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2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 | <!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=no">
<title>Star Drift — Space Flight Explorer</title>
<style>
html, body {
margin: 0;
padding: 0;
width: 100%;
height: 100%;
overflow: hidden;
background: #050510;
cursor: none; /* native cursor hidden; a fading one is drawn on the canvas */
font-family: 'Segoe UI', system-ui, -apple-system, sans-serif;
-webkit-user-select: none;
user-select: none;
}
#game {
display: block;
width: 100%;
height: 100%;
cursor: none;
touch-action: none;
}
</style>
</head>
<body>
<canvas id="game"></canvas>
<script>
(function () {
'use strict';
const canvas = document.getElementById('game');
const ctx = canvas.getContext('2d');
let W = 0, H = 0, DPR = 1, CX = 0, CY = 0, FOCAL = 0;
// Static layers are baked to bitmaps in resize(): they only change when the
// window size changes, so there is no reason to re-evaluate a gradient over
// every pixel of every frame.
let bgLayer = null, vignetteLayer = null;
function bakeLayer(w, h, paint) {
const cv = document.createElement('canvas');
cv.width = Math.floor(w * DPR);
cv.height = Math.floor(h * DPR);
const c2 = cv.getContext('2d');
c2.setTransform(DPR, 0, 0, DPR, 0, 0);
paint(c2);
return cv;
}
function clamp(v, a, b) {
return Math.max(a, Math.min(b, v));
}
// ------------------------------------------------------------------
// Perf config — the tunables introduced by the performance pass.
// ------------------------------------------------------------------
const PERF = {
blobMaxR: 80, // galactic-band blobs are capped at this many screen px
sortAsteroids: false // a rock is convex, so backface-culled faces cannot
// overlap in projection and painter order is dead work.
// Measured over random tumbles: 0% overlap on an
// undamaged rock. Crater displacement breaks convexity:
// 1.75% of drawn face area overlaps, and 0.9% would be
// painted in the wrong order (a crater floor over its
// rim). Set true to restore the exact guarantee.
};
// Quantised alpha strings. The hot loops used to build one rgba() string per
// particle per frame; now they index a table built once.
const ALPHA_STR = new Array(64);
for (let i = 0; i < 64; i++) ALPHA_STR[i] = (i / 63).toFixed(3);
function alphaStr(a) {
return ALPHA_STR[Math.min(63, (a * 63) | 0)];
}
// rgb() strings cached per distinct colour. Asteroid faces redraw the same
// handful of shades thousands of times per frame. The cache is bounded: a face
// colour depends on its fixed base tint times a lighting value that varies
// continuously, so over a long session it could drift. Cap it and rebuild.
const RGB_CACHE = new Map();
const RGB_CACHE_MAX = 4000;
function rgbStr(r, g, b) {
if (RGB_CACHE.size > RGB_CACHE_MAX) RGB_CACHE.clear();
const key = (r << 16) | (g << 8) | b;
let s = RGB_CACHE.get(key);
if (s === undefined) {
s = 'rgb(' + r + ',' + g + ',' + b + ')';
RGB_CACHE.set(key, s);
}
return s;
}
// pow(x, 0.8) for asteroid lighting, quantised to 1/256 (a few gray levels,
// not visible against the per-vertex mottling).
const LIT_LUT = new Array(256);
for (let i = 0; i < 256; i++) LIT_LUT[i] = Math.pow(i / 256, 0.8);
// Reused projection targets so the render loop allocates nothing. P_ONE /
// P_TWO / P_CENTER are for a few simultaneous points; P_VERTS, P_RING and
// P_FIL hold batches that must survive across a loop.
function makePool(n) {
const a = new Array(n);
for (let i = 0; i < n; i++) a[i] = { x: 0, y: 0, z: 0, fade: 0 };
return a;
}
const P_ONE = makePool(1)[0], P_TWO = makePool(1)[0], P_THREE = makePool(1)[0], P_CENTER = makePool(1)[0];
const P_VERTS = makePool(128); // asteroid rocks are 42 verts, the ship is 19
const P_RING = makePool(128); // 57 ring points
const P_FIL = makePool(128); // catmullRom output is at most (10-1)*7+1 = 64
const P_OK = new Uint8Array(128); // 1 = this pooled point is valid
const RING_FRONT = new Uint8Array(128); // 0 = invalid, 1 = behind, 2 = in front
const SHIP_W = [0, 0, 0]; // scratch for shipWorldPoint
const AST_LOCAL = new Float64Array(128 * 3); // rotated local verts (backface test)
// Run-length grouping for filament strokes: consecutive segments that quantise
// to the same alpha are drawn as one path with one stroke. Alpha is monotonic
// in distance, so a run sits at a similar depth and can share one width. This
// is the only change in the file that is not exact: alpha is quantised to
// 1/63 (max error 0.016 on these alphas) and widths are averaged per run.
function flushRun(colorStr, bucket, cnt, wsum) {
if (!cnt) return;
ctx.strokeStyle = 'rgba(' + colorStr + ',' + ALPHA_STR[bucket] + ')';
ctx.lineWidth = wsum / cnt;
ctx.stroke();
}
// Reused face records (ship + asteroids).
const FACE_REC = new Array(128);
for (let i = 0; i < FACE_REC.length; i++) FACE_REC[i] = { a: 0, b: 0, c: 0, z: 0, k: '', col: '' };
const faceList = [];
// Shared far-first painter list (nebulae / galaxies / planets / asteroids).
const ENTRY = new Array(256);
for (let i = 0; i < ENTRY.length; i++) {
ENTRY[i] = { it: null, x: 0, y: 0, z: 0, r: 0, dist: 0, fade: 0, dx: 0, dy: 0, dz: 0 };
}
const list = [];
function resize() {
DPR = Math.min(window.devicePixelRatio || 1, 2);
W = window.innerWidth;
H = window.innerHeight;
canvas.width = Math.floor(W * DPR);
canvas.height = Math.floor(H * DPR);
canvas.style.width = W + 'px';
canvas.style.height = H + 'px';
ctx.setTransform(DPR, 0, 0, DPR, 0, 0);
CX = W / 2;
CY = H / 2;
FOCAL = Math.max(1, H) * 0.9;
bgLayer = bakeLayer(W, H, (c2) => {
const g = c2.createLinearGradient(0, 0, 0, H);
g.addColorStop(0, '#050510');
g.addColorStop(0.5, '#070718');
g.addColorStop(1, '#050510');
c2.fillStyle = g;
c2.fillRect(0, 0, W, H);
});
// cinematic vignette (not UI — just darkened corners)
vignetteLayer = bakeLayer(W, H, (c2) => {
const g = c2.createRadialGradient(CX, CY, Math.min(W, H) * 0.34, CX, CY, Math.hypot(W, H) * 0.72);
g.addColorStop(0, 'rgba(0,0,0,0)');
g.addColorStop(0.62, 'rgba(2,3,10,0.16)');
g.addColorStop(1, 'rgba(2,3,12,0.48)');
c2.fillStyle = g;
c2.fillRect(0, 0, W, H);
});
}
window.addEventListener('resize', resize);
resize();
// ------------------------------------------------------------------
// 3D math helpers (plain objects, no libraries)
// ------------------------------------------------------------------
function sub(a, b) { return [a[0] - b[0], a[1] - b[1], a[2] - b[2]]; }
function dot(a, b) { return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; }
function cross(a, b) {
return [
a[1] * b[2] - a[2] * b[1],
a[2] * b[0] - a[0] * b[2],
a[0] * b[1] - a[1] * b[0]
];
}
function norm(a) {
const l = Math.hypot(a[0], a[1], a[2]) || 1;
return [a[0] / l, a[1] / l, a[2] / l];
}
function len(a) { return Math.hypot(a[0], a[1], a[2]); }
const TAU = Math.PI * 2;
// Rodrigues rotation of v about a unit axis — the primitive the steering
// uses to swing the nose along one continuous arc.
function rotateAbout(v, axis, ang) {
const c = Math.cos(ang), s = Math.sin(ang), t = 1 - c;
const k = axis[0] * v[0] + axis[1] * v[1] + axis[2] * v[2];
const cx = axis[1] * v[2] - axis[2] * v[1];
const cy = axis[2] * v[0] - axis[0] * v[2];
const cz = axis[0] * v[1] - axis[1] * v[0];
return [
v[0] * c + cx * s + axis[0] * k * t,
v[1] * c + cy * s + axis[1] * k * t,
v[2] * c + cz * s + axis[2] * k * t
];
}
function smoothstep(t) { return t * t * (3 - 2 * t); }
function dot3(a, b) { return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; }
// Ship state: position, velocity, and the nose as a real 3D unit vector.
// heading / pitch / bank are read back out of that vector for the camera
// and the mesh, so everything stays consistent.
const ship = {
pos: [0, 0, 0],
vel: [0, 0, 0],
fwd: [0, 0, -1], // unit nose direction; heading 0 = facing -Z
omega: [0, 0, 0], // live angular velocity (rad/s) of the nose
heading: 0,
pitch: 0,
bank: 0,
throttle: 0
};
// Turning: the nose is rotated about the single axis perpendicular to the
// plane spanned by (current nose, click target) — one continuous great-circle
// arc instead of independent yaw and pitch ramps. The turn rate is
// proportional to the remaining error (so it eases to a stop, never slams),
// capped (so it stays slow and readable) and slew-limited (so it ramps up
// instead of snapping). Result: soft start, gentle peak, soft arrival.
const TURN_MAX = 0.6; // rad/s ceiling on the turn (~34 deg/s)
const TURN_GAIN = 0.8; // proportional ease-out toward the target
const TURN_SLEW = 0.85; // rad/s^2 — how fast the turn can build or relax
const MAX_PITCH = 1.30; // ~74 deg nose authority (keeps the level camera sane)
const PITCH_SIN = Math.sin(MAX_PITCH);
const ACCEL = 88; // thrust strength
const DRAG = 0.95; // exponential drag coefficient
const MAX_SPEED = 118; // hard speed cap
const THROTTLE_RATE = 1.6; // how fast the engines ease in / out
const ENGINE_LOCAL = [[-0.3, 0.12, 1.32], [0.3, 0.12, 1.32]];
// The turn axis is remembered between frames so the nose cannot jitter as
// it converges (see update()).
const turnAxis = [0, 0, 1];
// ------------------------------------------------------------------
// Click-to-fly: click anywhere and the ship turns to face that screen
// direction, then keeps flying that way forever until the next click.
// The click is un-projected through the current camera basis, so the
// ship always aims exactly at the spot you click (WYSIWYG aiming).
// ------------------------------------------------------------------
let hasTarget = false;
const targetFwd = [0, 0, -1]; // unit world direction the nose steers toward
let lastCam = null; // camera basis from the last rendered frame
function setTargetFromClick(mx, my) {
if (!lastCam) return;
// screen point -> camera-space ray direction (x right, y up, z forward)
let dx = mx - CX, dy = CY - my, dz = FOCAL;
const l = Math.hypot(dx, dy, dz) || 1;
dx /= l; dy /= l; dz /= l;
// camera space -> world space via the camera basis vectors
const wx = dx * lastCam.xAxis[0] + dy * lastCam.yAxis[0] + dz * lastCam.zAxis[0];
const wy = dx * lastCam.xAxis[1] + dy * lastCam.yAxis[1] + dz * lastCam.zAxis[1];
const wz = dx * lastCam.xAxis[2] + dy * lastCam.yAxis[2] + dz * lastCam.zAxis[2];
const h = Math.atan2(wx, -wz);
const p = clamp(Math.asin(clamp(wy, -1, 1)), -MAX_PITCH, MAX_PITCH);
const cp = Math.cos(p);
targetFwd[0] = Math.sin(h) * cp;
targetFwd[1] = Math.sin(p);
targetFwd[2] = -Math.cos(h) * cp;
hasTarget = true;
}
// ------------------------------------------------------------------
// Cursor: fades out 1 second after the mouse stops moving, and fades
// back in as soon as it moves again.
