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Angle between two vectors

atan2(cross, dot) gives the signed angle from a to b in the range (−π, π]. Using both products together is robust where acos(dot / (|a||b|)) loses precision near 0 and ±π.

See also: Dot product as projection and 2D cross product — the two ingredients.

Pseudocode

dot   = a.x * b.x + a.y * b.y
cross = a.x * b.y - a.y * b.x
angle = atan2(cross, dot)        // signed, in (-π, π]

Source

const ox = 150, oy = 150
const ax = 90, ay = 0
const bx = mouseX - ox
const by = mouseY - oy

const dot   = ax * bx + ay * by
const cross = ax * by - ay * bx
const angle = Math.atan2(cross, dot)