Math, Colors, Vectors, Timers, Collision, Collision3D, and ECS

These are the small, high-frequency helpers most games and agents use constantly.

`aura.math`

Methods and constants:

• lerp(a, b, t)
• clamp(value, min, max)
• random()
• random(max)
• random(min, max)
• distance(x1, y1, x2, y2)
• angle(x1, y1, x2, y2)
• PI
• TAU

Alias helpers:

• aura.math.vec2 === aura.vec2
• aura.math.vec3 === aura.vec3

Color constructors and constants

Canonical color helpers:

• aura.rgb(r, g, b)
• aura.rgba(r, g, b, a)
• aura.Color.RED
• aura.Color.GREEN
• aura.Color.BLUE
• aura.Color.WHITE
• aura.Color.BLACK
• aura.Color.YELLOW
• aura.Color.CYAN
• aura.Color.MAGENTA
• aura.Color.TRANSPARENT

Compatibility aliases still seen in older code/docs:

• aura.color(...)
• aura.colors.*

New code should prefer rgb, rgba, and Color.*.

`aura.vec2`

Constructor and pure helpers:

• aura.vec2(x, y)
• aura.vec2.add(a, b)
• aura.vec2.sub(a, b)
• aura.vec2.scale(v, s)
• aura.vec2.dot(a, b)
• aura.vec2.length(v)
• aura.vec2.normalize(v)
• aura.vec2.distance(a, b)
• aura.vec2.lerp(a, b, t)

`aura.vec3`

Constructor and pure helpers:

• aura.vec3(x, y, z)
• aura.vec3.add(a, b)
• aura.vec3.sub(a, b)
• aura.vec3.scale(v, s)
• aura.vec3.dot(a, b)
• aura.vec3.cross(a, b)
• aura.vec3.length(v)
• aura.vec3.normalize(v)
• aura.vec3.distance(a, b)
• aura.vec3.lerp(a, b, t)

`aura.timer`

Timer/time helpers:

• after(delay, callback)
• every(interval, callback)
• cancel(timerId)
• getDelta()
• getTime()

Use cases:

• delayed actions
• repeated gameplay timers
• time sampling inside update logic

`aura.collision`

Primitive collision checks:

• rectRect(a, b)
• rectPoint(rect, point)
• circleCircle(a, b)
• circlePoint(circle, point)
• circleRect(circle, rect)

Batch helpers:

• rectRectBatch(...)
• rectPointBatch(...)
• circleCircleBatch(...)
• circlePointBatch(...)
• circleRectBatch(...)

Use cases:

• arcade hit checks
• deterministic batch overlap probes
• quick gameplay collision without a full physics world

`aura.collision3d`

3D collision helpers:

• boxBox(a, b)
• boxBoxContact(a, b)
• sphereSphere(a, b)
• sphereBox(sphere, box)
• sphereBoxContact(sphere, box)
• raySphere(ray, sphere)
• raySphereHit(ray, sphere)
• rayBox(ray, box)
• rayBoxHit(ray, box)
• pointBox(point, box)
• pointSphere(point, sphere)
• spherePlane(sphere, plane)
• rayPlane(ray, plane)
• rayPlaneHit(ray, plane)
• rayTriangle(ray, v0, v1, v2)
• capsuleCapsule(aStart, aEnd, aRadius, bStart, bEnd, bRadius)
• closestPoint(shape, point)
• sphereCast(start, end, radius, target)
• movingBoxBox(a, velocityA, b, velocityB, dt)

Return-shape notes:

• overlap checks return boolean
• the older boolean probes remain raySphere(...), rayBox(...), rayPlane(...), sphereBox(...), and boxBox(...)
• raySphereHit(...), rayBoxHit(...), rayPlaneHit(...), and rayTriangle(...) return false on miss or invalid input, or { hit: true, t, point, normal } on hit
• sphereBoxContact(...) and boxBoxContact(...) return false on miss or invalid input, or { hit: true, depth, point, normal } on hit
• capsuleCapsule(...), sphereCast(...), and movingBoxBox(...) return false on miss or invalid input
• successful sweep-style hits return { hit: true, toi, point, normal } where toi is the normalized hit fraction in [0, 1] over the authored sweep interval

Use cases:

• simple 3D overlap checks without spinning up a full aura.physics3d world
• editor/tooling probes
• deterministic geometry intersection helpers
• common gameplay sweeps such as projectile volumes, soft camera probes, and moving AABB checks without requiring physics bodies

`aura.ecs`

ECS-lite helper namespace:

• createEntity()
• removeEntity(entityId)
• addComponent(entityId, componentName, value)
• getComponent(entityId, componentName)
• system(name, fn, order?)
• run(dt)

Notes:

• This is an opt-in deterministic helper, not a replacement for the host loop.
• A common pattern is calling aura.ecs.run(dt) from aura.update(dt).