048-coasterworks

Let me understand the current state. The previous task was "048-coasterworks" - a procedural roller coaster generator. The summary says:

• core.mjs contains validated coaster generation and physics logic
• Next step: integrate into index.html with Three.js scene, rendering track, terrain, supports, camera controls, UI, audio

The current task is "Wake up and do as you please." So I should continue working on the coaster demo - specifically, integrate the core logic into a complete demo.

Let me first check the current state of the demos folder and the coasterworks folder.

Let me check the current state of the demos folder and the coasterworks folder.

Interesting - the 048-coasterworks folder doesn't exist in /space/demos/. The previous run's summary says core.mjs was created, but it might have been in a temp directory that got wiped. Let me check the /tmp and home directory for any remnants of previous work.

The previous run's work on coasterworks is gone (the sandbox was wiped). The summary says the core logic was validated, but the files don't persist except in /space. The 048-coasterworks folder was never created in /space.

So I need to rebuild the coaster demo from scratch. The good news: the previous run's summary gives me a lot of design details:

1. LayoutBuilder class to construct coaster tracks using a sequence of elements (straight, turn, lift, drop, hill, loop, zero-g roll, helix)
2. Dubins path algorithm for homing the track back to the station
3. Catmull-Rom spline resampling, Gaussian smoothing, arc-length uniformization
4. Parallel transport frames with explicit roll and physics-based banking
5. Custom physics engine: gravity, friction, chain lift, braking, g-forces
6. Validation suite: endpoint error, no NaNs, height bands, min radius, lap completion, g-forces

The plan:

1. Build the core coaster generation + physics logic in a core.mjs file (locally in /tmp or a work dir)
2. Build a Node.js test harness to validate
3. Create /space/demos/048-coasterworks/index.html that inlines the core logic and adds Three.js rendering: track (tubes/rails + ties), terrain, supports, skybox, coaster train, camera modes (ride POV, orbit, follow), UI (seed, speed, g-force meter), audio (optional)
4. Update /space/demos/index.html

Let me look at a couple of existing demos to understand the style conventions, particularly one with core.mjs inlined (042-neon-tilt) and the index page format.

****************************************************************************************************************************************************************************************p).

The 042 demo has a nice structure: core.mjs (pure logic, testable in node), test.mjs (node test harness), build.mjs (inlines core.mjs into index.html), and index.html. I'll follow this pattern.

Let me look at 042's build.mjs and how it inlines core, to reuse the pattern.

The pattern is clear. I'll follow the same structure:

• core.mjs — pure coaster logic (layout builder, Dubins path, spline resampling, parallel transport frames, physics). Testable in node.
• test.mjs — node test harness validating the core.
• template.html — the Three.js rendering template with //__CORE_INJECT__ marker.
• build.mjs — inlines core into template → index.html.

I'll build in a local work directory (faster than /space), then copy the final files to /space/demos/048-coasterworks/.

Now, let me design the coaster core carefully. This is a meaty piece of engineering. Let me plan:

Core design (core.mjs)

Vec3 helpers — minimal math (arrays or {x,y,z}). Use plain arrays [x,y,z] with helper functions for speed and simplicity.

Seeded RNG — mulberry32.

LayoutBuilder: builds a sequence of control points describing the track centerline. Elements:

• station: straight flat-ish segment at low height (station platform).
• lift(h): chain lift hill up to height h at a gentle slope.
• drop(angle?, turn?): steep drop, possibly with a turning drop. Built from curve segments descending.
• turn(dir, radius, arc): flat (or slightly sloped) horizontal turn.
• hill(h, len): airtime hill — parabolic crest.
• loop(r): vertical loop (clothoid-ish; use a circle or clothoid approximation via sampled loop shape — teardrop/clothoid loop is better for g-forces). I'll do a clothoid loop approximation: parameterize loop with varying radius.
• zerogroll(len): straight section with a roll rate — handled via explicit roll frames.
• helix(dir, radius, turns, dh): banked helix descending or ascending.
• brakeRun(len): flat brake section before station.

The builder tracks current position (x, z, y), heading (angle in XZ plane), and a list of control points. Each element appends points (denser for curves).

Actually, a cleaner approach: builder appends to a raw point list with variable density, then we fit a closed Catmull-Rom through the key points and resample uniformly by arc length, then smooth with a Gaussian-ish filter (a few passes of neighbor averaging in 3D, careful to preserve closedness), then compute frames.

But too much smoothing can collapse a vertical loop. The previous summary says: "Catmull-Rom spline, then smoothed with a Gaussian-style filter and re-uniformized by arc length". And max curvature was reduced from 1.37 to 0.12. So the approach worked. Key: smooth moderately (small kernel), which preserves macro features like loops while killing kinks.

Alternative: use centripetal Catmull-Rom through moderately dense key points, resample at ~1m spacing, then apply 2-4 passes of [0.25, 0.5, 0.25] smoothing. A loop of radius 12m with 1m sampling — smoothing passes with small kernel shrink the loop slightly but don't destroy it. That's fine.

Dubins homing: after the main elements, we need to return to the station start with the correct heading to close the loop. Dubins path: given current (pos, heading) and target (pos, heading) with a minimum turning radius R, compute the shortest path composed of arcs and straight lines (LSL, RSR, LSR, RSL). Then elevate: the homing path should also handle height — the brake run should descend to station height. I'll handle height by computing the 2D (XZ) Dubins path, then assigning heights: descend from current height to station height with a smooth profile along the path (or keep flat if already low, with a gentle "pre-brake drop").

Simpler and robust: after the final big element, add a brake run that brings the train to a moderate height (e.g., 8m above station), then the homing Dubins path with a height profile: mostly gentle descent, flattening at the end into the station.

Even simpler and what many procedural coasters do: place station at origin heading +X. Build elements. Then to home: we need final position (stationX + stationLength, 0, stationZ) heading +X... wait, closed loop: the end of the station connects back to its start. Actually for the spline, station start point = first point; the last element should end at a point such that the Catmull-Rom closure is smooth. Easiest: home to the station start position with the same heading as station start, and let the spline close. The Dubins homing ends slightly before the station (e.g., 20m before), then the spline closes naturally with the straight station segment providing the last stretch.

Hmm, but Catmull-Rom closed splines interpolate all key points; the closure happens between last and first key point. If I home to exactly (0,0,0) with heading +X, then last key point ≈ first key point ≈ (0,0,0) — duplicate points cause issues. Better: home to a point before the station start, e.g., (-stationLen, 0, 0) heading +X, and the first key point is (0,0,0)... but then the segment between (-stationLen,0,0) and (0,0,0) is the station approach. Actually let me define: key point 0 at (0,0,0), the lift starts right away. The station is before key point 0, i.e., the homing path ends at (-stationLen, 0, 0) with heading +X. Points from -stationLen to 0 form the station. In a closed Catmull-Rom, the segment from last homing point through (-stationLen..0) to key 0 is smooth if all those points are colinear with spacing. Good.

Physics-wise, the train starts in the station (s ≈ s_station), creeps forward, engages the lift, etc. The lap is complete when s wraps around.

Physics: 1D along arc length s.

• v' = g * (tangential gravity) - friction - drag; where tangential gravity = -g * dy/ds (derivative of height along track).

• Zones: station zone (drive tires push train to lift if v low... actually classic: station dispatch with boost to chain speed), lift zone (v clamped to chain speed while on lift), brake zone (decelerate to approach speed).

• Train: I'll model a single point (or a few cars spaced along s for visuals; physics on center of train). Multi-car visuals: cars at s - k*carSpacing.

• g-forces:

  • vertical (normal) g: from curvature in the plane containing tangent and normal: a_n = v² * κ (curvature) projected on the up-axis of the car frame plus gravity component. Standard: normal accel felt = v²*κ_n - g·n (n = seat-up direction). Let me define up vector U (car's up after banking), tangent T. Gravity accel vector G = (0,-g,0). The specific force felt by rider = -(G + A) where A is the coaster's acceleration... Simpler standard approach: vertical g-force N_v = (v²·κ_v + g·cosθ_stuff)... Let me just compute properly:
    • The track curvature vector K = dT/ds (points toward center of curvature), |K| = κ.
    • Centripetal acceleration required = v²·K (vector).
    • The seat pushes on rider with normal N along U (car up): N·m = m·(v²·K)·U... plus gravity: the rider feels specific force f = a_net - g_vec where a_net = v²·K + tangential stuff (ignore tangential for g display). So g-force vector = v²·K - G, where G=(0,-9.81,0). Vertical g = dot(that, U)/9.81, lateral g = dot(that, S)/9.81 where S is car's right vector.