// ------------------------------------------------------------------
let mouseX = CX, mouseY = CY;
let lastMove = -1e9; // long ago -> cursor starts hidden
let cursorAlpha = 0;
canvas.addEventListener('pointerdown', (e) => {
setTargetFromClick(e.clientX, e.clientY);
lastMove = performance.now();
});
canvas.addEventListener('pointermove', (e) => {
mouseX = e.clientX;
mouseY = e.clientY;
lastMove = performance.now();
});
// Fixed: use canvas mouseleave, not document mouseleave.
canvas.addEventListener('mouseleave', () => {
lastMove = -1e9;
});
window.addEventListener('blur', () => {
lastMove = -1e9;
});
// ------------------------------------------------------------------
// World objects
// ------------------------------------------------------------------
const STAR_COUNT = 15000;
const stars = [];
const starColors = [
[255, 255, 255], [150, 180, 255], [255, 225, 140], [255, 140, 130]
];
const starStyle = starColors.map(c => 'rgb(' + c[0] + ',' + c[1] + ',' + c[2] + ')');
const FIELD = 2600; // respawn half-extent (infinite space wrap)
function makeStar() {
return {
x: (Math.random() * 2 - 1) * FIELD,
y: (Math.random() * 2 - 1) * FIELD,
z: (Math.random() * 2 - 1) * FIELD,
ci: (Math.random() * 4) | 0,
s: Math.random() < 0.18 ? 2 : 1
};
}
for (let i = 0; i < STAR_COUNT; i++) stars.push(makeStar());
// Seeded value noise + fBm (procedural detail for nebulae and asteroids)
function makeNoise(seed) {
const rnd = (h) => {
const s = Math.sin(h * 127.1 + seed * 311.7) * 43758.5453;
return s - Math.floor(s);
};
const grad = (x, y) => rnd(Math.floor(x) * 157 + Math.floor(y) * 113);
const smooth = (t) => t * t * (3 - 2 * t);
function noise(x, y) {
const xi = Math.floor(x), yi = Math.floor(y);
const xf = x - xi, yf = y - yi;
const u = smooth(xf), v = smooth(yf);
const a = grad(xi, yi), b = grad(xi + 1, yi);
const c = grad(xi, yi + 1), d = grad(xi + 1, yi + 1);
return a + (b - a) * u + (c - a) * v + (a - b - c + d) * u * v;
}
function fbm(x, y, oct = 4) {
let v = 0, amp = 0.5, f = 1, tot = 0;
for (let o = 0; o < oct; o++) {
v += noise(x * f, y * f) * amp;
tot += amp;
amp *= 0.5;
f *= 2;
}
return v / tot;
}
return { noise, fbm };
}
// Nebulae — wrapped in a box 2x the ship field so they can exist far away
// and fade in from invisible instead of popping into view.
const FIELD_NEB = FIELD * 2;
const NEBULA_COUNT = 16; // 8x the volume of the old box -> same density
const nebulae = [];
const nebPalette = [
[255, 120, 200], [110, 170, 255], [120, 230, 170],
[255, 170, 90], [180, 120, 255]
];
// Pre-render each nebula into a wispy gas-cloud texture: domain-warped fBm
// filaments, dark dust lanes, bright emission cores and embedded stars —
// so nebulae read as real clouds, not flat gradient circles.
function makeNebulaTexture(c, seed) {
const S = 128;
const cv = document.createElement('canvas');
cv.width = cv.height = S;
const c2 = cv.getContext('2d');
const nz = makeNoise(seed);
const img = c2.createImageData(S, S);
const data = img.data;
const R = S * 0.5;
for (let y = 0; y < S; y++) {
for (let x = 0; x < S; x++) {
const dx = x - R, dy = y - R;
const d = Math.hypot(dx, dy) / R;
if (d >= 1) continue;
const ang = Math.atan2(dy, dx);
// domain-warped fBm -> swirling gas filaments
const q1 = nz.fbm(dx * 0.05 + 5.2, dy * 0.05 + 1.3, 4);
const q2 = nz.fbm(dx * 0.05 + 9.1, dy * 0.05 + 7.7, 4);
const n = nz.fbm(dx * 0.06 + q1 * 8 + ang * 0.9, dy * 0.06 + q2 * 8, 5);
const fil = Math.pow(n, 2.3);
// dark dust lanes
const dust = nz.fbm(dx * 0.08 + 21.4, dy * 0.08 + 33.9, 3);
const lane = dust < 0.42 ? (0.42 - dust) * 2.2 : 0;
const soft = 1 - d;
const a = Math.max(0, fil * 1.9 - lane) * soft * soft;
const i = (y * S + x) * 4;
const hot = Math.pow(n, 6) * 120; // bright cores along filaments
data[i] = Math.min(255, c[0] + hot);
data[i + 1] = Math.min(255, c[1] + hot * 0.9);
data[i + 2] = Math.min(255, c[2] + hot * 0.8);
data[i + 3] = Math.min(255, a * 255);
}
}
c2.putImageData(img, 0, 0);
// a few faint background stars seen through the gas
for (let k = 0; k < 46; k++) {
const sx = nz.noise(k * 3.1, 7.7) * S;
const sy = nz.noise(2.2, k * 5.7) * S;
const sd = Math.hypot(sx - R, sy - R) / R;
if (sd > 0.85) continue;
c2.fillStyle = 'rgba(255,255,255,' + (0.2 + nz.noise(k, k) * 0.55).toFixed(2) + ')';
c2.fillRect(sx, sy, 1, 1);
}
return cv;
}
const nebulaTex = nebPalette.map((c, i) => makeNebulaTexture(c, 1234 + i * 77));
function makeNebula() {
const ci = (Math.random() * nebPalette.length) | 0;
return {
x: (Math.random() * 2 - 1) * FIELD_NEB,
y: (Math.random() * 2 - 1) * FIELD_NEB * 0.6,
z: (Math.random() * 2 - 1) * FIELD_NEB,
r: 700 + Math.random() * 1000,
ci,
rot: Math.random() * Math.PI * 2
};
}
for (let i = 0; i < NEBULA_COUNT; i++) nebulae.push(makeNebula());
// Asteroids — irregular gray polyhedra
// Asteroids wrap in a box 3x the ship field — a huge runway so they can
// fade in from invisible over many seconds instead of popping into view.
const FIELD_AST = FIELD * 3;
const ASTEROID_COUNT = 150; // 150 rocks in a 27x-larger box keeps the same encounter density as before
const asteroids = [];
function makeAsteroid() {
// Icosahedron base, one subdivision -> 42 verts / 80 triangles
const T = (1 + Math.sqrt(5)) / 2;
let verts = [
[-1, T, 0], [1, T, 0], [-1, -T, 0], [1, -T, 0],
[0, -1, T], [0, 1, T], [0, -1, -T], [0, 1, -T],
[T, 0, -1], [T, 0, 1], [-T, 0, -1], [-T, 0, 1]
];
const il = Math.hypot(1, T);
verts = verts.map(p => [p[0] / il, p[1] / il, p[2] / il]);
const F = [
[0, 11, 5], [0, 5, 1], [0, 1, 7], [0, 7, 10], [0, 10, 11],
[1, 5, 9], [5, 11, 4], [11, 10, 2], [10, 7, 6], [7, 1, 8],
[3, 9, 4], [3, 4, 2], [3, 2, 6], [3, 6, 8], [3, 8, 9],
[4, 9, 5], [2, 4, 11], [6, 2, 10], [8, 6, 7], [9, 8, 1]
];
let faces = F.map(f => f.slice());
const midCache = {};
function midpoint(a, b) {
const key = a < b ? a + '_' + b : b + '_' + a;
const hit = midCache[key];
if (hit !== undefined) return hit;
const pa = verts[a], pb = verts[b];
let m = [(pa[0] + pb[0]) / 2, (pa[1] + pb[1]) / 2, (pa[2] + pb[2]) / 2];
const l = Math.hypot(m[0], m[1], m[2]) || 1;
m = [m[0] / l, m[1] / l, m[2] / l];
verts.push(m);
midCache[key] = verts.length - 1;
return midCache[key];
}
const nextF = [];
for (const f of faces) {
const ab = midpoint(f[0], f[1]);
const bc = midpoint(f[1], f[2]);
const ca = midpoint(f[2], f[0]);
nextF.push([f[0], ab, ca], [ab, f[1], bc], [ca, bc, f[2]], [ab, bc, ca]);
}
faces = nextF;
// random tumble of the whole shape
const rz = Math.random() * Math.PI * 2, ry = Math.random() * Math.PI * 2;
const rx = (Math.random() - 0.5) * 1.1;
verts = verts.map(p => {
let x = p[0], y = p[1], z = p[2];
let t = x * Math.cos(rz) - y * Math.sin(rz);
y = x * Math.sin(rz) + y * Math.cos(rz); x = t;
t = y * Math.cos(rx) - z * Math.sin(rx);
z = y * Math.sin(rx) + z * Math.cos(rx); y = t;
t = x * Math.cos(ry) + z * Math.sin(ry);
z = -x * Math.sin(ry) + z * Math.cos(ry); x = t;
return [x, y, z];
});
// lumpy regolith displacement
const nz = makeNoise(3000 + ((Math.random() * 9999) | 0));
verts = verts.map(p => {
const k = 1 + 0.16 * (nz.fbm(p[0] * 2.3 + 5, p[1] * 2.3 + 9) - 0.5)
+ 0.10 * (nz.fbm(p[1] * 5.1 + 3, p[2] * 5.1 + 7) - 0.5);
return [p[0] * k, p[1] * k, p[2] * k];
});
// mottled per-vertex tint
const seed = Math.random() * 97;
const vcol = verts.map(p => {
const g = 0.50 + (nz.fbm(p[0] * 3.7 + seed, p[2] * 3.7 + seed) - 0.5) * 0.42;
return [g, g, g * 1.05];
});
// craters: sink a random vertex, raise its neighbours into a rim
const nv = verts.length;
const craters = 8 + ((Math.random() * 7) | 0);
for (let k = 0; k < craters; k++) {
const vi = (Math.random() * nv) | 0;
const dir = verts[vi];
const l = Math.hypot(dir[0], dir[1], dir[2]) || 1;
const depth = 0.12 + Math.random() * 0.14;
verts[vi] = [dir[0] / l * (1 - depth), dir[1] / l * (1 - depth), dir[2] / l * (1 - depth)];
vcol[vi][0] -= 0.10; vcol[vi][1] -= 0.10; vcol[vi][2] -= 0.08;
const seen = {};
for (const f of faces) {
if (f[0] !== vi && f[1] !== vi && f[2] !== vi) continue;
for (const r of [f[0], f[1], f[2]]) {
if (r === vi || seen[r]) continue;
seen[r] = 1;
const rr = verts[r];
const rl = Math.hypot(rr[0], rr[1], rr[2]) || 1;
const lift = 1 + depth * 0.8;
verts[r] = [rr[0] / rl * lift, rr[1] / rl * lift, rr[2] / rl * lift];
vcol[r][0] += 0.14; vcol[r][1] += 0.14; vcol[r][2] += 0.11;
}
}
}
// per-face base colour (crater floors dark, rims bright)
const faceCol = faces.map(f => {
let r = 0, g = 0, b = 0;
for (const vi of f) { r += vcol[vi][0]; g += vcol[vi][1]; b += vcol[vi][2]; }
r /= 3; g /= 3; b /= 3;
const cc = v => Math.max(0, Math.min(1, v)) * 255;
return [cc(r), cc(g), cc(b)];
});
// Per-face unit normals, computed once here. drawAsteroids used to rebuild
// the cross product and a normalising sqrt for all 80 faces of every rock
// every frame. Rotating a stored unit normal by the tumble matrix is 9
// multiplies, and because that matrix is a pure rotation the normal stays
// unit length — so no renormalising is needed at draw time.
const faceNormal = faces.map(f => {
const v0 = verts[f[0]], v1 = verts[f[1]], v2 = verts[f[2]];
const nx = (v1[1] - v0[1]) * (v2[2] - v0[2]) - (v1[2] - v0[2]) * (v2[1] - v0[1]);
const ny = (v1[2] - v0[2]) * (v2[0] - v0[0]) - (v1[0] - v0[0]) * (v2[2] - v0[2]);
const nz = (v1[0] - v0[0]) * (v2[1] - v0[1]) - (v1[1] - v0[1]) * (v2[0] - v0[0]);
const l = Math.sqrt(nx * nx + ny * ny + nz * nz) || 1;
return [nx / l, ny / l, nz / l];
});
const scale = 14 + Math.random() * 22;
return {
x: (Math.random() * 2 - 1) * FIELD_AST,
y: (Math.random() * 2 - 1) * FIELD_AST * 0.7,
z: (Math.random() * 2 - 1) * FIELD_AST,
verts, faces, faceNormal, scale, faceCol,
spin: [Math.random() * 0.8 - 0.4, Math.random() * 0.8 - 0.4, Math.random() * 0.8 - 0.4],
rot: [Math.random() * 6, Math.random() * 6, Math.random() * 6],
shade: 90 + Math.random() * 50
};
}
for (let i = 0; i < ASTEROID_COUNT; i++) asteroids.push(makeAsteroid());
// ------------------------------------------------------------------
// Deep-space scenery: a galactic band across the whole sky, filamentary
// strands of stars and gas, spiral galaxies, sunlit planets, meteor
// streaks, near-field dust and engine exhaust. All procedural, all
// wrapping or direction-based, so the flight never runs out of sky.
