Physics · function

exactAcos

Math.acos, reproducibly. Outside [-1, 1] this answers NaN, as Math.acos does.

Explained in Your first game, Rigid bodies.

function exactAcos(x: number): number

import { exactAcos } from '@driftengine/physics';

Parameters

Parameter	Type	Description
`x`	`number`

In depth

Three branches rather than one, and the split at ±0.5 is the reason it is accurate near the ends: acos has infinite derivative at ±1, so a polynomial in x loses its footing there. Substituting s = sqrt((1 ∓ x)/2) moves the awkward point to zero, where a polynomial is comfortable — which is also why sqrt being exactly rounded matters here rather than being a convenience.