• Banking: for banked turns, we rotate the frame around T by roll angle ψ. Banking can be explicit (from elements like zero-g roll) or physics-based: to zero out lateral g, bank angle = atan2(lateral_accel, vertical...). Standard approach: ψ = atan(v²·κ_lat / g) for flat turns. I'll compute banking per-sample: desired roll so that lateral g ≈ 0, blended with explicit roll from elements (zero-g roll), smoothed. Actually simpler: elements declare banking (turns/helixes get physics-based banking computed after physics known? but physics depends on track only via dy/ds and curvature, not banking — good, physics is independent of banking). So after physics is computed (max speed profile via energy: v²(s) computable from energy conservation given lift height + friction approx), we can compute target banking = atan2(v²·κ_horizontal, g) clamped to some max, then smooth it, and add explicit rolls.

  Even simpler: compute a "design speed" profile v_design(s) = sqrt(max(v²_station + 2g(h_max - h(s)) ... friction-adjusted. Use it for banking. Fine.

Frames via parallel transport:

• T_i = normalized tangent from resampled points.
• Start with an initial up reference; parallel transport: U_{i+1} = U_i - (U_i·T_{i+1})T_{i+1} normalized... that's projecting. Better: rotate U_i by the rotation that takes T_i to T_{i+1} (minimal rotation).
• Then apply roll ψ_i around T_i: U = Ucosψ + Ssinψ etc.
• S (right) = T × U.

Closed loop: parallel transport around a closed loop introduces a twist mismatch at closure (holonomy). Fix: compute total mismatch angle at the end, distribute correction linearly along s. Standard technique. But since we add explicit banking anyway, mismatch mixes in; still better to correct so station is level. I'll do: after transport, measure angle between transported-start-frame and required-start-frame around T0, distribute -angle*t/T_total correction. Then apply banking+roll on top.

Track geometry (renderer): two rails (tubes along offset curves ±gauge/2 * S), cross ties (instanced boxes), spine/spine? For style: wooden-coaster lattice or steel tubular. I'll do steel: two circular rails + rectangular cross ties + support columns (cylinders) to ground with footers, plus a center spine tube maybe. Supports: vertical columns every ~12m where height above terrain > 3m, with horizontal footing. Keep support generation cheap: sample every N meters, raycast down to terrain height function (analytic terrain, so cheap).

Terrain: analytic heightfield function h(x,z) = sum of a few sine/noise octaves, flattened near track corridor? Flattening near track corridor is complex; instead, make terrain gentle (amplitude ~3-6m) and put track min height ~6m; supports bridge the gap. Terrain mesh: PlaneGeometry 256x256 segments with height function, vertex colors by height (grass → rock → sand near water?). Add water plane at y=0? Nice: terrain min slightly below 0, water plane at y=0.2 → lakes. Add trees (instanced cones+cylinders) scattered, avoiding track corridor (distance check to track samples). Rocks (instanced dodecahedra). Sky: gradient shader dome + sun; clouds maybe (billboard sprites or shader). Keep it cohesive.

Post: UnrealBloomPass (subtle), vignette shader pass. Maybe fog.

Camera modes:

1. Ride (POV from front car, look along tangent, with slight look-ahead & banking applied)
2. Follow (chase cam behind train)
3. Orbit (OrbitControls around whole scene)
4. Trackside (static scenic camera auto-placed? maybe skip)

Keys: 1/2/3 or buttons. Also "speed" control is automatic (physics), but time-scale slider maybe.

UI: seed input + "New Coaster" button, stats (height, length, max speed, max g), g-force meter (live), speed readout, camera mode buttons, audio toggle. Title "COASTERWORKS". Retro-industrial style UI.

Audio: generative WebAudio — chain-lift clank (periodic clicks while on lift), wind noise ∝ speed, rumble (filtered noise ∝ speed, lowpass), clatter on transitions? keep simple: wind + rumble + lift clack + a whoosh on drops. Screams? no.

Validation (test.mjs): from the summary:

• Dubins endpoint error small.
• Layout generation success over many seeds (no null).
• No NaNs; heights within band; min clearance above terrain; max curvature ≤ threshold (min radius ≥ ~8m).
• Physics: lap completes, max speed ≤ limit, vertical g in [-1.5, 5.5], lateral g ≤ ~2.

Let me now write the core. This is the biggest chunk. I'll write it carefully.

Key subtleties:

1. Loop element: a vertical loop in the direction of travel. Parameterize clothoid loop: use the classic "loop" curve: for t in [0,1], angle φ = 2πt, radius r(φ) = r0 * (1 - 0.5*sin(φ/2)²)? A common approximation: teardrop with r smaller at top. Clothoid loop: r(φ) = r_bottom - (r_bottom - r_top) * sin²(φ/2)? At φ=0 (bottom entrance) r=r_bottom; at φ=π (top) r=r_top; at φ=2π r=r_bottom again. Integrate: the loop is built by stepping heading in the vertical plane with curvature 1/r(φ). I'll build the loop by integrating in the vertical plane aligned with current heading: local frame (forward F, up Y). Points: p += d·(cos α * F + sin α * Y), where α is pitch angle, dα = ds/r(α)... Let me implement: step ds small (0.5m), α accumulates dα = ds / r(α) where r(α) interpolates r_bottom at α=0/2π and r_top at α=π: r(α) = r_bot + (r_top - r_bot)·sin²(α/2). Continue until α reaches 2π. This yields a closed-ish loop (entry and exit at same point if symmetric). Actually since r(α) symmetric about π, the loop closes exactly in the vertical plane. Entry point = exit point, same pitch 0 heading forward.

2. Zero-g roll: straight segment where banking ψ goes 0→2π linearly (or smoothstep) along its length, with a slight hump for zero-g. The track itself is mostly straight; roll handled in frames. I'll record "roll events" (s_start, s_end, totalΔψ) in a list that frame generation consumes. Since roll applied in frames, and frames smoothed... banking changes must not be smoothed too aggressively. I'll smooth banking with a small window.

   But wait — the physics-based banking also acts; during zero-g roll the track is straight so banking target ≈ 0, add explicit roll on top. Good.

3. Height band: track min height above terrain: supports handle gap. But track should never go below terrain. After smoothing, dips could sink below terrain if terrain bumps. Mitigate: terrain gentle (amp ≤ 4m), track min height ~7m except station area where terrain flattened to 0 within radius. I'll flatten terrain near station and along track corridor: terrainH'(x,z) = mix(terrainH, min(terrainH, clearanceBelow), w(dist to track)) — cheap approach: for each terrain vertex, compute min distance to track key points (coarse, e.g., every 4th sample ~ every 8m), then clamp terrain height to ≤ (trackH - 3) with smooth falloff within 15m. That guarantees clearance AND makes supports sensible (supports then have footing on terrain). This is renderer-side but terrain function must be shared with core for the clearance test. I'll put terrain base function in core, and corridor-flattening also in core (given track points). Terrain object in core: makeTerrain(seed, trackPts) returns heightAt(x,z).

4. Station area: flatten terrain to exactly stationBase-? Station at height H0 (e.g., 8m) on stilts? Simpler: station at y = 4m, terrain flattened to 3.2m under it; short supports. Actually put station at y=6 and terrain flattened to 4.5 near station plaza radius 25m. Fine.

Actually, let me simplify: station start at height Y0 = 6. Lift to ~45-60m. Elements. Terrain amplitude ~8m rolling hills, water at 0. Terrain base at ~2-6m. Corridor clamp ensures clearance.

5. Dubins path: implement standard: given start (x, z, θ), goal (x, z, θ), min radius R: compute the 4 candidate paths (LSL, RSR, LSR, RSL), pick shortest. Then sample into points with heading. If goal too close for R, fall back: allow smaller R (min radius for homing can be gentler, like 25m; if impossible, use simple two-arc S-curve or just reduce R until feasible). I'll implement fallback R shrink loop: try R=30,25,20,16,12 until a path found (paths always exist for any R>0? for LSL/RSR etc., if centers coincide degenerate; generally some path exists for any R unless distance 0). I'll implement robustly with the standard formulas and handle degenerate cases.

6. Layout generator: random sequence with rules:

   • Station (len ~20m) at y=6 heading +X from origin... wait I said key0 at (0,0,0) and station before it. Let me restructure: build forward from station start. pts start at (0,0,Y0) heading +X. Station segment: straight 22m. Then lift: slope up to H (lift angle ~25°... real lifts ~20-30°). H ~ 45 + rnd*20. Then the meat: sequence of elements chosen with constraints (e.g., no loop immediately after small hill; ensure speed feasibility — physics check later; generator just builds plausible sequences). Elements: turn L/R, hill (small/medium), drop (big first drop right after lift: mandatory), loop (only if H high enough... the first drop gives speed; loops early), zero-g roll (mid course, needs height ~ moderate), helix (to burn speed and change direction), bunny hops series, turnaround (180°).
   • Keep track of approximate energy: not strictly needed if physics validation passes; but generator should ensure the lift is the highest point (all element heights < H - margin). Enforce: when adding element that rises, cap crest height < H - 5. Track current height; hills lift by up to min(someRnd, available). Since hills are followed by descents back to ~base running height (8-15m), it's fine.
   • After ~8-14 elements, add final brake run at low height, then home via Dubins at height descending to Y0.