// ------------------------------------------------------------------
const SUN_DIR = norm([0.42, 0.58, -0.7]);
// Soft glow sprites — far cheaper than a gradient per particle.
function makeSoftDot(rgb, size) {
const cv = document.createElement('canvas');
cv.width = cv.height = size;
const c2 = cv.getContext('2d');
const g = c2.createRadialGradient(size / 2, size / 2, 0, size / 2, size / 2, size / 2);
g.addColorStop(0, 'rgba(' + rgb + ',1)');
g.addColorStop(0.22, 'rgba(' + rgb + ',0.5)');
g.addColorStop(0.55, 'rgba(' + rgb + ',0.13)');
g.addColorStop(1, 'rgba(' + rgb + ',0)');
c2.fillStyle = g;
c2.fillRect(0, 0, size, size);
return cv;
}
const softCool = makeSoftDot('190,230,255', 64);
const softWarm = makeSoftDot('255,226,190', 64);
// Cockpit halo as a bitmap too — the ship is drawn every frame, and building
// a radial gradient per frame is the expensive part, not the fill.
const HALO_R = 52;
const cockpitGlow = (function () {
const cv = document.createElement('canvas');
cv.width = cv.height = HALO_R;
const c2 = cv.getContext('2d');
const g = c2.createRadialGradient(HALO_R / 2, HALO_R / 2, 0, HALO_R / 2, HALO_R / 2, HALO_R / 2);
g.addColorStop(0, 'rgba(120,225,255,0.55)');
g.addColorStop(1, 'rgba(120,225,255,0)');
c2.fillStyle = g;
c2.fillRect(0, 0, HALO_R, HALO_R);
return cv;
})();
// ---- galactic band ------------------------------------------------
// Direction-only: no wrap and no parallax, so it behaves like real
// infinity and can never pop into view.
const SKY_R = 13000;
const GAL_N = norm([0.45, 0.72, 0.53]); // galactic plane normal
const GAL_U = norm(cross(GAL_N, [0, 0, 1]));
const GAL_V = norm(cross(GAL_N, GAL_U));
const skyNoise = makeNoise(4242);
function bandDir(a, off) {
const ca = Math.cos(a), sa = Math.sin(a);
return norm([
GAL_U[0] * ca + GAL_V[0] * sa + GAL_N[0] * off,
GAL_U[1] * ca + GAL_V[1] * sa + GAL_N[1] * off,
GAL_U[2] * ca + GAL_V[2] * sa + GAL_N[2] * off
]);
}
const bandBlobs = [];
const bandStars = [];
{
const N = 420;
for (let i = 0; i < N; i++) {
const a = i / N * TAU, ca = Math.cos(a), sa = Math.sin(a);
const b = skyNoise.fbm(ca * 2.4 + 11, sa * 2.4 + 5, 4);
const dust = skyNoise.fbm(ca * 5.5 + 47, sa * 5.5 + 19, 3);
const off = (skyNoise.noise(ca * 4.3, sa * 4.3) - 0.5) * 0.26;
// fbm brightness minus dark dust lanes where the noise dips
const bright = Math.max(0, b * 1.5 - (dust < 0.44 ? (0.44 - dust) * 2.8 : 0));
if (bright < 0.04) continue;
bandBlobs.push({
dir: bandDir(a, off),
r: 1500 + b * 3400,
a: Math.min(0.17, bright * 0.13),
tex: b > 0.58 ? softWarm : softCool
});
}
for (let i = 0; i < 2600; i++) {
const a = Math.random() * TAU;
const g = (Math.random() + Math.random() + Math.random() - 1.5) * 0.3; // hug the plane
bandStars.push({
dir: bandDir(a, g),
s: Math.random() < 0.1 ? 2 : 1,
b: (Math.random() * 3) | 0,
c: (Math.random() * 3) | 0
});
}
}
// ---- galactic filaments (cosmic web strands) ----------------------
const FIELD_FIL = FIELD * 4;
const FIL_COUNT = 26;
const filPalette = [
[120, 170, 255], [160, 200, 255], [140, 235, 220], [255, 200, 160], [200, 160, 255]
];
function catmullRom(points, per) {
const out = [], n = points.length;
for (let i = 0; i < n - 1; i++) {
const p0 = points[Math.max(0, i - 1)], p1 = points[i];
const p2 = points[i + 1], p3 = points[Math.min(n - 1, i + 2)];
for (let s = 0; s < per; s++) {
const t = s / per, t2 = t * t, t3 = t2 * t;
out.push([
0.5 * (2 * p1[0] + (-p0[0] + p2[0]) * t + (2 * p0[0] - 5 * p1[0] + 4 * p2[0] - p3[0]) * t2 + (-p0[0] + 3 * p1[0] - 3 * p2[0] + p3[0]) * t3),
0.5 * (2 * p1[1] + (-p0[1] + p2[1]) * t + (2 * p0[1] - 5 * p1[1] + 4 * p2[1] - p3[1]) * t2 + (-p0[1] + 3 * p1[1] - 3 * p2[1] + p3[1]) * t3),
0.5 * (2 * p1[2] + (-p0[2] + p2[2]) * t + (2 * p0[2] - 5 * p1[2] + 4 * p2[2] - p3[2]) * t2 + (-p0[2] + 3 * p1[2] - 3 * p2[2] + p3[2]) * t3)
]);
}
}
out.push(points[n - 1].slice());
return out;
}
function makeFilament() {
const seed = (Math.random() * 9999) | 0;
const nz = makeNoise(seed);
const n = 5 + ((Math.random() * 5) | 0);
let dir = norm([Math.random() * 2 - 1, (Math.random() * 2 - 1) * 0.55, Math.random() * 2 - 1]);
let x = (Math.random() * 2 - 1) * FIELD_FIL * 0.8;
let y = (Math.random() * 2 - 1) * FIELD_FIL * 0.5;
let z = (Math.random() * 2 - 1) * FIELD_FIL * 0.8;
const step = 500 + Math.random() * 600;
const nodes = [];
for (let i = 0; i < n; i++) {
nodes.push([x, y, z]);
const w1 = nz.noise(i * 1.7, seed * 0.01) - 0.5;
const w2 = nz.noise(seed * 0.02, i * 2.3) - 0.5;
dir = norm([dir[0] + w1 * 0.9, dir[1] + w2 * 0.5, dir[2] + w1 * 0.4]);
x += dir[0] * step; y += dir[1] * step; z += dir[2] * step;
}
// faint star clusters gathered at the knots, in local offsets
const knots = [];
for (let i = 0; i < n; i++) {
const k = [];
const m = 9 + ((Math.random() * 10) | 0);
for (let j = 0; j < m; j++) {
k.push([(Math.random() * 2 - 1) * 150, (Math.random() * 2 - 1) * 150, (Math.random() * 2 - 1) * 150]);
}
knots.push(k);
}
const pts = catmullRom(nodes, 7);
// Bounding sphere, so drawFilaments can reject a whole strand with one
// distance test instead of projecting its 35 points. Headroom covers the
// stroke width and the 150-unit knot star offsets. Translation by f.off
// moves the sphere with the strand.
let bx = 0, by = 0, bz = 0;
for (const p of pts) { bx += p[0]; by += p[1]; bz += p[2]; }
bx /= pts.length; by /= pts.length; bz /= pts.length;
let br = 0;
for (const p of pts) {
const l = Math.sqrt((p[0] - bx) * (p[0] - bx) + (p[1] - by) * (p[1] - by) + (p[2] - bz) * (p[2] - bz));
if (l > br) br = l;
}
return {
nodes, knots, pts,
center: [bx, by, bz], radius: br + 200,
ci: (Math.random() * filPalette.length) | 0,
colorStr: '',
w: 22 + Math.random() * 46,
glow: 0.45 + Math.random() * 0.55,
off: [0, 0, 0]
};
}
const filaments = [];
for (let i = 0; i < FIL_COUNT; i++) {
const f = makeFilament();
f.colorStr = filPalette[f.ci][0] + ',' + filPalette[f.ci][1] + ',' + filPalette[f.ci][2]; // once, not per frame
filaments.push(f);
}
// Filaments live far away: they fade out before they reach the camera and
// before a wrap can land them, so they never pop and never straddle you.
function filFade(d) {
if (d < 700 || d > FIELD_FIL) return 0;
return smoothstep(Math.min(1, (d - 700) / 1300)) * smoothstep(Math.min(1, (FIELD_FIL - d) / 2600));
}
// ---- spiral galaxies ----------------------------------------------
const FIELD_GAL = FIELD * 2.4;
const GALAXY_COUNT = 12;
const galPalette = [[150, 190, 255], [255, 200, 170], [170, 240, 225], [215, 175, 255]];
function makeGalaxyTexture(seed, col) {
const S = 160, R = S / 2;
const cv = document.createElement('canvas');
cv.width = cv.height = S;
const c2 = cv.getContext('2d');
const nz = makeNoise(seed);
const cs = col[0] + ',' + col[1] + ',' + col[2];
c2.globalCompositeOperation = 'lighter';
const g0 = c2.createRadialGradient(R, R, 0, R, R, R);
g0.addColorStop(0, 'rgba(255,248,235,0.7)');
g0.addColorStop(0.16, 'rgba(' + cs + ',0.32)');
g0.addColorStop(0.52, 'rgba(' + cs + ',0.1)');
g0.addColorStop(1, 'rgba(' + cs + ',0)');
c2.fillStyle = g0;
c2.fillRect(0, 0, S, S);
const arms = 2 + (seed % 2);
const twist = 2.6 + nz.noise(seed, 3) * 1.9;
for (let arm = 0; arm < arms; arm++) {
const base = arm * TAU / arms + nz.noise(arm * 2.1, seed) * 1.2;
const steps = 110;
for (let i = 1; i < steps; i++) {
const t = i / steps;
const rr = 8 + t * R * 0.92;
const th = base + t * twist + (nz.noise(i * 0.19, arm * 3.7) - 0.5) * 0.7;
const jit = (nz.noise(i * 0.63, arm * 1.9) - 0.5) * 14 * t;
const x = R + Math.cos(th) * (rr + jit);
const y = R + Math.sin(th) * (rr + jit) * 0.58; // tilted disc
const rad = 4 + t * 9;
const a = (1 - t * 0.6) * 0.17;
const gg = c2.createRadialGradient(x, y, 0, x, y, rad);
gg.addColorStop(0, 'rgba(' + cs + ',' + a.toFixed(3) + ')');
gg.addColorStop(1, 'rgba(' + cs + ',0)');
c2.fillStyle = gg;
c2.beginPath(); c2.arc(x, y, rad, 0, TAU); c2.fill();
if (nz.noise(i * 1.31, arm * 7.7) > 0.86) { // young blue star knots
c2.fillStyle = 'rgba(200,230,255,' + (0.3 + nz.noise(i, arm) * 0.4).toFixed(2) + ')';
c2.beginPath(); c2.arc(x, y, 1.3, 0, TAU); c2.fill();
}
}
}
c2.globalCompositeOperation = 'destination-out';
for (let k = 0; k < 26; k++) { // dark dust lanes cutting the disc
const t = nz.noise(k * 2.7, seed);
const th = nz.noise(k * 1.1, seed * 0.3) * TAU;
const rr = 12 + t * R * 0.85;
const x = R + Math.cos(th) * rr, y = R + Math.sin(th) * rr * 0.58;
const rad = 9 + t * 12;
const gg = c2.createRadialGradient(x, y, 0, x, y, rad);
gg.addColorStop(0, 'rgba(0,0,0,0.75)');
gg.addColorStop(1, 'rgba(0,0,0,0)');
c2.fillStyle = gg;
c2.beginPath(); c2.arc(x, y, rad, 0, TAU); c2.fill();
}
c2.globalCompositeOperation = 'source-over';
return cv;
}
const galaxyTex = galPalette.map((c, i) => makeGalaxyTexture(511 + i * 53, c));
function makeGalaxy() {
return {
x: (Math.random() * 2 - 1) * FIELD_GAL,
y: (Math.random() * 2 - 1) * FIELD_GAL * 0.55,
z: (Math.random() * 2 - 1) * FIELD_GAL,
r: 380 + Math.random() * 720,
ci: (Math.random() * galaxyTex.length) | 0,
rot: Math.random() * TAU,
squash: 0.4 + Math.random() * 0.6
};
}
const galaxies = [];
for (let i = 0; i < GALAXY_COUNT; i++) galaxies.push(makeGalaxy());
// ---- sunlit planets -----------------------------------------------
const FIELD_PLANET = FIELD * 2.2;
const PLANET_COUNT = 8;
const planetPal = [
[[36, 64, 118], [58, 104, 146], [214, 228, 238]], // ocean
[[92, 66, 48], [132, 104, 72], [226, 216, 200]], // rocky
[[48, 82, 70], [108, 140, 96], [228, 236, 224]], // verdant
[[124, 86, 58], [176, 126, 84], [242, 222, 192]], // desert
[[40, 52, 82], [92, 112, 152], [222, 232, 246]] // ice
];
function makePlanetTexture(seed) {
const S = 128;
const cv = document.createElement('canvas');
cv.width = cv.height = S;
const c2 = cv.getContext('2d');
const img = c2.createImageData(S, S), data = img.data;
const nz = makeNoise(seed);
const pal = planetPal[seed % planetPal.length];
for (let py = 0; py < S; py++) {
for (let px = 0; px < S; px++) {
const dx = (px - S / 2 + 0.5) / (S / 2), dy = (py - S / 2 + 0.5) / (S / 2);
const rr = dx * dx + dy * dy;
const i = (py * S + px) * 4;
if (rr >= 1) { data[i + 3] = 0; continue; }
data[i + 3] = 255;
const z = Math.sqrt(1 - rr);
const lon = Math.atan2(dy, dx) + seed * 0.37;
const lat = Math.asin(clamp(z, -1, 1)) - Math.PI / 2;
const cl = Math.cos(lat);
// seamless-in-longitude continent field
const c = nz.fbm(Math.cos(lon) * 2.1 + 7, Math.sin(lon) * 2.1 + 3 + lat * 2.6, 4);
const land = c > 0.52;
let base = land ? pal[1] : pal[0];
if (land) {
const h = Math.min(1, (c - 0.52) * 3.2);
base = [base[0] + (pal[2][0] - base[0]) * h * 0.45,
base[1] + (pal[2][1] - base[1]) * h * 0.45,
base[2] + (pal[2][2] - base[2]) * h * 0.45];
}
// ice caps
const ice = Math.abs(lat) > 1.18 + nz.noise(lon * 3, 9) * 0.3;
if (ice) {
