Math

The $math natives cover what the operators don’t. Positions and directions are vec3, and z is up.

Distance between two points

let a: vec3 = vec3(0, 0, 0)
let b: vec3 = vec3(300, 400, 0)
let far: float = $math.distance(a, b)
let close_enough: bool = far < 500.0

Direction from one point to another

let from: vec3 = vec3(0, 0, 0)
let to: vec3 = vec3(10, 0, 0)
let direction: vec3 = $math.normalize(to - from)

normalize makes a vector length 1, so it’s pure direction.

Blend between two values

$math.lerp(a, b, t) gives a when t is 0, b when t is 1, and in between for anything between:

let halfway: float = $math.lerp(0.0, 100.0, 0.5)
let spot: vec3 = $math.lerp(vec3(0, 0, 0), vec3(0, 0, 200), 0.25)

Keep a value in range

let requested: float = 140.0
let volume: float = $math.clamp(requested, 0.0, 100.0)
let fraction: float = $math.saturate(1.4) // clamp to 0..1

Map one range onto another

Turn a distance of 0–1000 into a strength of 1–0:

let distance: float = 250.0
let strength: float = $math.map_range(0.0, 1000.0, 1.0, 0.0, distance)

Random numbers

let roll: int = $math.randi(1, 6) // 1 to 6, both included
let jitter: float = $math.randf(-5.0, 5.0)

Caution

Random numbers differ between machines. For anything players must agree on, pick on the server and replicate the result.

Angles

The engine works in radians. Convert, and build or read rotations:

let radians: float = $math.deg2rad(90.0)
let turned: vec4 = $math.rotation_from_axis_angle(vec3(0, 0, 1), radians)
let angles: vec3 = $math.eulers_from_rotation(turned)
let yaw: float = angles.z

eulers_from_rotation gives roll, pitch and yaw as x, y and z.

More

Waves (sin, cos), rounding (floori, ceili, roundi), min, max, abs, dot, cross, slerp for rotations: see the math reference.