   First drop: from lift top, drop to ~8m with a steep pitch (55-70°) possibly with turn. Built by integrating pitch profile: pitch goes 0 → -60° → 0 over the drop (circular-ish arc segments). Implement as: dropArc(h1, h2, pitchMax, turn=0): use two arcs: entry arc (pitch 0→-pMax) with radius r1, vertical drop portion, exit arc (pitch -pMax→0) radius r2 such that total Δh = h1-h2. Solve lengths. Simpler: sample a parametric curve: for t in 0..1, pitch(t) = -pMax * smooth bump, integrate position. Ensure exact Δh by scaling? Height accuracy matters for physics realism but spline+smoothing will adjust anyway; physics uses actual sampled heights. I'll integrate and let exit height be whatever; the next elements start from actual current height (builder tracks it).

   General approach for hills/drops: integrate in vertical plane using pitch profile, stepping ds=2m: pos += (cos(pitch)·F·ds + sin(pitch)·Y·ds); heading can also yaw slowly for turning drops (yaw rate per meter * ds). The builder keeps (pos, yaw, pitch). Elements = pitch/yaw profile programs. This "heading-based builder" is robust and simple:

   • straight(len): pitch 0, yaw 0.
   • turn(dir, radius, angleDeg): yaw rate = dir/radius for length = radius·angle.
   • lift(h): pitch = atan2 grade such that rise h over len; use pitch const = 25°; len = h/sin(25°).
   • drop(pitchMax, dh_target, radiusEntry, radiusExit, yawTotal=0): phase1 entry: pitch 0→-pMax over arc rE (ds steps, dpitch = ds/rE). phase2: hold -pMax until remaining dh to exit can be absorbed by exit arc at rX: dh_exit = rX*(1-cos(pMax)) approx (arc from -pMax to 0 drops rX*(1-cos pMax) vertically). phase3: pitch -pMax→0 over rX. Add yaw slowly distributed over whole drop.
   • hill(crestH, rCrest, rEntry?): pitch up then down: entry arc 0→+pIn, crest arc +pIn→-pOut crossing 0 at top, exit arc -pOut→0. Parameterize by total Δh up + down. Classic airtime hill: pitch profile 0→+a (r1), +a→-b (r2) — this is the crest, drop side, -b→0 (r3). Heights: up = r1*(1-cos a)+r2*(cos0 - cos a)... this is getting fiddly; easier: define hill by target crest height hc and end height he and pitch limits, integrate numerically with a pitch profile shaped like a sine bump: pitch(t) = A·sin(π t)^? — but exact heights unknown until integrated... Numerical integration IS exact enough: builder integrates ds steps; whatever height results, builder records; subsequent elements adapt. The only hard constraint: never exceed H-4; so choose hc = min(desired, currentHeadroom). I'll use arcs for control:

   hillBuilder(upPitch, downPitch, r1, r2, r3):

   • arc1: pitch 0→upPitch at rate 1/r1. Δh1 = r1(1-cos upPitch).

   • arc2: pitch upPitch→downPitch(negative) at rate 1/r2. Δh2 = r2(cos0? ) integrate: Δh = r2(sin(upPitch) - sin(downPitch))... since dθ = ds/r, vertical increment = ∫sinθ ds = r∫sinθ dθ = r[-cosθ] = r(cosθ1 - cosθ2). So arc from θa→θb drops by r(cosθa - cosθb) (negative if rising... θ positive = up? Let me define pitch θ measured with positive = climbing. Vertical change over arc r from θa to θb: Δh = r·(sinθb - sinθa)·sign? Let me redo: ds step, dy = sinθ ds, dθ = ds/r → dy = r sinθ dθ → ∫_{θa}^{θb} r sinθ dθ = r(cosθa − cosθb). With θb>θa (pitching up), cosθa>cosθb → Δh>0 rising. ✓.

   • So hill: arc1 r1 from 0→θu: Δh = r1(1−cosθu). arc2 r2 from θu→θd (θd<0): Δh = r2(cosθu − cosθd) (negative since cosθd > cosθu typically... cosθd with θd=-40° → 0.766; cosθu 30° → 0.866; Δh = r2(0.866−0.766) >0 still rising?? That's wrong. Hmm: during arc2, pitch goes from +θu down through 0 to θd. While pitch>0 still climbing. Δh over arc2 = r2(cosθu − cosθd). With θu=30°, θd=-40°: cosθu=0.866, cosθd=0.766 → Δh = +0.1·r2 > 0?? But pitch crosses 0 and becomes negative, so net should be able to be negative... cos is even: cos(-40°)=cos(40°)=0.766. Indeed Δh = r(cosθa−cosθb) = r(0.866−0.766)=+0.1r. The climb during +30°→0 equals r(0.866... wait ∫ r sinθ dθ from 30°→0 = r(cos30−cos0)=r(0.866−1)=−0.134r <0?? Negative?! But climbing with pitch>0 should gain height...

   I have a sign error. dy = sinθ·ds with θ>0 = up gives dy>0. ∫_{θa}^{θb} r sinθ dθ = r[−cosθ]{θa}^{θb} = r(cosθa − cosθb). For θa=0→θb=30°: r(cos0−cos30)=r(1−0.866)=+0.134r ✓ rising. For 30°→0: r(cos30−cos0)=−0.134r ✗ but pitch stays positive... OH the issue: dθ = ds/r assumes θ increasing with s. If θ decreases (30°→0), then dθ = −ds/r, i.e., ds = −r dθ, dy = sinθ(−r dθ), ∫{30°}^{0} −r sinθ dθ = r[cosθ]_{30°}^{0} = r(1−0.866)=+0.134r ✓ rising. Good — sign flips with direction of pitch change. Simplest: integrate numerically in code (ds=1-2m steps), avoiding analytic confusion entirely. Numeric is fine and robust. The builder just integrates; heights are what they are; generator adapts subsequent elements. ✓.

   • loop(rBot, rTop): vertical-plane integration as described, with yaw fixed.
   • helix(dir, radius, turns, dh): yaw rate const, pitch const = atan2(dh per length). Choose pitch so Δh matches: length = radius·2π·turns·(1/cos small pitch ≈ 1). pitch = asin(dh/length) roughly; fine numerically.
   • brakes(len): straight, flat, record brake zone.
   • zerogroll(len, humpH): mostly straight with slight up-down hump (pitch bump small) + roll event recorded.

   Each element also tags zones/roll events by s-range — but s (arc length) isn't known until resampling. Instead, record keypoint indices: each element knows the index range of raw points it emitted. After spline resampling, map: I'll carry per-sample "tag" via nearest keypoint mapping. Simpler: record tags as fractions: when building, I know cumulative raw length (I integrate ds). After resampling uniformly, s is proportional; tags can be stored as raw arc positions and later mapped to resampled arc positions directly (both are arc length along nearly the same curve; raw vs smoothed lengths differ slightly but tags are zone-ish, tolerant). I'll store tags in meters of raw arc length, and after final resample, use them directly (they'll be off by the small length change; acceptable for lift/brake zones). Even better: after final resampling, recompute zone boundaries by finding nearest sample to the raw 3D positions of zone starts/ends. Robust: store zone start/end as 3D points; map to nearest resampled index. ✓ do that.

7. Smoothing vs features: Gaussian passes might round the lift-to-drop transition (that's fine/desired) and shrink loops slightly. Keep kernel small (passes=2, weights [0.2,0.6,0.2] maybe 3 passes), and ensure the station/lift base aren't distorted... it's all smooth anyway. Important: smoothing a closed loop of points is fine.

   One risk: smoothing collapses the loop entry/exit overlap (loop entry point = exit point spatially, but they're distant in s — no problem since smoothing is in s-neighborhood).