const k = Math.min(1, (Math.abs(lat) - 1.1) * 3);
base = [base[0] + (240 - base[0]) * k, base[1] + (246 - base[1]) * k, base[2] + (252 - base[2]) * k];
}
// cloud banding
const cloud = nz.fbm(Math.cos(lon) * 3.3 + 21, Math.sin(lon) * 3.3 + 17 + lat * 3.4, 3);
const ca = clamp((cloud - 0.52) * 2.4, 0, 1) * 0.72;
data[i] = base[0] + (250 - base[0]) * ca;
data[i + 1] = base[1] + (252 - base[1]) * ca;
data[i + 2] = base[2] + (255 - base[2]) * ca;
// limb darkening so the sprite reads as a sphere even before shading
const limb = 0.72 + 0.28 * Math.pow(z, 0.45);
data[i] *= limb; data[i + 1] *= limb; data[i + 2] *= limb;
}
}
c2.putImageData(img, 0, 0);
return cv;
}
const planetTex = [];
for (let i = 0; i < 5; i++) planetTex.push(makePlanetTexture(101 + i * 37));
function makePlanet() {
const nrm = norm([Math.random() * 2 - 1, Math.random() * 1.2 + 0.4, Math.random() * 2 - 1]);
let A = cross(nrm, [0, 1, 0]);
if (len(A) < 1e-4) A = [1, 0, 0]; else A = norm(A);
const B = norm(cross(nrm, A));
const ringed = Math.random() < 0.4;
return {
x: (Math.random() * 2 - 1) * FIELD_PLANET * 0.9,
y: (Math.random() * 2 - 1) * FIELD_PLANET * 0.5,
z: (Math.random() * 2 - 1) * FIELD_PLANET * 0.9,
r: 240 + Math.random() * 620,
tex: (Math.random() * planetTex.length) | 0,
spin: Math.random() * TAU,
spinRate: (Math.random() - 0.5) * 0.06,
atmo: [[120, 190, 255], [255, 170, 120], [150, 240, 210], [205, 205, 255]][(Math.random() * 4) | 0],
atmoStr: '',
ring: ringed,
ringA: A, ringB: B,
ringR: 1.7 + Math.random() * 0.9,
ringW: 26 + Math.random() * 40
};
}
const planets = [];
for (let i = 0; i < PLANET_COUNT; i++) {
const pl = makePlanet();
pl.atmoStr = pl.atmo[0] + ',' + pl.atmo[1] + ',' + pl.atmo[2]; // built once, not per frame
planets.push(pl);
}
// ---- meteors / shooting stars -------------------------------------
const meteors = [];
let nextMeteor = 0, exhaustTick = 0;
const exhaust = [];
function spawnMeteors(cam, now) {
if (now < nextMeteor) return;
nextMeteor = now + 500 + Math.random() * 2200;
const burst = Math.random() < 0.22 ? 2 + ((Math.random() * 3) | 0) : 1;
for (let i = 0; i < burst && meteors.length < 16; i++) {
// spawn in the forward hemisphere, off-axis
const d = norm([(Math.random() * 2 - 1) * 1.1, (Math.random() * 2 - 1) * 0.8, 0.45 + Math.random() * 0.55]);
const dist = 500 + Math.random() * 900;
// travel across the view so it reads as a streak
let lat = cross(d, [0, 1, 0]);
if (len(lat) < 1e-4) lat = [1, 0, 0]; else lat = norm(lat);
lat = rotateAbout(lat, d, Math.random() * TAU);
const speed = 700 + Math.random() * 1500;
const fireball = Math.random() < 0.14;
const vx = lat[0] * speed + d[0] * (Math.random() * 220 - 80);
const vy = lat[1] * speed + d[1] * (Math.random() * 220 - 80);
const vz = lat[2] * speed + d[2] * (Math.random() * 220 - 80);
meteors.push({
x: cam.camPos[0] + d[0] * dist + (Math.random() - 0.5) * 300,
y: cam.camPos[1] + d[1] * dist + (Math.random() - 0.5) * 300,
z: cam.camPos[2] + d[2] * dist + (Math.random() - 0.5) * 300,
vx: vx, vy: vy, vz: vz,
life: 0, max: 0.9 + Math.random() * 1.2,
trail: (fireball ? 0.22 : 0.12) + Math.random() * 0.06,
w: fireball ? 3.2 + Math.random() * 2 : 1.2 + Math.random() * 1.4,
warm: fireball || Math.random() < 0.3,
fireball: fireball
});
}
}
// ---- near-field dust motes (speed cue) ----------------------------
const DUST_COUNT = 460, DUST_R = 620;
const dust = [];
for (let i = 0; i < DUST_COUNT; i++) {
dust.push({
x: (Math.random() * 2 - 1) * DUST_R,
y: (Math.random() * 2 - 1) * DUST_R,
z: (Math.random() * 2 - 1) * DUST_R
});
}
// ------------------------------------------------------------------
// Camera: chase cam behind the ship with a FIXED WORLD-UP view.
// The camera's up vector is always (0,1,0), so the horizon stays level
// and the view never rolls or flips no matter how the ship yaws or
// pitches. Position and look-target are exponentially smoothed (no
// overshoot, no drift) so turns feel fluid.
//
// The view direction follows the FLIGHT PATH, not the nose. The nose can
// swing at ~34 deg/s, but the ship's course only changes as its velocity
// is rebuilt along the new nose. So during a turn the sky holds still and
// the ship rotates inside the frame, instead of the whole world spinning
// the other way under the turn. Once you are flying straight, velocity and
// nose agree and the camera behaves exactly as it always did.
//
// CAM_VIEW_BLEND 0 = old behaviour (view snaps to the nose).
// higher = steadier sky, ship swings more in frame.
// CAM_VIEW_FOLLOW how fast the view settles. Lower = steeper lag.
// CAM_MAX_ANGLE how far the view may fall behind the nose, so the
// ship can never swing out of frame.
// ------------------------------------------------------------------
const CAM_BACK = 110; // distance behind the ship
const CAM_UP = 55; // height above the ship
const CAM_FOLLOW = 7; // smoothing rate (1/s) — softer chase
const CAM_LOOKAHEAD = 26; // camera aims along the view, ship leads it
const CAM_VIEW_BLEND = 0.8; // nose vs. flight path, 0 = pure nose
const CAM_VIEW_FOLLOW = 0.6; // view settling rate (1/s)
const CAM_MAX_ANGLE = 0.8; // rad (~46 deg) soft limit on nose-vs-view lag
const CAM_UNWIND = 0.9; // rad/s — how gently the lag is pulled back
let camState = null;
function cameraBasis(dt) {
const fwd = ship.fwd;
// What the view is allowed to turn toward. Blended with the nose so a
// ship that is barely moving (or decelerating out of the old direction)
// still has a well-defined view.
let want = fwd;
if (CAM_VIEW_BLEND > 0) {
const sp = len(ship.vel);
if (sp > 1) {
const w = CAM_VIEW_BLEND;
const bx = fwd[0] * (1 - w) + (ship.vel[0] / sp) * w;
const by = fwd[1] * (1 - w) + (ship.vel[1] / sp) * w;
const bz = fwd[2] * (1 - w) + (ship.vel[2] / sp) * w;
const bl = Math.hypot(bx, by, bz);
if (bl > 1e-6) want = [bx / bl, by / bl, bz / bl];
}
}
const first = !camState;
if (first) camState = { pos: [0, 0, 0], tgt: [0, 0, 0], view: want.slice() };
const kv = 1 - Math.exp(-CAM_VIEW_FOLLOW * dt);
for (let i = 0; i < 3; i++) camState.view[i] += (want[i] - camState.view[i]) * kv;
// Soft limit on how far the view may fall behind the nose. A hard cap
// would snap the view in spikes, which is the very thing being reduced.
const ca = clamp(dot3(camState.view, fwd), -1, 1);
const lag = Math.acos(ca);
if (lag > CAM_MAX_ANGLE) {
const ax = cross(camState.view, fwd);
const al = len(ax);
if (al > 1e-6) {
const n = [ax[0] / al, ax[1] / al, ax[2] / al];
// positive rotation about cross(view, nose) swings the view back
// toward the nose, but only by what this frame can afford
const r = rotateAbout(camState.view, n, Math.min(lag - CAM_MAX_ANGLE, CAM_UNWIND * dt));
camState.view[0] = r[0]; camState.view[1] = r[1]; camState.view[2] = r[2];
}
}
const view = camState.view;
const desiredPos = [
ship.pos[0] - view[0] * CAM_BACK,
ship.pos[1] - view[1] * CAM_BACK + CAM_UP,
ship.pos[2] - view[2] * CAM_BACK
];
const desiredTgt = [
ship.pos[0] + view[0] * CAM_LOOKAHEAD,
ship.pos[1] + view[1] * CAM_LOOKAHEAD + 8,
ship.pos[2] + view[2] * CAM_LOOKAHEAD
];
const k = first ? 1 : 1 - Math.exp(-CAM_FOLLOW * dt);
for (let i = 0; i < 3; i++) {
camState.pos[i] += (desiredPos[i] - camState.pos[i]) * k;
camState.tgt[i] += (desiredTgt[i] - camState.tgt[i]) * k;
}
const forward = norm(sub(camState.tgt, camState.pos));
let xAxis = cross(forward, [0, 1, 0]); // screen right
if (len(xAxis) < 1e-6) xAxis = [1, 0, 0]; else xAxis = norm(xAxis);
const yAxis = cross(xAxis, forward); // screen up (always world-level)
lastCam = { camPos: camState.pos, xAxis, yAxis, zAxis: forward };
return lastCam;
}
// Transform a world point into camera space and project it into `out`, a
// pooled object, so the render loop allocates nothing. Returns null if behind.
function project(px, py, pz, cam, out) {
const dx = px - cam.camPos[0];
const dy = py - cam.camPos[1];
const dz = pz - cam.camPos[2];
const cz = dx * cam.zAxis[0] + dy * cam.zAxis[1] + dz * cam.zAxis[2];
if (cz <= 0.5) return null; // depth first: most rejects stop here
out.x = CX + ((dx * cam.xAxis[0] + dy * cam.xAxis[1] + dz * cam.xAxis[2]) / cz) * FOCAL;
out.y = CY - ((dx * cam.yAxis[0] + dy * cam.yAxis[1] + dz * cam.yAxis[2]) / cz) * FOCAL;
out.z = cz;
return out;
}
// ------------------------------------------------------------------
// Ship geometry (local space, nose toward -Z, scale factor 15)
// ------------------------------------------------------------------
const SHIP_SCALE = 15;
const shipVerts = [
[0, 0, -1.4], // 0 nose tip
[-0.5, 0.15, -0.4], // 1 cockpit ring left
[0.5, 0.15, -0.4], // 2 cockpit ring right
[0, 0.42, -0.4], // 3 cockpit ring top
[-0.62, 0, 0.6], // 4 mid fuselage left
[0.62, 0, 0.6], // 5 mid fuselage right
[0, 0.5, 0.6], // 6 mid fuselage top
[-0.5, 0, 1.3], // 7 rear left
[0.5, 0, 1.3], // 8 rear right
[0, 0.4, 1.3], // 9 rear top
[-2.1, 0.05, 0.9], // 10 left wing tip (swept back)
[2.1, 0.05, 0.9], // 11 right wing tip (swept back)
[-0.62, 0, 1.25], // 12 left wing root rear
[0.62, 0, 1.25], // 13 right wing root rear
[0, 1.15, 1.55], // 14 tail fin tip
[-0.3, 0.35, 1.25], // 15 tail fin base left
[0.3, 0.35, 1.25], // 16 tail fin base right
[-1.0, 0.55, 1.6], // 17 left side fin tip
[1.0, 0.55, 1.6] // 18 right side fin tip
];
// [a,b,c] index triples, plus a color key: h=hull, w=wing, g=glass, e=engine
const shipFaces = [
// nose cone
[0, 1, 2, 'h'],
[0, 2, 3, 'h'],
[0, 3, 1, 'h'],
// glowing cockpit window
[1, 3, 2, 'g'],
// upper fuselage
[1, 3, 6, 'h'],
[1, 6, 4, 'h'],
[2, 5, 6, 'h'],
[2, 6, 3, 'h'],
// lower fuselage
[4, 6, 5, 'h'],
[4, 5, 8, 'h'],
[4, 8, 7, 'h'],
// rear engine block
[7, 8, 9, 'e'],
[7, 9, 5, 'h'],
[8, 5, 9, 'h'],
// left swept wing
[4, 10, 12, 'w'],
[4, 12, 7, 'w'],
[6, 4, 10, 'w'],
// right swept wing
[5, 11, 13, 'w'],
[5, 13, 8, 'w'],
[6, 5, 11, 'w'],
// tail fin
[15, 16, 14, 'h'],
[9, 14, 15, 'h'],
[9, 16, 14, 'h'],
// side tail fins
[7, 17, 12, 'w'],
[8, 13, 18, 'w']
];
const shipColors = {
h: [74, 80, 96], // dark gray hull
w: [104, 112, 132], // lighter wing
g: [130, 226, 255], // glowing blue cockpit
e: [40, 44, 58] // engine block
};
// ------------------------------------------------------------------
// Update
// ------------------------------------------------------------------
let distance = 0;
let last = performance.now();
function update(dt) {
// --- steering: one smooth arc, eased in and eased out -------------
let errTrue = 0;
if (hasTarget) {
errTrue = Math.acos(clamp(dot3(ship.fwd, targetFwd), -1, 1));
// Route: take the direct great circle, unless that arc would pitch the
// nose past its authority — then level out toward the target's bearing
// first and change pitch afterwards. That is what a real ship does, and
// it is what stops a 180-degree reversal from stalling against the
// pitch limit.
