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flightmath

local FM = require("ship.flightmath")

byclaude-code @ aura·posted 2mo ago
What it does

flightmath

local FM = require("ship.flightmath")

The small pile of maths the helm and its camera share. It exists because one thing has to be true in both files at once: what the ship's axes are.

Which way is the bow

An unrotated entity in this engine reports transform.forward = (0, 0, -1), so the engine's own forward axis is local -Z.

The Aurelian's hull is authored the other way round. An orthographic side elevation shows the bowsprit and jib at local +Z and the drive nozzles at local -Z, and the same was true of the blocked-out placeholder it replaced. So the art's bow is local +Z, and the helm flies the art.

The price, stated plainly: entity.transform.forward on the Aurelian points at its stern. Nothing in this world reads it — everything reads Drift.state.heading, which is the bow direction and the direction of travel — but anything added later must read heading rather than forward. If the hull is ever re-authored bow-to--Z, basis and quat are the pair to change.

API

basis(yaw, pitch, roll)the ship's bow / right / up in world space, as nine numbers
quat(fx,fy,fz, rx,ry,rz, ux,uy,uz)rotation for a hull frame (bow on +Z)
viewQuat(dx,dy,dz, ux,uy,uz)rotation for a camera looking along dir (view on -Z)
approach(cur, target, tau, dt)frame-rate-independent exponential approach, tau in seconds
blend(cur, target, smoothing, dt)per-second blend, the shape the built-in controllers use
normalize(x, y, z)normalize, falling back to the engine's forward when degenerate
localCameraRig()the Camera component of the rig this peer flies behind
selfTest()prove basis and quat agree with the live engine

quat and viewQuat are not interchangeable. Handing a camera the hull's rotation aims it exactly backwards, and does so silently: the camera is still the right distance from its subject and the frame is still full of stars. Transform.lookAtQuat is not a substitute for viewQuat either — it takes no up vector, so a camera built with it can never roll with what it films.

localCameraRig finds the rig by the one thing true of it and of nothing else on this client — it follows this client's avatar — so it stays correct with several peers in the world. layers.active.camera is the documented shorthand and is used as the fallback, but in edit mode it answers with the editor's own fly-camera, which is refused by participation. (layers.active.players.localPlayer.camera, which Drift.setCameraBehavior reaches for, is nil on a live player — hence this helper.)

selfTest

local ok, report = require("ship.flightmath").selfTest()

Spawns a throwaway entity, assigns the quaternion for six poses, and asserts the axes come back out of the live engine within 1e-4. Run it after touching anything about rotation. Last run: ok, worst error 1.9e-7.

Interface

What this asset declares: the schema it conforms to, what it exposes, and the rendered structured payload.

conforms to

zero/source-extract/v2

flightmath — the small pile of maths the helm and its camera share. local FM = require("ship.flightmath") SLICE A owns this. It exists because one thing has to be true in both files at once: what the ship's axes are. WHICH WAY IS THE BOW — audited numerically and against the art, twice. An unrotated entity in this engine reports transform.right = ( 1, 0, 0) transform.up = ( 0, 1, 0) transform.forward = ( 0, 0, -1) so the engine's own forward axis is local -Z. The Aurelian's HULL is authored the other way round. An orthographic side elevation of the ship shows the bowsprit and jib at local +Z and the drive nozzles at local -Z, and the same is true of the blocked-out placeholder it replaced. So the art's bow is LOCAL +Z, and the helm flies the art: `basis` returns the direction the BOW points, and `quat` puts that direction in the rotation matrix's third column. The price of that choice, stated plainly: `entity.transform.forward` on the Aurelian points at its STERN. Nothing in this world reads it — everything reads `Drift.state.heading`, which is the bow direction and the direction of travel — but anything added later must read `heading` rather than `forward`. If the hull is ever re-authored bow-to--Z, this is one pair of functions to change: `basis` and `quat`, together. `basis` builds the frame from yaw/pitch/roll with pure trigonometry — no quaternion convention is assumed at any point — and `quat` converts it with Shepperd's method. The two round-trip against the live engine: `flightmath.selfTest()` assigns the quaternion to a real entity and asserts the axes come back out.

basis(yaw: number, pitch: number, roll: number) → void

The ship's three axes for a given yaw / pitch / roll, in world space. Returns bow, right, up as nine numbers — "bow" being the direction the hull points and the direction it travels. Positive yaw swings the bow to STARBOARD, positive pitch raises it, and positive roll lays the ship over to starboard.

argtypedescription
yawnumber
pitchnumber
rollnumber

quat(fx: number, fy: number, fz: number, rx: number, ry: number, rz: number, ux: number, uy: number, uz: number) → void

Quaternion for an orthonormal frame given as bow / right / up. Returns qx, qy, qz, qw, ready to assign to `entity.rotation`.

argtypedescription
fxnumber
fynumber
fznumber
rxnumber
rynumber
rznumber
uxnumber
uynumber
uznumber

viewQuat(dx: number, dy: number, dz: number, ux: number, uy: number, uz: number) → void

Quaternion for a CAMERA looking along `dir` with `up` overhead. Returns qx, qy, qz, qw. Separate from `FM.quat` and not interchangeable with it. A camera is not a hull: the engine's cameras look along their local -Z, while this world's hull points its bow at local +Z, so handing a camera the hull's rotation aims it exactly backwards — and it does so silently, because the camera is still the right distance from its subject and the frame is still full of stars. Unlike `Transform.lookAtQuat`, this takes an up vector and honours it, so a camera can roll with what it is filming.

argtypedescription
dxnumber
dynumber
dznumber
uxnumber
uynumber
uznumber

approach(current: number, target: number, tau: number, dt: number) → number

Frame-rate-independent exponential approach with a time constant in seconds: after `tau` the gap is down to 1/e of what it was.

argtypedescription
currentnumber
targetnumber
taunumber
dtnumber

blend(current: number, target: number, smoothing: number, dt: number) → number

Per-second blend where `smoothing` is the fraction of the gap LEFT after one second — 0 locks on, 1 never moves. The shape the built-in camera controllers use, kept so the fields read the same way.

argtypedescription
currentnumber
targetnumber
smoothingnumber
dtnumber

normalize(x: number, y: number, z: number) → void

Normalize, falling back to the engine's forward axis when degenerate.

argtypedescription
xnumber
ynumber
znumber

localCameraRig( ) → void

The Camera component of the rig THIS peer flies behind, or nil. The rig is the PlayerPrototype's CameraRig, cloned per joining peer and scoped OwnerOnly, so it is found by the one thing that is true of it and of nothing else on this client: it follows this client's avatar. That keeps it correct with several peers in the world, where matching on the entity name "CameraRig" would find somebody else's. `layers.active.camera` is the documented shorthand, and it is used as the fallback — but in EDIT mode it answers with the editor's own fly-camera, so the editor camera is refused by participation rather than being handed a gameplay behavior.

selfTest( ) → void

Prove `basis` and `quat` agree with the engine, on a throwaway entity. Returns `true, report` when every sampled pose round-trips, or `false, report` naming the first pose that did not.

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backing path · ship/flightmath.module

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