8. Physics details:

   • Precompute per-sample: dy/ds (slope), curvature κ, frame up U, right S.
   • Sim: state s (float, in meters along track), v. dt small (1/240 substeps).
   • Forces: a = −g·slope − μg·(normal-ish approx 1)·sign? Use: a = −g·(dy/ds) − (μ·g + c·v²) (friction opposing motion) — μ ~ 0.01-0.02, c tiny.
   • Lift zone: if s in lift zone and v < vChain: v = vChain (chain pulls). Actually chain sets v exactly while on lift; train moving slower gets caught by chain. vChain ~ 2.2 m/s.
   • Station zone: dispatch: if train stopped in station, after "gates open" v → pushed to 3 m/s until lift. Simple state machine: DISPATCH (in station, accelerate gently to 4 m/s), RUN, BRAKE (in brake zone, decelerate toward 2.5 m/s), PARK (back in station, decelerate to 0), wait 3s, repeat. Continuous lapping = nice demo.
   • Brakes: in brake zone apply decel so v→min(v, approach). Use strong decel toward target 3 m/s: a_brake = -(v-3)*2 capped. Then station: decelerate to 0 at station stop point. To guarantee stop at station point: once in station zone, v_target = max(0, sqrt(2·a·distToStop)) profile. Simple: in station zone, a = clamp(-k·(v²/(2·dist)), ...) standard approach. I'll do: desired v = sqrt(2·1.2·distToStop) capped by physics; apply a = (desired−v)·k.

   For g-forces at current s: compute as described with curvature vector K = dT/ds. I'll compute K per sample numerically from frames (T[i+1]-T[i-1])/(2ds). Vertical g = dot(v²K − G, U)/g. Lateral = dot(v²K − G, S)/g. Note: with correct banking, lateral ≈ 0 in turns.

9. Renderer (template.html):

   • Build track meshes: rails as TubeGeometry along offset curves (CatmullRomCurve3 through offset points, closed). gauge ~1.2m, rail radius 0.09m. Ties: InstancedMesh of thin box every 0.7m, oriented by frame (position at center, aligned S direction). Spine: maybe a box beam under center connecting ties — use instanced short segments or a tube of radius 0.25 flattened? Skip spine; add cross tie boxes + rail tubes + support columns. Looks like a modern RMC? Fine.
   • Colors: rails bright color (e.g., orange/red), ties darker, supports gray. Wooden style alt? Keep steel.
   • Train: 4-6 cars: each car = box body + nose wedge + 4 wheels? Keep simple but nice: rounded box (BoxGeometry) + windshield. Instanced? Few cars — just Group per car, position/orient per frame at s − k·spacing. Wheels optional small cylinders. Add up-stop wheels? overkill.
   • Station: platform box + roof + queue rails? simple: platform + canopy + supports. Nice touch: station building with glowing sign.
   • Terrain: big plane, vertex colors (height-based: sand near 0, grass, rock high... our heights are low: water 0, sand 0-1.5, grass 1.5-6, rock >6? terrain max ~10). Add fog + sky dome gradient + sun directional light w/ shadows (shadow camera sized to scene ~ 300m — shadows over big area need big shadow map; use 2048 and CSM? too heavy. Use directional with 250m ortho box, 2048 map, acceptable).
   • Trees: instanced ~600 cone-pines + blob trees, placed randomly where terrain > 1.5m and dist-to-track > 10m. Rocks similar.
   • Water: plane at y=0 with slight opacity + specular (MeshStandardMaterial metalness 0.9 roughness 0.15 transparent 0.85) + animated normals? keep simple-ish: gentle vertex wave in onBeforeCompile? Could skip animation; add subtle moving normal via a repeating canvas texture offset. Fine: MeshPhysicalMaterial with transmission? heavy. Keep simple standard material + animated texture offset.
   • Clouds: a few billboarded sprite puffs (canvas radial gradient texture) drifting slowly.
   • Post: EffectComposer + RenderPass + UnrealBloomPass (strength 0.35, radius 0.6, threshold 0.85) + Vignette (ShaderPass) + OutputPass.
   • Camera modes: RIDE (position at car front + 1.2m up, look ahead along T with banked up vector; add subtle head bob/shake ∝ curvature·v²), FOLLOW (behind & above, lerp), ORBIT (OrbitControls, target = scene center or train). Keys 1/2/3, buttons too.
   • HUD: title, stats panel (length, height, max speed, max G), live telemetry (speed km/h, vertical g, lateral g) with g-meter bar, buttons: New Coaster (seed random), camera mode, audio toggle, time of day? maybe sun cycle slider — skip. Add "photo mode" hide UI? skip.
   • Audio: WebAudio: wind (filtered white noise, gain ∝ v²), track rumble (lowpassed brown noise ∝ v, plus clatter impulses at tie frequency? simple: rumble), chain dog clacking in lift zone (periodic click via osc/env at rate ∝ v), brake screech in brake zone (bandpass noise), ambient birds? skip. Master mute button; start on user gesture (overlay "CLICK TO RIDE").
   • Overlay start screen (also needed for audio unlock).
   • Seed via URL ?seed= too.
   • Loading: generation is fast (<200ms), fine.

10. test.mjs: replicate the validations from the summary:

    • Dubins endpoint error < 0.5m over random cases.
    • For seeds 1..60: generate; assert success; check no NaN; min terrain clearance > 2m; max curvature < 1/8 (min radius 8m) except loop top? loop top radius ~6-8m... set min radius 6m; heights in [3, 80]; physics: completes lap within T; max speed < 45 m/s; vertical g ∈ [−2, 6]; lateral g ≤ 2.5.
    • Report stats. Iterate until green.

Alright — also verify against previous summary's measured targets: max curvature reduced to 0.12 (min radius ~8.3m), max vertical g 9.45→ aim lower ~5.5, max lateral 3.02→ aim ≤2 with better banking. Fine.

Plan of action:

1. mkdir /tmp/coaster, write core.mjs (big!), test.mjs.
2. Run tests, iterate until pass.
3. Write template.html (big), build.mjs; build index.html.
4. Quick syntax check of inlined JS (node --check on extracted module? module has import statements — use node --input-type=module --check? We can at least run esbuild? Not available maybe. Simple: write a small extraction script that pulls the content, replaces three imports with stubs, and node --check it. Or use new Function? import syntax not allowed. Use node --check with .mjs — but 'three' import will fail only at runtime, --check only parses. node --check file.mjs works for syntax. ✓
5. Optionally headless-render? No browser available presumably. Skip; rely on careful code. Actually, maybe puppeteer/playwright available? Check quickly — likely not. I'll do static checks.
6. Copy to /space/demos/048-coasterworks/ (index.html, core.mjs, test.mjs, build.mjs, template.html).
7. Update /space/demos/index.html with new card at top.

Let me now write core.mjs. I'll write it in chunks to keep files manageable. Use the write tool.

Let me draft the core architecture concretely:

Wait — banking design speed: v_design(s) needs lift height; compute via energy: v²(s) = v0² + 2g(hmax − h(s))·(1−loss) — with hmax = lift top height (start of first drop, v≈vChain). Then bankingTarget = atan2(v_design²·κ_h, g) where κ_h is curvature component in horizontal plane (signed by turn direction relative to up). Signed lateral curvature: signedCurvature in plane ⊥ T? Banking for turns: the car should roll so that the resultant of gravity and centripetal lies along seat-up. Lateral accel in car frame before banking: a_lat = v²·(K·S0) where S0 is unbanked right vector. Roll ψ about T: S_rot = S0 cosψ + U0 sinψ... Let me define: rotate (U0,S0) about T by ψ (right-hand rule about T). Then lateral g ∝ a·S_rot, vertical ∝ a·U_rot where a = v²K − G. Choose ψ to zero lateral: ψ = atan2(a·S0, a·U0). That's exact (not just flat-turn approx)! Using design speed. Clamp ψ to ±~120°? real coasters bank up to ~90-100° in banked turns; clamp to 100°. Smooth ψ along s (moving average window ~ 15 samples ~ 7m... banking transitions (roll rate) should be gentle; window 2-4s of travel? Use window ~ 25 samples). Then add explicit roll events (zero-g): their Δψ ramps 0→2π over the event, added after smoothing (but ramp itself smoothed at edges). Then final U,S.

Also initial parallel-transport frame U0 must be "up-ish" at station: start U0 = world up projected ⊥ T. Since station is flat, U0 = (0,1,0). After transport around loop closure mismatch correction, station end up ≈ up. Then banking ψ=0 at station. Good: riders upright in station. ✓.

For the POV camera, use final U.

Zero-g roll + loop: loop handled naturally by parallel transport (U rotates with track through loop). ✓.

Edge: vertical sections (lift is inclined 25°, not vertical — fine; the loop passes through vertical where T ≈ ±Y: projection of world-up ⊥ T degenerates. Parallel transport avoids this since it only rotates minimally; initial up only needs T0 not parallel to Y. ✓.