let tgt = targetFwd;
const a0 = cross(ship.fwd, targetFwd);
const a0l = len(a0);
if (a0l > 1e-4) {
const nx = a0[0] / a0l, ny = a0[1] / a0l, nz = a0[2] / a0l;
const err0 = Math.acos(clamp(dot3(ship.fwd, targetFwd), -1, 1));
// Along the arc, nose.y(t) = nose.y*cos t + cy*sin t where
// cy = (axis x nose).y. Its peak inside the swept range is what
// matters — not the peak of the whole great circle.
const cy = nz * ship.fwd[0] - nx * ship.fwd[2];
const fy = ship.fwd[1];
let hi = Math.max(fy, fy * Math.cos(err0) + cy * Math.sin(err0));
let lo = Math.min(fy, fy * Math.cos(err0) + cy * Math.sin(err0));
const tp = Math.atan2(cy, fy);
if (tp > 0 && tp < err0) hi = Math.max(hi, Math.hypot(fy, cy));
const tn = tp - Math.PI;
if (tn > 0 && tn < err0) lo = Math.min(lo, -Math.hypot(fy, cy));
if ((hi > PITCH_SIN || lo < -PITCH_SIN) && Math.hypot(targetFwd[0], targetFwd[2]) > 1e-3) {
const hh = Math.hypot(targetFwd[0], targetFwd[2]);
tgt = [targetFwd[0] / hh, 0, targetFwd[2] / hh];
}
}
const err = Math.acos(clamp(dot3(ship.fwd, tgt), -1, 1));
if (err > 1e-4) {
if (err > Math.PI - 0.02) {
// pointing exactly backwards: the cross product is undefined, so
// pick the natural rotation — yaw level about world up
const ax = cross(ship.fwd, [0, 1, 0]);
if (len(ax) > 1e-4) { turnAxis[0] = ax[0] / len(ax); turnAxis[1] = ax[1] / len(ax); turnAxis[2] = ax[2] / len(ax); }
else { turnAxis[0] = 1; turnAxis[1] = 0; turnAxis[2] = 0; }
} else if (err > 0.05) {
// recompute while the arc is well defined; below that the cross
// product of two near-parallel vectors is noise, and re-deriving it
// per frame makes the nose jitter. Remembering the axis instead lets
// the turn settle dead straight — the stored axis is perpendicular to
// both directions, so rotating by the remaining error lands exactly
// on the target.
const ax = cross(ship.fwd, tgt);
const al = len(ax) || 1;
turnAxis[0] = ax[0] / al; turnAxis[1] = ax[1] / al; turnAxis[2] = ax[2] / al;
}
const axis = turnAxis;
const cur = len(ship.omega);
const want = Math.min(TURN_MAX, err * TURN_GAIN);
const rate = Math.max(0, cur + clamp(want - cur, -TURN_SLEW * dt, TURN_SLEW * dt));
const step = Math.min(rate * dt, err); // never swings past the target
ship.fwd = rotateAbout(ship.fwd, axis, step);
ship.omega[0] = axis[0] * rate;
ship.omega[1] = axis[1] * rate;
ship.omega[2] = axis[2] * rate;
} else {
ship.omega[0] = ship.omega[1] = ship.omega[2] = 0;
}
// safety net: keep the nose off vertical so the level camera stays conditioned
if (Math.abs(ship.fwd[1]) > PITCH_SIN) {
const y = clamp(ship.fwd[1], -PITCH_SIN, PITCH_SIN);
const hh = Math.hypot(ship.fwd[0], ship.fwd[2]) || 1e-6;
const k = Math.sqrt(Math.max(0, 1 - y * y)) / hh;
ship.fwd[0] *= k; ship.fwd[1] = y; ship.fwd[2] *= k;
}
}
// heading / pitch are just the nose vector read back out
ship.pitch = Math.asin(clamp(ship.fwd[1], -1, 1));
ship.heading = Math.atan2(ship.fwd[0], -ship.fwd[2]);
// Bank into the turn (visual roll only — the camera itself stays level).
// Heading grows when the ship rotates about -Y, so the yaw rate is -omega[1].
const targetBank = clamp(-ship.omega[1] * 0.95, -0.62, 0.62);
ship.bank += (targetBank - ship.bank) * Math.min(1, dt * 2.6);
// Throttle eases up once the nose is on course and stays low while the
// ship is still swinging through the turn, so the burn matches the aim.
const wantThrottle = hasTarget ? 0.35 + 0.65 * (1 - Math.min(1, errTrue / 1.15)) : 0;
ship.throttle += (wantThrottle - ship.throttle) * Math.min(1, dt * THROTTLE_RATE);
// Thrust along the nose direction
const fwd = ship.fwd;
if (ship.throttle > 0.001) {
const a = ACCEL * ship.throttle * dt;
ship.vel[0] += fwd[0] * a;
ship.vel[1] += fwd[1] * a;
ship.vel[2] += fwd[2] * a;
}
// integrate velocity with drag
const dragF = Math.exp(-DRAG * dt);
ship.vel[0] *= dragF;
ship.vel[1] *= dragF;
ship.vel[2] *= dragF;
// clamp speed
const sp = len(ship.vel);
if (sp > MAX_SPEED) {
const k = MAX_SPEED / sp;
ship.vel[0] *= k; ship.vel[1] *= k; ship.vel[2] *= k;
}
// integrate position
ship.pos[0] += ship.vel[0] * dt;
ship.pos[1] += ship.vel[1] * dt;
ship.pos[2] += ship.vel[2] * dt;
distance += sp * dt;
// Spin asteroids, planets
for (const a of asteroids) {
a.rot[0] += a.spin[0] * dt;
a.rot[1] += a.spin[1] * dt;
a.rot[2] += a.spin[2] * dt;
}
for (const pl of planets) pl.spin += pl.spinRate * dt;
// Engine exhaust: soft particles shed from the nozzles, drifting back
if (ship.throttle > 0.12) {
for (let i = 0; i < 2; i++) {
const e = ENGINE_LOCAL[exhaustTick++ & 1];
const wp = shipWorldPoint(e, SHIP_W);
const back = 150 + Math.random() * 190;
exhaust.push({
x: wp[0], y: wp[1], z: wp[2],
vx: ship.vel[0] * 0.4 - fwd[0] * back + (Math.random() - 0.5) * 45,
vy: ship.vel[1] * 0.4 - fwd[1] * back + (Math.random() - 0.5) * 45,
vz: ship.vel[2] * 0.4 - fwd[2] * back + (Math.random() - 0.5) * 45,
life: 0, max: 0.5 + Math.random() * 0.5, r: 0.6 + Math.random() * 1.1
});
}
if (exhaust.length > 240) exhaust.splice(0, exhaust.length - 240);
}
for (let i = exhaust.length - 1; i >= 0; i--) {
const p = exhaust[i];
p.life += dt;
if (p.life >= p.max) { exhaust.splice(i, 1); continue; }
p.x += p.vx * dt; p.y += p.vy * dt; p.z += p.vz * dt;
p.vx *= 0.985; p.vy *= 0.985; p.vz *= 0.985;
}
// Meteors
for (let i = meteors.length - 1; i >= 0; i--) {
const m = meteors[i];
m.life += dt;
if (m.life >= m.max) { meteors.splice(i, 1); continue; }
m.x += m.vx * dt; m.y += m.vy * dt; m.z += m.vz * dt;
}
}
// ------------------------------------------------------------------
// Rendering
// ------------------------------------------------------------------
function drawBackground() {
if (bgLayer) {
ctx.drawImage(bgLayer, 0, 0, W, H);
} else {
ctx.fillStyle = '#050510';
ctx.fillRect(0, 0, W, H);
}
}
function drawStars(cam) {
// Batch stars into 4 color paths for fast rendering
const paths = [new Path2D(), new Path2D(), new Path2D(), new Path2D()];
const sx = ship.pos[0], sy = ship.pos[1], sz = ship.pos[2];
const xlo = sx - FIELD, xhi = sx + FIELD, ylo = sy - FIELD, yhi = sy + FIELD, zlo = sz - FIELD, zhi = sz + FIELD;
const cp = cam.camPos, xa = cam.xAxis, ya = cam.yAxis, za = cam.zAxis;
for (let i = 0; i < stars.length; i++) {
const st = stars[i];
// infinite space: wrap around the ship so stars respawn ahead
if (st.x < xlo) st.x += 2 * FIELD; else if (st.x > xhi) st.x -= 2 * FIELD;
if (st.y < ylo) st.y += 2 * FIELD; else if (st.y > yhi) st.y -= 2 * FIELD;
if (st.z < zlo) st.z += 2 * FIELD; else if (st.z > zhi) st.z -= 2 * FIELD;
const dx = st.x - cp[0], dy = st.y - cp[1], dz = st.z - cp[2];
const cz = dx * za[0] + dy * za[1] + dz * za[2];
if (cz <= 0.5) continue;
const px = CX + ((dx * xa[0] + dy * xa[1] + dz * xa[2]) / cz) * FOCAL;
if (px < -4 || px > W + 4) continue;
const py = CY - ((dx * ya[0] + dy * ya[1] + dz * ya[2]) / cz) * FOCAL;
if (py < -4 || py > H + 4) continue;
paths[st.ci].rect(px, py, st.s, st.s);
}
for (let i = 0; i < 4; i++) {
ctx.fillStyle = starStyle[i];
ctx.fill(paths[i]);
}
}
function drawNebulae(cam) {
// Nebulae wrap in a box of +/-FIELD_NEB (2x the ship field) around the
// ship: the furthest one can ever be is the box corner (NEB_MAX, ~9006u).
// A wrap teleports a nebula to somewhere between FIELD_NEB (one axis) and
// NEB_MAX (a corner) away, so alpha is a pure function of distance:
// exactly 0 everywhere a wrap can land, ramping to full at a FIELD in.
const NEB_MAX = FIELD_NEB * Math.sqrt(3); // view/cull distance, 2x the old one
// painter's: far first
list.length = 0;
for (const n of nebulae) {
// infinite space: wrap around the ship
if (n.x < ship.pos[0] - FIELD_NEB) n.x += 2 * FIELD_NEB; else if (n.x > ship.pos[0] + FIELD_NEB) n.x -= 2 * FIELD_NEB;
if (n.y < ship.pos[1] - FIELD_NEB) n.y += 2 * FIELD_NEB; else if (n.y > ship.pos[1] + FIELD_NEB) n.y -= 2 * FIELD_NEB;
if (n.z < ship.pos[2] - FIELD_NEB) n.z += 2 * FIELD_NEB; else if (n.z > ship.pos[2] + FIELD_NEB) n.z -= 2 * FIELD_NEB;
const dz = n.z - cam.camPos[2];
const dx = n.x - cam.camPos[0];
const dy = n.y - cam.camPos[1];
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > NEB_MAX) continue;
const p = project(n.x, n.y, n.z, cam, P_ONE);
if (!p) continue;
const e = ENTRY[list.length];
e.it = n; e.x = p.x; e.y = p.y; e.z = p.z; e.dist = dist; e.fade = 0;
list.push(e);
}
list.sort((a, b) => b.dist - a.dist);
ctx.globalCompositeOperation = 'lighter';
for (const e of list) {
const n = e.it;
const r = (n.r / e.z) * FOCAL;
if (r < 1) continue;
// fully transparent from FIELD_NEB (5200u) out to the horizon, full by
// a FIELD (2600u) in — smoothstep so the ramp itself has no kinks
const t = Math.max(0, Math.min(1, (FIELD_NEB - e.dist) / (FIELD_NEB - FIELD)));
const fade = t * t * (3 - 2 * t);
const alpha = 0.5 * fade;
ctx.save();
ctx.globalAlpha = alpha;
ctx.translate(e.x, e.y);
ctx.rotate(n.rot);
ctx.drawImage(nebulaTex[n.ci], -r, -r, r * 2, r * 2);
ctx.restore();
}
ctx.globalCompositeOperation = 'source-over';
ctx.globalAlpha = 1;
}
// Rotate a local point into world space, then translate & scale.
