A   B   .       .----> A
^  ¬    |\      |   
| /     | \     |  
|/      V  \    V 
.       B   A   B

Answer 1

You can achieve this using a dot product. dot(a, b) == a.x*b.x + a.y*b.y can be used to find whether vectors are perpendicular:

var dot = a.x*b.x + a.y*b.y
if(dot > 0)
    console.log("<90 degrees")
else if(dot < 0)
    console.log(">90 degrees")
else
    console.log("90 degrees")

Put another way. dot > 0 tells you if a is “in front of” b.

---

Assume b is on the right of a. Rotating b 90 degrees counterclockwise puts it in front of a.
Now assume b is on the left of a. Rotating b 90 degrees counterclockwise puts it behind a.

Therefore, the sign of dot(a, rot90CCW(b)) tells you whether b is on the right or left of a, where rot90CCW(b) == {x: -b.y, y: b.x}.

Simplyifying:

var dot = a.x*-b.y + a.y*b.x;
if(dot > 0)
    console.log("b on the right of a")
else if(dot < 0)
    console.log("b on the left of a")
else
    console.log("b parallel/antiparallel to a")