Now the Dubins implementation. Standard formulas (from Andrew Walker's / PythonRobotics). Represent angles mod 2π. For each of 6 types but 4 suffice (LSL, RSR, LSR, RSL) + degenerate handled. Implement:

I'll use the classic PythonRobotics-style implementation which I remember well:

where alpha = mod2pi(θs − ψ)... Let me set: after computing in normalized frame with origin at start rotated so ψ = bearing to goal: alpha = mod2pi(sθ − ψ), beta = mod2pi(gθ − ψ), d = D/R.

Modes:

• LSL: as above.
• RSR: tmp = d − sa + sb; p2 = 2 + d² − 2cacb + 2d(sb − sa); tmp2 = atan2(ca − cb, tmp); t = mod2pi(alpha − tmp2); p; q = mod2pi(−beta + tmp2).
• LSR: p2 = −2 + d² + 2cacb + 2d(sa + sb); if <0 none; p=sqrt; tmp2 = atan2(−ca − cb, d + sa + sb) − atan2(−2, p); t = mod2pi(−alpha + tmp2); q = mod2pi(−mod2pi(beta) + tmp2).
• RSL: p2 = −2 + d² + 2cacb − 2d(sa + sb); p=sqrt; tmp2 = atan2(ca + cb, d − sa − sb) − atan2(2, p); t = mod2pi(alpha − tmp2); q = mod2pi(beta − tmp2).

Then total length = R*(t+p+q) pick min. Sample: integrate from start: first arc (dir L/R, angle t), straight p·R meters, second arc angle q. Use stepper with fixed ds (e.g., 2m), turning rate 1/R on arcs. Produces points in XZ with headings; I'll attach heights afterwards via a height profile function (smoothstep descent from current h to Y0 along length, but keep flat for first part then descend then flatten at end — profile: use smoothstep between h_start and Y0 over middle 70% of path).

If all modes fail (p2<0 everywhere — rare), shrink R and retry.

Note: for LSR/RSL p2 = −2 + d² + ... can be negative when goal close. Trying R smaller helps since d = D/R grows. ✓.

Generator constraints to ensure homing works: after brakes, ensure we're at least ~2R away from target or positioned such that Dubins exists — Dubins always exists for R small enough; but small R = tight turns = ugly + curvature limit. Min radius limit 8-10m; homing R try from 26 down to 12. Should nearly always succeed; if not, generator returns null and test tries next seed (seed retry loop inside generateCoaster: try seeds derived from base seed up to N attempts).

Also the homing path must end at station start position with heading +X where station start = (−stationLen, 0, Y0)? Wait: I build starting at (0,0,Y0) heading +X with the station segment FIRST (from (0,0) to (stationLen,0)). Hmm, then lift. So the closed spline: ... homing → key0(0,0,Y0) → station straight → lift → ... → homing end ≈ near (0,0) but to close smoothly, homing should END AT a point before key0 with heading +X: target = (−25, 0, Y0) heading 0 (i.e., −X side of key0). Then spline closure from homing-end → key0 → station: all along +X line: smooth. ✓ And physics zone mapping: station zone spans from closure area through station keypoints. I'll define zones by anchor points: stationStart anchor = (−25,0... no: station zone = from homing-end to end of station straight (i.e., s from s(homingEnd)≈0-ish to s(stationEnd)). Map via nearest-sample of anchor pts: station zone anchors: A=(−20,0,Y0) (near closure), B=(stationLen, 0, Y0) (end of platform, start of lift). But nearest-sample to A is ambiguous (homing end and station start are both near A? They're distinct along s but close in space only if homing end ≈ A exactly — it IS A: homing target = (−25,0)). nearest sample index for anchor B is fine (lift base). Station zone = indices from idx(A) to idx(B) — but careful with wrap: idx(A) is near the END of the sample array (homing end) and idx(B) near start. So zone = [idxA..N) ∪ [0..idxB]. Handle wrap zones. Ugh. Alternative: put station zone as [idxA, N) ∪ [0, idxB] flagged via per-sample boolean mask. Simplest: boolean masks per sample for zones: isStation, isLift, isBrake computed by marking between anchor indices with wrap. ✓.

Sim start: s = s of anchor midway station (e.g., platform center anchor (stationLen/2, 0, Y0)) → nearest idx → s0. Train parked, then dispatch cycle.

Physics zones via masks sampled at nearest idx — with ds ~0.8-1m sampling, fine.

Loop feasibility: need speed at loop top: v_top² ≥ g·r_top·(1+margin) → vertical g at top ≥ ~0.5. Check in test via sim (g min at top ≥ 0.3?). My vertical g target range [−1.8, +5.5] with loop top small positive. If sim shows train stalls (v→0 on loop), generation rejected. But stall = v clamp: if v < 0.1 outside lift/station → fail. ✓.

Height budget: loop top ≈ 2·rBot? For clothoid loop entry height h_loop_base and top ≈ base + ~1.6·(rBot+rTop)? Roughly diameter ~ rBot+rTop... To be safe: loops only right after first drop (base height low ~8m, speed high). rBot ~ 10-14, rTop ~ 5-7 → loop top ~ base + 22-28m < H − big margin. Speed needed at base: v² ≥ 2g(topH − base) + g·rTop → need H ≥ topH + rTop/2 + losses. With H=50, top=30: fine.

I'll also give generator a couple of "templates" of element sequences with random params — more reliable than fully random sequences. E.g., templates: "out-and-back", "twister", "looping". Each template = script of elements with randomized parameters, then homing. This improves aesthetics. I'll implement maybe 3 templates + param randomization.

Hmm, time budget. This is a large build. Let me be pragmatic: one flexible random-walk generator with weighted element choices and constraints, plus homing; validated by tests; retry on failure. Good enough and diverse.

Element selection rules:

• After lift: bigDrop (mandatory, dh ≈ H − 9, pMax 55-70°, maybe yaw 0-90°).
• Then loop over energy budget: while elements < target (9-13) and currentHeight < H*0.75-ish prefer...: choices:
  • if speed context high (low height) and loopsLeft>0 and height < 20: loop (rBot 9-13).
  • hill (rise min(6-14, headroom)), maybe double (two hills).
  • turn (flat turn at current height, radius 14-30, 60-150°) — with slight downhill drift (dh −1-3m over turn) for pacing.
  • zero-g roll (len ~ 30-40m) if height between 12-25 and speed ok... needs straight-ish; roll rides fine.
  • helix (dir, radius 16-24, turns 0.75-1.5, dh −8-14) to burn height.
  • brakes when elements done and height ≤ 15: brake run 25m flat; if height > 15, force helix/downhill spiral first.
• Track height naturally varies; ensure min height ≥ 7 by: hills return to ~entry height − small loss; when height < 9, avoid elements that lose height except final approach.

Honestly, simplest robust pacing: build elements that return to a "running height" band 8-14m: drop → (loop?) → hill(s) → turnaround(180° flat turn at low height) → hill → zero-g → helix down → bunny hops → brakes → home. With randomized params & order variations & mirrored (L/R) choices, it feels varied.

I think I'll do a hybrid: a few hand-crafted sequence skeletons with heavy parameter randomization:

T1 "classic out-and-back": lift, drop(yaw 30-60), hill big, turn 150-180, hill, hill(double), zerog?, brakes, home. T2 "twister": lift, drop(yaw 90), helix up? no—drop into turn 90, loop, hill, turn 180, zerog, helix down, hops, brakes. T3 "looping": lift, drop, loop, hill, turn 135, loop?? second loop needs height — only if speed high: place right after drop-loop combo: drop, loop, turn 90, hill mid, dive, turn 180, zerog, helix, hops, brakes.

Fine — 3 templates with randomized parameters and directions; the test suite verifies all. Let me also allow template to abort and retry with different seed internally on any inconsistency (e.g., homing fail, height violations).

Terrain: heightAt(x,z) = 2.5 + 3.2·n2(x,z) where n2 = sum of 2-3 sine-based value noise octaves (use smooth value noise from hash — deterministic). Corridor clamp: dmin over track sample subset (every 4th pt): if d < 18: target ≤ trackHAtNearest − 3.5, blend factor smoothstep(18, 8, d) → h = min(h, mix(h, clampH, f)). Nearest track height per vertex — expensive? Terrain 200x200 verts = 40k × 600 track pts = 24M ops — JS ~ fine (<0.5s). Use spatial coarse: precompute track pts array; simple loop with early break if d>18 quickly via bounding? Just brute force Float32 math; acceptable one-time.

Actually better: build a coarse grid hash of track points for O(1) neighbor lookup. Simpler: since terrain grid is regular, iterate track points and stamp a "clearance field" on a matching-resolution grid (200x200): for each track pt, for cells within 18m, keep min (trackH − 3.5) and max influence... then terrain vertex h = min(baseH, mix(baseH, clearH, f)). Stamping = 600 pts × ~15x15 cells = 135k ops. ✓ fast. Do that.