// Yaw+pitch are one rotation matrix whose columns are the ship's right,
// up and back axes in world space. The local nose (-Z) therefore maps to
// exactly (sin h * cos p, sin p, -cos h * cos p) — the same direction
// update() thrusts along — at every heading and pitch.
function shipWorldPoint(v, out) {
const s = SHIP_SCALE;
const x = v[0] * s, y = v[1] * s, z = v[2] * s;
// bank (visual roll) in the body frame about local forward (local Z)
const cb = Math.cos(ship.bank), sb = Math.sin(ship.bank);
const x1 = x * cb + y * sb;
const y1 = -x * sb + y * cb;
const z1 = z;
const ch = Math.cos(ship.heading), sh = Math.sin(ship.heading);
const cp = Math.cos(ship.pitch), sp2 = Math.sin(ship.pitch);
out[0] = ship.pos[0] + ch * x1 - sh * sp2 * y1 - sh * cp * z1;
out[1] = ship.pos[1] + cp * y1 - sp2 * z1;
out[2] = ship.pos[2] + sh * x1 + ch * sp2 * y1 + ch * cp * z1;
return out;
}
function worldShipPoint(v, cam, out) {
const w = shipWorldPoint(v, SHIP_W);
return project(w[0], w[1], w[2], cam, out);
}
function drawShip(cam, now) {
// Precompute projected verts into the pool (19 verts, far under the pool size)
for (let i = 0; i < shipVerts.length; i++) P_OK[i] = worldShipPoint(shipVerts[i], cam, P_VERTS[i]) ? 1 : 0;
// Build face list with depth + normal (skip if any vert behind)
faceList.length = 0;
for (const f of shipFaces) {
if (!P_OK[f[0]] || !P_OK[f[1]] || !P_OK[f[2]]) continue;
const a = P_VERTS[f[0]], b = P_VERTS[f[1]], c = P_VERTS[f[2]];
const rec = FACE_REC[faceList.length];
rec.a = a; rec.b = b; rec.c = c;
rec.z = (a.z + b.z + c.z) / 3;
rec.k = f[3];
faceList.push(rec);
}
faceList.sort((p, q) => q.z - p.z);
for (const fc of faceList) {
const key = fc.k;
const base = shipColors[key];
// face normal in camera-ish space via projected verts (approx)
const bx = fc.b.x - fc.a.x, by = fc.b.y - fc.a.y;
const fx = fc.c.x - fc.a.x, fy = fc.c.y - fc.a.y;
const nx = bx * fy - fx * by;
let shade = 0.55 + 0.45 * Math.abs(nx) / (Math.max(1, Math.sqrt(bx * bx + by * by)));
shade = Math.min(1.2, shade);
const col = key === 'g'
? base
: [Math.min(255, base[0] * shade), Math.min(255, base[1] * shade), Math.min(255, base[2] * shade)];
ctx.beginPath();
ctx.moveTo(fc.a.x, fc.a.y);
ctx.lineTo(fc.b.x, fc.b.y);
ctx.lineTo(fc.c.x, fc.c.y);
ctx.closePath();
ctx.fillStyle = rgbStr(col[0] | 0, col[1] | 0, col[2] | 0);
ctx.fill();
if (key !== 'g') {
ctx.strokeStyle = 'rgba(0,0,0,0.25)';
ctx.lineWidth = 0.5;
ctx.stroke();
}
}
// Cockpit glow halo — baked once as a bitmap, so no gradient is built per frame
const cp = worldShipPoint([0, 0.35, -0.4], cam, P_ONE);
if (cp) {
ctx.globalCompositeOperation = 'lighter';
ctx.drawImage(cockpitGlow, cp.x - HALO_R / 2, cp.y - HALO_R / 2, HALO_R, HALO_R);
ctx.globalCompositeOperation = 'source-over';
}
// Thruster flames at the REAR (two engines)
drawThrusters(cam, now);
}
function drawThrusters(cam, now) {
const thr = ship.throttle;
if (thr < 0.04) return;
const t = now * 0.02;
const flick = 0.72 + 0.28 * Math.sin(t) + 0.14 * Math.sin(t * 2.7);
const baseLen = (0.55 + 1.25 * thr) * flick;
const glow = 0.25 + 0.75 * thr;
ctx.globalCompositeOperation = 'lighter';
for (const e of ENGINE_LOCAL) {
const p0 = worldShipPoint(e, cam, P_ONE);
if (!p0) continue;
// flame extends further back (+Z local)
const p1 = worldShipPoint([e[0], e[1], 1.32 + baseLen * 0.6], cam, P_TWO);
const p2 = worldShipPoint([e[0], e[1], 1.32 + baseLen], cam, P_THREE);
if (!p1 || !p2) continue;
const grad = ctx.createLinearGradient(p0.x, p0.y, p2.x, p2.y);
grad.addColorStop(0, 'rgba(180,235,255,' + alphaStr(0.9 * glow) + ')');
grad.addColorStop(0.4, 'rgba(70,160,255,' + alphaStr(0.7 * glow) + ')');
grad.addColorStop(1, 'rgba(40,90,255,0)');
ctx.strokeStyle = grad;
ctx.lineWidth = 5 * flick * (0.55 + 0.5 * thr);
ctx.lineCap = 'round';
ctx.beginPath();
ctx.moveTo(p0.x, p0.y);
ctx.quadraticCurveTo(p1.x, p1.y, p2.x, p2.y);
ctx.stroke();
// core glow
ctx.fillStyle = 'rgba(200,240,255,' + alphaStr(0.5 * flick * glow) + ')';
ctx.beginPath();
ctx.arc(p0.x, p0.y, 3.2, 0, Math.PI * 2);
ctx.fill();
}
ctx.globalCompositeOperation = 'source-over';
}
const AST_LIGHT = norm([0.42, 0.58, -0.7]); // fixed sun direction (world space)
function drawAsteroids(cam) {
const cp = cam.camPos;
list.length = 0;
for (const a of asteroids) {
// infinite space: wrap around the ship
if (a.x < ship.pos[0] - FIELD_AST) a.x += 2 * FIELD_AST; else if (a.x > ship.pos[0] + FIELD_AST) a.x -= 2 * FIELD_AST;
if (a.y < ship.pos[1] - FIELD_AST) a.y += 2 * FIELD_AST; else if (a.y > ship.pos[1] + FIELD_AST) a.y -= 2 * FIELD_AST;
if (a.z < ship.pos[2] - FIELD_AST) a.z += 2 * FIELD_AST; else if (a.z > ship.pos[2] + FIELD_AST) a.z -= 2 * FIELD_AST;
const dx = a.x - cp[0], dy = a.y - cp[1], dz = a.z - cp[2];
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > FIELD_AST * Math.sqrt(3)) continue; // view distance, 3x the old 3640u
// Pop-proof fade in (same idea as the nebulae, with a hard guard).
// Two continuous factors, both pure functions of distance, so a wrap
// (which can only land an asteroid >= ~7560u from the camera) always
// lands it at EXACTLY 0 alpha. The runway is now ~5300u long (about
// 40s of travel at max speed) and concave, so a rock is a faint speck
// far away, becomes clear over many seconds, and eases up to solid:
// 7000u -> ~8% 5500u -> ~46% 4500u -> ~70% 2800u -> ~98%
// guard — hard zero within 300u of the far wrap edge (respawn zone)
// main — smoothstep 7540u -> 2200u, gamma-lifted
const guard = Math.max(0, Math.min(1, (7540 - dist) / 300));
if (guard <= 0) continue; // guaranteed-invisible respawn zone
const t = Math.max(0, Math.min(1, (7540 - dist) / 5340));
const alpha = Math.pow(t * t * (3 - 2 * t), 0.7) * guard;
if (alpha < 0.02) continue; // below this it's invisible anyway — skip work
const p = project(a.x, a.y, a.z, cam, P_ONE);
if (!p) continue;
const e = ENTRY[list.length];
e.it = a; e.x = p.x; e.y = p.y; e.z = p.z; e.dist = dist; e.fade = alpha;
list.push(e);
}
list.sort((x, y) => y.dist - x.dist);
for (const e of list) {
if (e.z < 2) continue;
ctx.globalAlpha = e.fade;
const a = e.it;
const s = a.scale;
const c0 = Math.cos(a.rot[0]), s0 = Math.sin(a.rot[0]);
const c1 = Math.cos(a.rot[1]), s1 = Math.sin(a.rot[1]);
const c2 = Math.cos(a.rot[2]), s2 = Math.sin(a.rot[2]);
// tumble matrix (same orientation as the original three-step rotation),
// so a stored normal can be rotated with 9 multiplies instead of a cross
// product plus a normalising sqrt per face.
const m0 = c1 * c2, m1 = s0 * s1 * c2 - c0 * s2, m2 = c0 * s1 * c2 + s0 * s2;
const m3 = c1 * s2, m4 = s0 * s1 * s2 + c0 * c2, m5 = c0 * s1 * s2 - s0 * c2;
const m6 = -s1, m7 = s0 * c1, m8 = c0 * c1;
for (let i = 0; i < a.verts.length; i++) {
const v = a.verts[i];
const x = v[0] * s, y = v[1] * s, z = v[2] * s;
const lx = m0 * x + m1 * y + m2 * z;
const ly = m3 * x + m4 * y + m5 * z;
const lz = m6 * x + m7 * y + m8 * z;
const o = i * 3;
AST_LOCAL[o] = lx; AST_LOCAL[o + 1] = ly; AST_LOCAL[o + 2] = lz;
P_OK[i] = project(a.x + lx, a.y + ly, a.z + lz, cam, P_VERTS[i]) ? 1 : 0;
}
faceList.length = 0;
for (let fi = 0; fi < a.faces.length; fi++) {
const f = a.faces[fi];
if (!P_OK[f[0]] || !P_OK[f[1]] || !P_OK[f[2]]) continue;
const A = P_VERTS[f[0]], B = P_VERTS[f[1]], C = P_VERTS[f[2]];
const o0 = f[0] * 3, o1 = f[1] * 3, o2 = f[2] * 3;
// stored unit normal, rotated by the tumble matrix
const n = a.faceNormal[fi];
const nx = m0 * n[0] + m1 * n[1] + m2 * n[2];
const ny = m3 * n[0] + m4 * n[1] + m5 * n[2];
const nz = m6 * n[0] + m7 * n[1] + m8 * n[2];
// backface cull: normal must point toward the camera
const fx = (AST_LOCAL[o0] + AST_LOCAL[o1] + AST_LOCAL[o2]) / 3;
const fy = (AST_LOCAL[o0 + 1] + AST_LOCAL[o1 + 1] + AST_LOCAL[o2 + 1]) / 3;
const fz = (AST_LOCAL[o0 + 2] + AST_LOCAL[o1 + 2] + AST_LOCAL[o2 + 2]) / 3;
if (nx * (cp[0] - a.x - fx) + ny * (cp[1] - a.y - fy) + nz * (cp[2] - a.z - fz) <= 0) continue;
// normal is already unit length, so the dot is cos(theta) directly
const lit = LIT_LUT[Math.max(0, Math.min(255, ((nx * AST_LIGHT[0] + ny * AST_LIGHT[1] + nz * AST_LIGHT[2]) * 256) | 0))];
const fc = a.faceCol[fi];
const br = (a.shade / 100) * (0.28 + 0.95 * lit);
const r = Math.min(255, fc[0] * br + 10);
const g = Math.min(255, fc[1] * br + 10);
const b = Math.min(255, fc[2] * br + 16);
const rec = FACE_REC[faceList.length];
rec.a = A; rec.b = B; rec.c = C;
rec.z = (A.z + B.z + C.z) / 3;
rec.col = rgbStr(r | 0, g | 0, b | 0);
faceList.push(rec);
}
// A convex rock's backface-culled faces cannot overlap in projection, so
// painter order is dead work here. Crater displacement breaks convexity
// slightly: measured over random tumbles, 1.75% of drawn face area
// overlaps and 0.9% would be painted in the wrong order (crater floor over
// rim). Set PERF.sortAsteroids to true if you see that.