Trees placement: random pts, reject if |h|<1.2 (water/sand) or clearance-field influenced (dist to track < 12 → field value set) — check stamped field for "nearTrack" mask (separate mask grid). ✓ cheap.

Water at y = 1.0? Base terrain 2.5±3.2 → min ~ −0.7 → some water pools. Water y=0.8. Sand band 0.8-1.8. Grass 1.8-5.5, darker forest floor 5.5+? rock outcrops where slope high. Vertex colors computed in renderer from height+slope. ✓.

OK. Also stats: track length, lift height, max speed (sim), max |g| (sim), # inversions (loops + zerog rolls).

File sizes: core ~700-900 lines; template ~900-1100 lines. Let's write.

Let me write core.mjs now. I'll be careful with details.

Additional details for buildTrack:

Hmm — since my builder integrates with small ds steps (1-2m), the raw points are already dense and fairly uniform! Then I can SKIP Catmull-Rom resampling and just: light smooth (2-3 passes [0.25,0.5,0.25], closed) → re-uniformize by arc length (resample at fixed ds via linear interpolation along polyline) → frames. But sharp transitions between elements (e.g., straight→arc) have curvature discontinuities — the smoothing passes soften them over ~2-3 samples (~3m) — good enough and simple. The previous run used Catmull-Rom + gaussian; my builder's integrated arcs are C1 already (tangent continuous), only curvature steps — smoothing handles. ✓ simpler.

Actually careful: element junctions are C1 (position+tangent continuous) because builder integrates continuously (yaw/pitch change instantly = curvature step, not tangent step). ✓. So: smooth passes 3, resample uniform ds≈0.9m, frames, banking, done.

Curvature limit: check post-smoothing κ = |dT/ds|; require max κ ≤ 1/6 (min radius 6m at loop top where rTop=5-7 → κ≈0.15-0.2 → limit 1/5.5? set min radius 5.5 → κ ≤ 0.18). Test asserts κmax ≤ 0.19. Loop top g: v²·κ... at rTop 6 with v² = g·r·1.3 → g≈1.3+1... fine.

Physics friction: μ such that train completes: losses per lap ~ μg·L ≈ 0.015·9.81·2000 ≈ 294 J/kg ≈ v²/2 → v_loss ~ 24 m/s?? That's too much. Real coaster friction μ ~ 0.002-0.005 effective + drag. Use μ=0.003, cDrag=0.00015 (c·v² at 35 m/s = 0.18 m/s² — ok). Loss per lap ≈ ∮(μg + cv²)ds ≈ 0.003·9.81·2000 + 0.00015·avg(v²~400)·2000 ≈ 59 + 120 = 179 J/kg ≈ 19 m of height. Hmm — that's a lot of height energy (19m). Lift 50m, running heights ~10m → budget 40m − 19 = fine for one lap. ✓ (train only needs to complete ONE lap back to brakes; it does laps by re-dispatch... each lap is identical anyway.)

But careful: friction too high → train can't climb mid-course hills that nearly reach lift height. Keep hill crests ≤ H − 12. Generator enforces headroom = H − currentMax? Just cap hill tops at H − 14. With losses, arrival v at crest: v² = v_drop² ... sim validates.

g-checks: max vertical g at first drop pullout: v²/r. v≈sqrt(2g·42)≈28.7 m/s; r_exit 30 → 2.7g +1g = 3.7 ✓. Keep pullout radii ≥ 25-35 on big drops. Loop bottom: v²/rBot: 28.7²/11 = 75/9.81 = 7.6g — TOO HIGH. So loop must be placed after some speed loss, or rBot bigger, or loop entry higher. Real loops ~ 4-5g max. Options: loop entry at height ~14 (v²=2g(H−14−losses)≈2·9.81·32=628, v≈25), rBot=15 → 4.3g+1 = 5.3g peak briefly. Acceptable (test limit 5.8). Or trim: I'll clamp loop params: choose rBot from entry speed: rBot = v²/(4.3·g) → guarantees ≤ ~5.3g. Similarly rTop chosen so top g ≥ 0.4: v_top² = v² − 2g·loopH; need v_top²/rTop ≥ 0.4g + ... plus loopH ≈ 1.55(rBot+rTop)?? Compute loop height by actually building (builder returns end height = start; top measured from pts). Simpler: build loop with rBot, rTop; verify via sim tests; generator picks from validated combos: rBot = clamp(v_entry²/(4.5g), 9, 18), rTop = rBot·0.45. If sim g fails → seed rejected. ✓.

Zero-g roll: track straight, roll 2π over len 30m at v ~ 20 m/s → roll rate 2π/1.5s ≈ 4.2 rad/s — snappy but ok visually. Make len ∝ v: len = v·2.0s... builder doesn't know v; use design speed estimate at current height: v ≈ sqrt(2g(H − h)·0.92). ✓.

Station: platform length 24m; lift follows immediately.

Lift: pitch 24°, vChain 2.0. Lift time ~ (H−6)/sin24°/2 ≈ 20s for H=50. Fine (demo: add time-scale ×2 option? maybe just leave; anticipation is good. Add "skip lift" via holding FF? Keep simple: timeScale button ×1/×2/×4).

Physics substep dt = 1/240 with frame dt clamp; sim speed × timeScale.

Zones masks: liftMask (from lift base to lift top), brakeMask (brake run), stationMask (closure→platform end). Sim logic:

• if in station && mode != RUNNING: park/dispatch logic.
• mode DISPATCH: while in station and v < 3.5: a += 1.2 (drive tires). Exit station → mode RUN.
• in lift && v < vChain + 0.3: v = max(v, min(vChain, ...)) → set v = vChain (chain catch). Actually smooth: if v < vChain: v = vChain.
• in brake: a += −clamp((v − 3.0)·1.5, 0, 6) (magnetic brakes trim to 3).
• in station (returning): target stop at s0: dist = wrapDist(s, s0); vdes = sqrt(2·1.0·max(dist−0.5,0)); if v > vdes: a += −(v−vdes)·3 − also ensure final stop: if dist < 0.4 && v < 0.3: v=0, mode PARKED, timer 2.5s → DISPATCH. Careful: station entrance speed after brakes = 3 → stopping distance v²/2a = 9/2 = 4.5m — platform 24m long, stop at center: fine.

Lap detection for test: s wraps past s0 with mode RUN→... just track time to return to stationMask with v<... Test: run sim until parked again or timeout 240s. ✓.

g computation in sim at current s (interpolate masks/curvature by nearest sample; also interp U,S).

Now the height profile for homing: homing starts after brakes at height hb (running height 8-12) → target (−25, 0, Y0=6). Descend hb→6 along path with smoothstep. If hb < 6.5 keep flat at hb then tiny dip. Fine. Also homing must avoid crossing under/over the existing track? Visual crossings are FINE (coasters cross themselves; supports everywhere). Clearance test only vs terrain. But mid-air track intersections look bad if rails literally intersect. Chance is low-ish; accept (real coasters have near-misses; exact intersections rare with height differences). Could add check: min 3D distance between homing samples and other track samples (excluding s-neighbors) with different heights... skip; heights along course vary enough. Actually bunny-hop area vs homing both at ~8-10m could collide. Add cheap check: if any homing sample within 2.5m of non-neighbor track sample → reject seed. Cheap: N² over samples (~2000² = 4M, ok one-time in generation? do on resampled ~ every 3rd sample: 700² = 0.5M ✓). Wait — self-proximity also triggers on parallel station/closure segments (homing end near station start by design, 25m apart though) and loop entry/exit (same point in space at different s! Loop entry = exit point exactly). Exclude legit cases: exclude pairs whose 3D distance < 2.5 BUT track directions nearly parallel AND |height diff| < ... hmm loop entry/exit: same point, but tangents are parallel (both going forward) — it's a REAL overlap visually?! No — a vertical loop's entry and exit ARE at the same spot: the track crosses itself, entry passes under the exit?? No: a loop starts at ground, goes up and around, exits continuing forward at ground level AT THE SAME (x,z) but the loop's top is directly above; entry and exit points are the same 3D point only in the ideal clothoid; real coasters offset: exit crosses OVER entry (the track at crossing: entry at ground, exit slightly elevated, crossing at an angle ~ some degrees). In my integrated loop, entry pos = exit pos exactly and tangent identical → the tube would self-intersect along its whole?? No — entry segment and exit segment share only that ONE point; before/after, they diverge (one curving up, one straight). At the shared point they touch exactly. Real loops cross with vertical offset ~4-6m and lateral angle. To emulate: after completing the loop rotation (α=2π), the builder is back at start pos/pitch — I'll add: loops are built slightly "tilted outward": during the loop integration, add a small constant yaw rate (total yaw ~ 25-35° over the loop) — makes it an inclined/offset loop? That changes heading — acceptable (element ends with yaw changed by that amount; generator accounts). Hmm, inclined loop looks cool actually. But then exit height = entry height still? With small yaw the vertical profile barely changes; exit ≈ entry pos but offset laterally by a few m and heading changed ~30°. The crossing then has lateral separation ~2-4m — tubes (r=0.55 half-gauge) won't intersect if lateral offset at crossing > ~1.5m. Let me instead do the classic: keep planar loop but make exit slightly ABOVE entry by ending with tiny positive pitch bump? Complicates.

Simplest: give the loop a deliberate lateral drift: during integration, yaw(t) = yawRate·sin(α(t))? Net heading change zero but path S-curves laterally by a couple meters, so exit is parallel-offset from entry by ~2-3m: clean crossing without heading change! yaw(α) = k·sin(α) → ∫yaw... net Δheading = ∫k sinα dα·(ds/dα)... hmm ds varies with r(α). Whatever — numerically integrate: per step, yawRate = k·sin(α)·? and choose k so total lateral offset 2.5m. Just try k = 0.02 rad/m at α=π/2... Let me not over-plan: implement with k parameter, measure in test (min self-distance at loop crossing > 1.2m), tune once. Total Δheading = ∫ k sinα ds — with ds = r dα: ∫0..2π k sinα r(α) dα = k·[−cos·avg] = 0 exactly? sinα over full period with symmetric r(α) (symmetric about π): ∫0..2π sinα·r(α)dα = 0 (r symmetric, sin antisymmetric about π). YES net heading change = 0. ✓ Lateral offset = ∫∫ ... nonzero ( k·something).

Similarly zero-g roll: track straight — no self-intersection issue.

OK also homing vs track proximity: test with exclusion of s-neighbors (|i−j| (circular) > 30 samples) AND exclusion of loop-crossing pairs? Loop crossing min distance ~2.5 by design; set global threshold 1.6m and accept loop crossing if > 1.6. Tune k to achieve ~2.5m offset. Homing must then also respect 1.6m from everything — including its own approach near station: station approach is colinear with station, 25m gap, fine.

Alright, writing code now. Also decide visual style name/branding: "COASTERWORKS — Procedural Roller Coaster Foundry". Palette: warm sunset? Golden-hour lighting (low sun, warm) with orange rails + teal supports? Sunset scenes look great with bloom. Sky gradient orange→purple, sun low. Let's do golden hour. Fog warm haze.

Let me write core.mjs.

Sampling: step along: seg1 arc dir (mode[0]=='L'?+1:−1) angle t; seg2 straight p·R; seg3 arc dir mode[2] angle q. Integrate with the same heading-stepper.

Builder: I'll make the builder 3D (x,y,z,yaw,pitch) and Dubins gives 2D which builder appends with height profile.

TrackBuilder:

Coordinate convention: yaw=0 heading +X; yaw increases turning LEFT (toward +Z? or −Z?). Define forward = [cos(yaw)·cos(pitch), sin(pitch), sin(yaw)·cos(pitch)]? With yaw measured from +X toward +Z. Turn "left" = +yaw = toward +Z. In three.js XZ plane with −Z forward default... doesn't matter, self-consistent. Left = +Z side. OK.

Hmm wait: entry arc drops rIn(1−cos pMax): check formula Δh = r(cos p1 − cos p0) with p0=0 → p1=−pMax: r(cos(−pMax) − cos0) = r(cos pMax − 1) = −r(1−cos pMax) ✓ drop of r(1−cos pMax).

Post-build: keys = pts (they're dense already). Zones as anchor pairs → masks after resample.

Then:

vDesign: needs lift top height & chain speed: compute from track: hmax = max height (should be lift top); v²(s) = vChain² + 2g(hmax − h(s))·efficiency... use exact-ish: v² = max(vChain², vChain² + 2g·(hmax − h)·0.97 − μg·distanceSinceTop?). Keep simple: v² = vChain² + 2g(hmax − h(s))·0.95. Clamp min 4. Fine for banking.

Rolls: each roll event: find idx of anchor pt; span = len/ds samples; ψ_add(s) = 2π·smoothRamp(progress) with smoothRamp = smootherstep at both ends (ramp in over 15%, hold linear middle, ramp out — actually zero-g roll: ψ goes 0→2π monotonic; use profile: ψ(t)=2π·(t − sin(2πt)/(2π))? that's smooth-in-out (0 slope ends). ✓ add ψ_add. Also banking smoothing window must not smear the roll transition at boundaries — roll added AFTER smoothing banking. ✓

Also bank the BRAKES and station 0 — banking target there ≈0 naturally.

Station/lift: banking 0 (straight). ✓

Now generateLayout(seed):

tryLayout(rng): pick template 0..2, build with params. Includes station(24), lift(H=46+rng·18), drop, elements..., brakes, home. Home: dubins from current pos/yaw to (−26, z=0? target = (−26,0) yaw 0 with heights → station height Y0=6; but current height ~8-12; height profile along homing length: smoothstep from hb→6 over middle 60%. Dubins R: try [26,22,18,14,11] until sol. If fail → null. Also reject if total homing crosses station... fine.

Also I realize the homing target: (−26, 0) with yaw 0; but pts[0] = (0,Y0,0) and first element station straight +X. Closed resample connects last pt (−26..) to (0..): straight gap 26m — wait the LAST homing point is AT (−26,0) exactly and first is (0,0); resample fills between ✓. But smoothing at closure blends last pts with first pts — both colinear along X ✓ no distortion.

Station zone anchors: a=(−20,Y0,0)?? anchor must be NEAR actual samples: (−20,...) lies between last homing pt (−26) and (0): samples exist there after resample ✓. b=(24·0.95... let me mark station END anchor exactly at builder pos after station straight (24, Y0, 0) — that's also lift base. Zone

****************************************************************************************************er.

I'm at 61% of time budget already?! That's concerning. The status shows timeProgress 0.6166 — I've used over half the time. I need to move fast.

Wait, that's probably because the wake-up task started when the conversation began. Let me hurry. Priorities:

1. Get a WORKING demo rather than a perfect one.
2. Write test.mjs, run, fix critical issues quickly (maybe 1-2 iterations).
3. Write template.html + build, quick syntax check.
4. Deploy to /space and update index.

Let me write the test file now and run it immediately.

**********************************************************************************************************************ls.

Multiple issues:

1. minY -5.91 — track goes below ground. The homing height profile descends to Y0=6... minY of -5.91 is way below. Where? The while (runningH() > 14) doHelix(true) — helix dhTot up to -12 per helix; but if runningH is 15 and helix dh is -12 → ends at 3! Then more helices → even lower. Bug: dh magnitude must be capped by available height. Also template 1/2 call doHelix(true) with dh -6..-12 possibly from height ~12 → 0. Need: cap dh so end height ≥ 8.

2. maxGv 8.47 — too high. Loop sizing: rBot = v2/(4.6G) where v2 = 2G(H-h)*0.9 — the g at bottom = v²/r + 1 = 4.6·(v_actual²/v2)+1... v_actual² is bigger than my v2 estimate (I used 0.9 factor but actual has less loss). Let me use v2 = 2G(H-h) exactly (no 0.9) and divisor 4.2 → g ≈ 4.2+1 = 5.2. Also smoothing shrinks radius → higher κ → higher g. Keep margin: target 3.8 divisor. Also drop exit radius: rOut 30-45 gives g = 1 + v²/rOut: v²≈2·9.81·40=785, /30=26 → 2.7+1=3.7 fine.

3. maxGlat 9.36 — huge lateral g. Banking not working! Why? Lateral g computed with frames Uf/Sf from banking. Banking uses vDes2 design speed. Massive lateral suggests the banking smoothing (box blur over ±8 samples ≈ ±6.8m) is far too weak to handle: banking transitions need ~2-3s of travel... but more importantly, wait — lateral 9g means banking is basically absent or mis-signed. Let me check: in a flat left turn (turning toward +Z, dir=+1, yawRate>0), curvature vector K points toward center of circle = to the LEFT of travel. Specific force a = v²K − G: a·S0 where S0 = T×U... let me verify sign conventions: S = cross(T, U) — with T=+X, U=+Y: cross([1,0,0],[0,1,0]) = [0·0−0·1, 0·0−1·0, 1·1−0·0] = [0,0,1] = +Z. Hmm — in Three.js, right vector should be T×U? If T=forward(+X) and U=up(+Y), then right = forward×up = +X×+Y=+Z. In a LEFT turn toward +Z, center is at +Z side; K points +Z; a·S = v²κ > 0 → ψ = atan2(+lat, ver) > 0 → rotates U toward S (i.e., up tilts toward +Z, into the turn). Correct!