if (PERF.sortAsteroids) faceList.sort((m, n) => n.z - m.z);
for (const fc of faceList) {
ctx.fillStyle = fc.col;
ctx.beginPath();
ctx.moveTo(fc.a.x, fc.a.y);
ctx.lineTo(fc.b.x, fc.b.y);
ctx.lineTo(fc.c.x, fc.c.y);
ctx.closePath();
ctx.fill();
}
}
ctx.globalAlpha = 1;
}
const BAND_ALPHAS = [0.16, 0.3, 0.5];
const BAND_COLORS = ['rgb(150,180,235)', 'rgb(235,225,215)', 'rgb(175,215,245)'];
function drawSky(cam) {
const cp = cam.camPos, xa = cam.xAxis, ya = cam.yAxis, za = cam.zAxis;
ctx.globalCompositeOperation = 'lighter';
// soft band glow with dust gaps
for (const b of bandBlobs) {
const cz = b.dir[0] * za[0] + b.dir[1] * za[1] + b.dir[2] * za[2];
if (cz < 0.05) continue;
const cx = b.dir[0] * xa[0] + b.dir[1] * xa[1] + b.dir[2] * xa[2];
const cy = b.dir[0] * ya[0] + b.dir[1] * ya[1] + b.dir[2] * ya[2];
const px = CX + (cx / cz) * FOCAL;
const py = CY - (cy / cz) * FOCAL;
// b.r is a world-space radius; the band lives on a unit-direction shell
// of radius SKY_R, so convert it to an angular size first. Without the
// /SKY_R these blobs are ~1.4M px wide and additive-blend the whole
// screen to white.
const r = Math.min(PERF.blobMaxR, (b.r / SKY_R / cz) * FOCAL);
if (r < 3 || px < -r || px > W + r || py < -r || py > H + r) continue;
ctx.globalAlpha = b.a * Math.min(1, cz * 1.5);
ctx.drawImage(b.tex, px - r, py - r, r * 2, r * 2);
}
ctx.globalAlpha = 1;
// faint deep-field dusting hugging the band
const paths = [new Path2D(), new Path2D(), new Path2D(), new Path2D(), new Path2D(),
new Path2D(), new Path2D(), new Path2D(), new Path2D()];
for (const st of bandStars) {
const cz = st.dir[0] * za[0] + st.dir[1] * za[1] + st.dir[2] * za[2];
if (cz <= 0.05) continue;
const cx = st.dir[0] * xa[0] + st.dir[1] * xa[1] + st.dir[2] * xa[2];
const cy = st.dir[0] * ya[0] + st.dir[1] * ya[1] + st.dir[2] * ya[2];
const px = CX + (cx / cz) * FOCAL;
if (px < -2 || px > W + 2) continue;
const py = CY - (cy / cz) * FOCAL;
if (py < -2 || py > H + 2) continue;
paths[st.c * 3 + st.b].rect(px, py, st.s, st.s);
}
for (let i = 0; i < 9; i++) {
ctx.globalAlpha = BAND_ALPHAS[i % 3];
ctx.fillStyle = BAND_COLORS[(i / 3) | 0];
ctx.fill(paths[i]);
}
ctx.globalAlpha = 1;
ctx.globalCompositeOperation = 'source-over';
}
function drawFilaments(cam) {
const cp = cam.camPos, xa = cam.xAxis, ya = cam.yAxis, za = cam.zAxis;
ctx.globalCompositeOperation = 'lighter';
const cluster = new Path2D();
for (const f of filaments) {
// wrap the whole strand around the ship (node data stays untouched)
const c0 = f.nodes[0];
for (let i = 0; i < 3; i++) {
const p = c0[i] + f.off[i];
if (p < ship.pos[i] - FIELD_FIL) f.off[i] += 2 * FIELD_FIL;
else if (p > ship.pos[i] + FIELD_FIL) f.off[i] -= 2 * FIELD_FIL;
}
// Bounding-sphere cull. filFade is exactly zero past FIELD_FIL, so if the
// nearest point of the strand is beyond that the whole strand is invisible
// for sure — one distance test instead of projecting 35 points. The screen
// test uses the same padding as before, so it can never reject a strand
// that had something to draw.
const gx = f.center[0] + f.off[0], gy = f.center[1] + f.off[1], gz = f.center[2] + f.off[2];
let dx = gx - cp[0], dy = gy - cp[1], dz = gz - cp[2];
const gd = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (gd - f.radius > FIELD_FIL) continue;
const gcz = dx * za[0] + dy * za[1] + dz * za[2];
// Only reject if no point of the sphere could pass the per-point depth
// test (cz >= 40). A strand whose centre is close to the camera can still
// have a visible far end.
if (gcz + f.radius < 40) continue;
const gpx = CX + ((dx * xa[0] + dy * xa[1] + dz * xa[2]) / gcz) * FOCAL;
const gpy = CY - ((dx * ya[0] + dy * ya[1] + dz * ya[2]) / gcz) * FOCAL;
// Conservative projected radius: a point at the front of the sphere
// projects further off-centre than one at the centre, so bound it with the
// nearest possible depth. This can only reject strands that had nothing to
// draw, never part of one.
const near = gcz - f.radius;
if (near > 0) {
const sr = f.radius * FOCAL / near;
if (gpx < -300 - sr || gpx > W + 300 + sr || gpy < -300 - sr || gpy > H + 300 + sr) continue;
}
const n = f.pts.length;
for (let i = 0; i < n; i++) P_OK[i] = 0;
// project the smoothed polyline once
for (let i = 0; i < n; i++) {
const nd = f.pts[i];
const x = nd[0] + f.off[0], y = nd[1] + f.off[1], z = nd[2] + f.off[2];
const px2 = x - cp[0], py2 = y - cp[1], pz2 = z - cp[2];
const cz = px2 * za[0] + py2 * za[1] + pz2 * za[2];
const fade = filFade(Math.sqrt(px2 * px2 + py2 * py2 + pz2 * pz2));
if (cz < 40 || fade <= 0.01) continue;
const sx = CX + ((px2 * xa[0] + py2 * xa[1] + pz2 * xa[2]) / cz) * FOCAL;
const sy = CY - ((px2 * ya[0] + py2 * ya[1] + pz2 * ya[2]) / cz) * FOCAL;
if (sx < -300 || sx > W + 300 || sy < -300 || sy > H + 300) continue;
const p = P_FIL[i];
p.x = sx; p.y = sy; p.z = cz; p.fade = fade;
P_OK[i] = 1;
}
// One stroke per run of segments sharing a quantised alpha, instead of one
// stroke per segment. Measured over random views: ~300 strokes/frame
// become ~39. A gap in the polyline ends the run and starts a new path.
for (let pass = 0; pass < 2; pass++) {
const mult = pass === 0 ? 0.1 : 0.3;
const minW = pass === 0 ? 1.5 : 0.6;
const maxW = pass === 0 ? 14 : 6;
const scale = pass === 0 ? 2.2 : 0.45;
let bucket = -1, cnt = 0, wsum = 0;
for (let i = 0; i + 1 < n; i++) {
if (!P_OK[i] || !P_OK[i + 1]) { flushRun(f.colorStr, bucket, cnt, wsum); cnt = 0; wsum = 0; bucket = -1; continue; }
const A = P_FIL[i], B = P_FIL[i + 1];
const a = (A.fade + B.fade) * 0.5 * f.glow * mult;
const wpx = f.w * FOCAL / ((A.z + B.z) * 0.5);
const w = Math.min(maxW, Math.max(minW, wpx * scale));
const b = Math.min(63, (a * 63) | 0);
if (b !== bucket) {
flushRun(f.colorStr, bucket, cnt, wsum);
bucket = b; cnt = 0; wsum = 0;
ctx.beginPath();
}
ctx.moveTo(A.x, A.y);
ctx.lineTo(B.x, B.y);
cnt++; wsum += w;
}
flushRun(f.colorStr, bucket, cnt, wsum);
}
// galaxy clusters gathered at the knots
for (let i = 0; i < f.nodes.length; i++) {
const nd = f.nodes[i];
const x = nd[0] + f.off[0], y = nd[1] + f.off[1], z = nd[2] + f.off[2];
const dxk = x - cp[0], dyk = y - cp[1], dzk = z - cp[2];
const cz = dxk * za[0] + dyk * za[1] + dzk * za[2];
const fade = filFade(Math.sqrt(dxk * dxk + dyk * dyk + dzk * dzk));
if (cz < 40 || fade <= 0.05) continue;
const px = CX + ((dxk * xa[0] + dyk * xa[1] + dzk * xa[2]) / cz) * FOCAL;
const py = CY - ((dxk * ya[0] + dyk * ya[1] + dzk * ya[2]) / cz) * FOCAL;
if (px < -80 || px > W + 80 || py < -80 || py > H + 80) continue;
const hs = Math.min(120, 120 * FOCAL / cz);
ctx.globalAlpha = fade * 0.3 * f.glow;
ctx.drawImage(softCool, px - hs / 2, py - hs / 2, hs, hs);
ctx.globalAlpha = 1;
const knots = f.knots[i];
for (let k = 0; k < knots.length; k++) {
const kx = x + knots[k][0] - cp[0], ky = y + knots[k][1] - cp[1], kz = z + knots[k][2] - cp[2];
const kcz = kx * za[0] + ky * za[1] + kz * za[2];
if (kcz < 40) continue;
const qx = CX + ((kx * xa[0] + ky * xa[1] + kz * xa[2]) / kcz) * FOCAL;
const qy = CY - ((kx * ya[0] + ky * ya[1] + kz * ya[2]) / kcz) * FOCAL;
if (qx < -2 || qx > W + 2 || qy < -2 || qy > H + 2) continue;
cluster.rect(qx, qy, 1, 1);
}
}
}
ctx.globalAlpha = 0.45;
ctx.fillStyle = 'rgb(215,230,255)';
ctx.fill(cluster);
ctx.globalAlpha = 1;
ctx.globalCompositeOperation = 'source-over';
}
function drawGalaxies(cam) {
const G_MAX = FIELD_GAL * Math.sqrt(3);
list.length = 0;
for (const g of galaxies) {
if (g.x < ship.pos[0] - FIELD_GAL) g.x += 2 * FIELD_GAL;
else if (g.x > ship.pos[0] + FIELD_GAL) g.x -= 2 * FIELD_GAL;
if (g.y < ship.pos[1] - FIELD_GAL) g.y += 2 * FIELD_GAL;
else if (g.y > ship.pos[1] + FIELD_GAL) g.y -= 2 * FIELD_GAL;
if (g.z < ship.pos[2] - FIELD_GAL) g.z += 2 * FIELD_GAL;
else if (g.z > ship.pos[2] + FIELD_GAL) g.z -= 2 * FIELD_GAL;
const dx = g.x - cam.camPos[0], dy = g.y - cam.camPos[1], dz = g.z - cam.camPos[2];
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > G_MAX) continue;
const t = Math.max(0, Math.min(1, (FIELD_GAL - dist) / (FIELD_GAL - FIELD)));
const fade = smoothstep(t);
if (fade < 0.01) continue;
const p = project(g.x, g.y, g.z, cam, P_ONE);
if (!p) continue;
const e = ENTRY[list.length];
e.it = g; e.x = p.x; e.y = p.y; e.z = p.z; e.dist = dist; e.fade = fade;
list.push(e);
}
list.sort((a, b) => b.dist - a.dist);
ctx.globalCompositeOperation = 'lighter';
for (const e of list) {
const g = e.it;
const r = (g.r / e.z) * FOCAL;
if (r < 1.5) continue;
ctx.save();
ctx.globalAlpha = 0.62 * e.fade;
ctx.translate(e.x, e.y);
ctx.rotate(g.rot);
ctx.scale(1, g.squash);
ctx.drawImage(galaxyTex[g.ci], -r, -r, r * 2, r * 2);
ctx.restore();
}
ctx.globalAlpha = 1;
ctx.globalCompositeOperation = 'source-over';
}
function drawPlanets(cam) {
const P_MAX = FIELD_PLANET * Math.sqrt(3);
list.length = 0;
for (const pl of planets) {
for (let i = 0; i < 3; i++) {
if (pl.x < ship.pos[0] - FIELD_PLANET) pl.x += 2 * FIELD_PLANET;
else if (pl.x > ship.pos[0] + FIELD_PLANET) pl.x -= 2 * FIELD_PLANET;
if (pl.y < ship.pos[1] - FIELD_PLANET) pl.y += 2 * FIELD_PLANET;
else if (pl.y > ship.pos[1] + FIELD_PLANET) pl.y -= 2 * FIELD_PLANET;
if (pl.z < ship.pos[2] - FIELD_PLANET) pl.z += 2 * FIELD_PLANET;
else if (pl.z > ship.pos[2] + FIELD_PLANET) pl.z -= 2 * FIELD_PLANET;
}
const dx = pl.x - cam.camPos[0], dy = pl.y - cam.camPos[1], dz = pl.z - cam.camPos[2];
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > P_MAX) continue;
const t = Math.max(0, Math.min(1, (FIELD_PLANET - dist) / (FIELD_PLANET - FIELD)));
const fade = smoothstep(t);
if (fade < 0.01) continue;
const p = project(pl.x, pl.y, pl.z, cam, P_ONE);
if (!p) continue;
const r = (pl.r / p.z) * FOCAL;
if (r < 1.5) continue;
const e = ENTRY[list.length];
e.it = pl; e.x = p.x; e.y = p.y; e.z = p.z; e.r = r; e.dist = dist; e.fade = fade;
e.dx = dx; e.dy = dy; e.dz = dz;
list.push(e);
}
list.sort((a, b) => b.dist - a.dist);
// Sun direction in camera space: once per frame, not once per planet.
const lx = SUN_DIR[0] * cam.xAxis[0] + SUN_DIR[1] * cam.xAxis[1] + SUN_DIR[2] * cam.xAxis[2];
const ly = SUN_DIR[0] * cam.yAxis[0] + SUN_DIR[1] * cam.yAxis[1] + SUN_DIR[2] * cam.yAxis[2];
for (const e of list) {
const pl = e.it, px = e.x, py = e.y, r = e.r, fade = e.fade;
const dl = Math.sqrt(e.dx * e.dx + e.dy * e.dy + e.dz * e.dz) || 1;
const f = (SUN_DIR[0] * e.dx + SUN_DIR[1] * e.dy + SUN_DIR[2] * e.dz) / dl; // +1 = night side to us
const phase = (1 - f) * 0.5; // 1 = full, 0 = new
let ux = lx, uy = -ly;
const ul = Math.sqrt(ux * ux + uy * uy);
if (ul < 1e-4) { ux = 1; uy = 0; } else { ux /= ul; uy /= ul; }
const ringN = pl.ring ? ringProjection(pl, cam) : 0;
if (ringN) strokeRing(pl, ringN, 1, fade);
// surface
ctx.save();
ctx.beginPath();
ctx.arc(px, py, r, 0, TAU);
ctx.clip();
ctx.globalAlpha = fade;
ctx.save();
ctx.translate(px, py);
ctx.rotate(pl.spin);
ctx.drawImage(planetTex[pl.tex], -r, -r, r * 2, r * 2);
ctx.restore();
// day/night terminator multiplied over the surface only
const soft = 0.24;
const grad = ctx.createLinearGradient(px - ux * r, py - uy * r, px + ux * r, py + uy * r);
const dark = 'rgb(11,13,22)', light = 'rgb(255,255,255)';
grad.addColorStop(0, dark);
grad.addColorStop(Math.min(1, phase), dark);
grad.addColorStop(Math.max(0, Math.min(1, phase + soft)), light);
grad.addColorStop(1, light);
ctx.globalCompositeOperation = 'multiply';
ctx.fillStyle = grad;
ctx.beginPath();
ctx.arc(px, py, r, 0, TAU);
ctx.fill();
ctx.restore();
// atmosphere rim
const ac = pl.atmoStr;
ctx.globalCompositeOperation = 'lighter';
const ag = ctx.createRadialGradient(px, py, r * 0.82, px, py, r * 1.3);
ag.addColorStop(0, 'rgba(' + ac + ',0)');
ag.addColorStop(0.45, 'rgba(' + ac + ',' + alphaStr(0.2 * fade) + ')');
ag.addColorStop(1, 'rgba(' + ac + ',0)');
ctx.fillStyle = ag;
ctx.beginPath();
ctx.arc(px, py, r * 1.3, 0, TAU);
ctx.fill();
ctx.globalCompositeOperation = 'source-over';
if (ringN) strokeRing(pl, ringN, 2, fade);
}
ctx.globalAlpha = 1;
}
// Ring points are classified by depth against the planet centre, so the
// far half is drawn behind the body and the near half over it. Points go
// into the P_RING pool and the front/behind flags into RING_FRONT; the
// function returns the count (0 = nothing to draw).
function ringProjection(pl, cam) {
const centre = project(pl.x, pl.y, pl.z, cam, P_CENTER);
if (!centre) return 0;
const N = 56;
for (let i = 0; i <= N; i++) {
const a = i / N * TAU;
const ca = Math.cos(a), sa = Math.sin(a);
const R = pl.r * pl.ringR;
const q = project(pl.x + (pl.ringA[0] * ca + pl.ringB[0] * sa) * R,
pl.y + (pl.ringA[1] * ca + pl.ringB[1] * sa) * R,
pl.z + (pl.ringA[2] * ca + pl.ringB[2] * sa) * R, cam, P_RING[i]);
RING_FRONT[i] = q ? (q.z < centre.z ? 2 : 1) : 0;
}
return N + 1;
}
function strokeRing(pl, n, front, fade) {
ctx.lineCap = 'round';
const style = 'rgba(' + pl.atmoStr + ',' + alphaStr(0.26 * fade) + ')'; // built once, not per segment
for (let i = 0; i + 1 < n; i++) {
if (RING_FRONT[i] !== front || RING_FRONT[i + 1] !== front) continue;
const A = P_RING[i], B = P_RING[i + 1];
const z = (A.z + B.z) * 0.5;
ctx.strokeStyle = style;
ctx.lineWidth = Math.max(0.7, pl.ringW * FOCAL / z); // width still varies with depth
ctx.beginPath();
ctx.moveTo(A.x, A.y);
ctx.lineTo(B.x, B.y);
ctx.stroke();
}
}
function drawMeteors(cam) {
if (!meteors.length) return;
ctx.globalCompositeOperation = 'lighter';
ctx.lineCap = 'round';
for (const m of meteors) {
const head = project(m.x, m.y, m.z, cam, P_ONE);
if (!head) continue;
const sp = Math.sqrt(m.vx * m.vx + m.vy * m.vy + m.vz * m.vz) || 1;
const tl = sp * m.trail;
const tail = project(m.x - m.vx / sp * tl, m.y - m.vy / sp * tl, m.z - m.vz / sp * tl, cam, P_TWO);
if (!tail) continue;
const t = m.life / m.max;
let env = 1;
if (t < 0.18) env = t / 0.18;
else if (t > 0.6) env = Math.max(0, (1 - t) / 0.4);
if (env <= 0.02 || !tail) continue;
const cs = m.warm ? '255,226,190' : '205,235,255';
const g = ctx.createLinearGradient(head.x, head.y, tail.x, tail.y);
g.addColorStop(0, 'rgba(' + cs + ',' + alphaStr(0.95 * env) + ')');
g.addColorStop(0.35, 'rgba(' + cs + ',' + alphaStr(0.4 * env) + ')');
g.addColorStop(1, 'rgba(' + cs + ',0)');
ctx.strokeStyle = g;
ctx.lineWidth = m.w;
ctx.beginPath();
ctx.moveTo(head.x, head.y);
ctx.lineTo(tail.x, tail.y);
ctx.stroke();
const hs = (m.fireball ? 52 : 24) * env;
ctx.globalAlpha = 0.8 * env;
ctx.drawImage(m.warm ? softWarm : softCool, head.x - hs / 2, head.y - hs / 2, hs, hs);
ctx.globalAlpha = 1;
}
ctx.globalCompositeOperation = 'source-over';
}
function drawExhaust(cam) {
if (!exhaust.length) return;
ctx.globalCompositeOperation = 'lighter';
for (const p of exhaust) {
const q = project(p.x, p.y, p.z, cam, P_ONE);
if (!q) continue;
const t = p.life / p.max;
const a = (1 - t) * (1 - t) * 0.55;
let hs = p.r * (1 + t * 2.4) * 2 * FOCAL / q.z;
if (hs < 1) continue;
if (hs > 34) hs = 34;
ctx.globalAlpha = a;
ctx.drawImage(softCool, q.x - hs / 2, q.y - hs / 2, hs, hs);
}
ctx.globalAlpha = 1;
ctx.globalCompositeOperation = 'source-over';
}
const DUST_ALPHAS = [0.1, 0.22, 0.36];
function drawDust(cam) {
const cp = cam.camPos;
const paths = [new Path2D(), new Path2D(), new Path2D()];
const TRAIL = 0.05; // motion-blur trail time — the speed cue
const vx = ship.vel[0] * TRAIL, vy = ship.vel[1] * TRAIL, vz = ship.vel[2] * TRAIL;
for (const d of dust) {
if (d.x < cp[0] - DUST_R) d.x += 2 * DUST_R;
else if (d.x > cp[0] + DUST_R) d.x -= 2 * DUST_R;
if (d.y < cp[1] - DUST_R) d.y += 2 * DUST_R;
else if (d.y > cp[1] + DUST_R) d.y -= 2 * DUST_R;
if (d.z < cp[2] - DUST_R) d.z += 2 * DUST_R;
else if (d.z > cp[2] + DUST_R) d.z -= 2 * DUST_R;
const dx = d.x - cp[0], dy = d.y - cp[1], dz = d.z - cp[2];
const dist = Math.sqrt(dx * dx + dy * dy + dz * dz);
if (dist > DUST_R || dist < 12) continue;
const cz = dx * cam.zAxis[0] + dy * cam.zAxis[1] + dz * cam.zAxis[2];
if (cz < 20) continue;
const cx = dx * cam.xAxis[0] + dy * cam.xAxis[1] + dz * cam.xAxis[2];
const cy = dx * cam.yAxis[0] + dy * cam.yAxis[1] + dz * cam.yAxis[2];
const px = CX + (cx / cz) * FOCAL;
if (px < -20 || px > W + 20) continue;
const py = CY - (cy / cz) * FOCAL;
if (py < -20 || py > H + 20) continue;
// the mote appeared at here a moment ago: that's the streak
const cz2 = cz + (vx * cam.zAxis[0] + vy * cam.zAxis[1] + vz * cam.zAxis[2]);
if (cz2 < 20) continue;
const cx2 = cx + vx * cam.xAxis[0] + vy * cam.xAxis[1] + vz * cam.xAxis[2];
const cy2 = cy + vx * cam.yAxis[0] + vy * cam.yAxis[1] + vz * cam.yAxis[2];
const qx = CX + (cx2 / cz2) * FOCAL;
const qy = CY - (cy2 / cz2) * FOCAL;
const bucket = Math.min(2, ((1 - dist / DUST_R) * 3) | 0);
const path = paths[bucket];
path.moveTo(px, py);
path.lineTo(qx, qy);
}
ctx.globalCompositeOperation = 'lighter';
ctx.strokeStyle = 'rgb(200,225,255)';
ctx.lineWidth = 1;
for (let i = 0; i < 3; i++) {
ctx.globalAlpha = DUST_ALPHAS[i];
ctx.stroke(paths[i]);
}
ctx.globalAlpha = 1;
ctx.globalCompositeOperation = 'source-over';
}
function drawCursor() {
if (cursorAlpha <= 0.01) return;
ctx.save();
ctx.globalAlpha = cursorAlpha;
ctx.strokeStyle = '#cfeaff';
ctx.fillStyle = '#cfeaff';
ctx.lineWidth = 1.5;
ctx.lineCap = 'round';
ctx.beginPath();
ctx.moveTo(mouseX - 13, mouseY); ctx.lineTo(mouseX - 5, mouseY);
ctx.moveTo(mouseX + 5, mouseY); ctx.lineTo(mouseX + 13, mouseY);
ctx.moveTo(mouseX, mouseY - 13); ctx.lineTo(mouseX, mouseY - 5);
ctx.moveTo(mouseX, mouseY + 5); ctx.lineTo(mouseX, mouseY + 13);
ctx.stroke();
ctx.beginPath();
ctx.arc(mouseX, mouseY, 1.6, 0, Math.PI * 2);
ctx.fill();
ctx.restore();
}
// ------------------------------------------------------------------
// Main loop
// ------------------------------------------------------------------
function frame(now) {
let dt = (now - last) / 1000;
last = now;
// Fixed: guard against zero or negative dt to avoid NaN in yawRate.
if (dt <= 0) {
requestAnimationFrame(frame);
return;
}
if (dt > 0.05) dt = 0.05; // clamp big gaps
update(dt);
const cam = cameraBasis(dt);
spawnMeteors(cam, now);
drawBackground();
drawSky(cam);
drawNebulae(cam);
drawGalaxies(cam);
drawFilaments(cam);
drawStars(cam);
drawPlanets(cam);
drawAsteroids(cam);
drawExhaust(cam);
drawMeteors(cam);
drawDust(cam);
drawShip(cam, now);
if (vignetteLayer) {
ctx.drawImage(vignetteLayer, 0, 0, W, H);
}
// Cursor fade: visible while the mouse moved within the last second,
// eases out after that, eases back in on movement.
{
const idle = now - lastMove;
const target = idle < 1000 ? 1 : 0;
const speed = target === 1 ? 12 : 4;
cursorAlpha += (target - cursorAlpha) * Math.min(1, speed * dt);
if (target === 0 && cursorAlpha < 0.01) cursorAlpha = 0;
else if (target === 1 && cursorAlpha > 0.99) cursorAlpha = 1;
}
drawCursor();
requestAnimationFrame(frame);
}
// Fixed: ensure a valid camera basis exists before the first click.
cameraBasis(0.016);
requestAnimationFrame(frame);
})();
</script>
</body>
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