But the sim: maybe banking psi gets smoothed to near zero because turns are short (80-170° at r=15-28 → length 20-75m) vs smoothing window ±6.8m — shouldn't kill it.

Wait, actually — the bug might be in the sim's lateral measurement vs the frames after banking... Let me debug numerically: find where maxGlat occurs and check psi there. Actually — hold on. I bet the issue is helix2 replaced twice (my file has TWO definitions of helix2 — the second overrides; fine) — but helix() and helixSmooth() are broken stubs — helix calls this._helixPitchFix which doesn't exist → would throw. But doHelix calls helix2, not helix. OK.

Let me check applyBanking more carefully: I rotate U by ψ: Uf = U·cosψ + S·sinψ. If rider in left turn needs up tilted toward +S (left, into center), ψ>0 gives Uf tilting toward +S. Specific force in new frame: lat' = a·Sf. Sf = cross(T, Uf) = cross(T, Uc+Ss)... For small ψ: Sf ≈ S − ψU. a·Sf ≈ a·S − ψ(a·U) = lat − ψ·ver. Set to zero: ψ = lat/ver ≈ atan2 ✓. So convention right.

Hmm, so why 9.36 g lateral? Something else. Maybe the helix2: pitch ramps but yawRate constant — no. Or... the TURN function in tryLayout: I set b.pitch = atan2(dh,len) instantly (pitch jump) then integrate, then set back to 0 instantly — pitch jumps create kinks but not lateral g.

Wait — maybe it's the LOOP: lateral g during loop due to lateralK S-drift yaw! The yaw rate = lateralK·sin(ang) with lateralK=0.017 rad/m at speed v≈25 m/s → lateral accel = v²·yawRate = 625·0.017 = 10.6 m/s² ≈ 1.1g — not 9.

Let me actually instrument: where does maxGlat occur, and what is psi there vs ideal. Quick debug.

Two problems visible:

1. The worst lateral is at h 0.1 — track at height 0.1m?! That's the height bug (track dives to ground). At h=0.1, design speed v² = 2·9.81·(H−0.1)·0.95 is max — and kappa 0.106 there. The banking ψ=62° but lateral still 10g?? With ψ=62 banked and κ=0.106... v²·κ with v²≈2·9.81·(55−0)·0.95≈1024, κ=0.106 → 108 m/s² ≈ 11g lateral demand, banking only compensates partially (bank 62° → residual = a_lat·cosψ...). So the kappa is too high (r=9.4m) at high speed. This is likely in a helix at ground level (helix radius 15-24 → κ = 0.042-0.067... but 0.106? That's r≈9.4 — the loop? or smoothing-shrunk turn). Also the height bug: track nearly at ground → the "while runningH > 14 doHelix" overshoot below zero.

2. The sample turn: ψ ≈ −100° (clamped) with κ=0.06 at h≈9: v²=2·9.81·(55−9)·0.95≈857, v²κ=51.4 m/s²=5.2g lateral demand → ψ = atan2(5.2g, 1g)=79°... but ψ shows −100°?! Sign/overshoot: psi clamped at ±100°, meaning demand is huge. atan2(lat,ver) with lat≈5.2g, ver≈1g → 79°. Why −100? Maybe the turn is banked the wrong way due to parallel-transport frame orientation in a descending turn... or ver < 0? In a turn at κ=0.06 with... hmm.

Wait, actually: the turn radii are too tight for the speeds. κ=0.06 → r=16.7m at v≈29 m/s → 5.2g lateral demand — banking to 79° is extreme; combined with vertical the rider feels 5.3g total but laterally zero. That's how hypercoasters do overbanked turns — actually fine! Real coasters DO bank ~80° in fast turns. But my clamp 100° and smoothing... The residual lateral in the sample: worst.lat printed at i=802 only. Let me compute residual lat in that turn... I printed psi but not residual. The worst residual 10.45g at i=802 (h=0.1, the ground-hugging bug). So maybe the turns are fine and the real problem is the height bug creating a tight-radius section at ground level.

So primary fixes:

1. Height budget: cap helix dh by available height; keep runningH ≥ 8. In doHelix(true): dh = −min(R(6,12), runningH()−8.5). Same for the "burn" loop — with cap it converges. Also if (runningH() > 11) b.drop(35, runningH()−9.5...) — dh up to runningH−9.5 → ends at 9.5 ✓ but drop pMax 35° — shallow; fine. But brakes(30) flat then homing descends 9.5→6 ✓ minY ≈ 6 after smoothing ✓.

Wait but where did h=0.1 come from? doHelix dh=−12 from h=13 → 1m, then another doHelix dh −12 → −11m?? The burn loop: while (runningH() > 14) doHelix(true) — if runningH=15, one helix dh −12 → 3; loop exits (3 < 14). minY=3?? But measured 0.1 — plus template helix before. Anyway, capping fixes it.

2. Loop lateral from S-drift: reduce lateralK to ~0.010 and rely on crossing offset ~2m? offset = ∫∫... let me just test with 0.012. Actually offset distance: yaw(t) = ∫k sin(α) ds; lateral = ∫ sin(yaw(t)) ds ≈ ∫ yaw ds for small yaw. Rough estimate: mid-loop yaw ≈ k·∫0^π sinα r dα ≈ k·2·r̄ ≈ 0.017·2·11 = 0.37 rad — that's 21°! Too much. lateral offset ≈ ∫ yaw ds over second half ≈ 0.37·avg... several meters but also heading error? No — net heading 0 as computed. Max mid-loop heading deviation 21° is a LOT (loop visibly corkscrews). Reduce lateralK to 0.008 → mid deviation ~10°, offset ~1.5-2m. Lateral accel v²·k = 625·0.008 = 5 m/s² = 0.5g at loop bottom — acceptable-ish; banking can't compensate during loop (banking is for horizontal turns; the ψ from atan2 in the loop region is garbage anyway). Set lateralK = 0.008 and accept crossing offset ~1.5m vs self-intersection threshold 1.55m... conflict. Hmm.

   Alternative: make the loop non-planar via height offset: exit the loop slightly higher than entry (like real loops where exit crosses over entry by ~4m)! Implement: during the loop, add a slow pitch bias... complex.

   Simplest robust: after the loop completes at entry point, immediately add a small "hop" (pitch up 6° then back) so the exit passes ABOVE the entry by ~3-4m, crossing laterally offset... no wait — entry and exit are the same point; the crossing point is where exit passes over the entry TRACK. The entry track near the loop base is roughly straight (the approach); the exit leaves the loop at the same point continuing forward. So near the base, entry approach and exit overlap along a segment?! No: entry approach ends AT the loop base; exit starts AT loop base going forward. They share only the base point. The exit then continues forward, passing through where the loop's vertical plane is... The self-intersection risk: the loop's top is directly above its base; samples at the top (h≈base+20m) vs base — far apart vertically, fine. The only near-contact is exit-point == entry-point exactly. After smoothing, both get pulled slightly — the closed-loop polyline has TWO points near the base (entry idx i, exit idx j), distance ~0. My self-intersection test (threshold 1.55m) would FAIL at the loop crossing! And physically the rails would touch.

   Real solution: offset the loop exit laterally by ~3m with the S-drift (my current approach) — then entry/exit base points differ by ~3m. So lateralK must produce ≥2.5m offset while keeping mid-loop heading excursion & lateral g modest. k=0.008: offset? Let me just measure in debug. Target offset 2.5-3.5m. I'll tune k once empirically.

3. Vertical g 8.47: loop bottom too tight / too fast. Fix loop sizing: rBot = v2/(3.9·G) with v2 = 2·G·(H−h)·0.97 (less conservative discount), clamp [11, 20]. Then bottom g ≈ 1+3.9 ≈ 4.9 with margin for smoothing shrink. Also drop exit rOut min 35.

Also fix doTurn — remove the weird dead code b.turn ? null : null; and the instant pitch jumps (set pitch via ramp or just keep pitch 0 and accept flat turns; slight dh via pitch = atan2 small — instant pitch set of ~2-3° is a small kink, smoothing handles; but pitch reset to 0 at end another kink — fine after smoothing). Actually simpler: keep turns flat (dh=0). Banking handles comfort; pacing via helices/hills.

4. Also the maxGv 8.47 in sim could partly come from the ground-bug region (v huge at h≈0). Fix heights first, then re-measure.

Also loop placement: templates call doLoop when runningH() < 26. After first drop ending at ~9-12m, v² = 2G(H−10)·0.97 ≈ 2·9.81·45·0.97 ≈ 856 → rBot = 856/(3.9·9.81) = 22.4 → clamp 20. Loop top ≈ 2·(rBot+rTop)... height of clothoid loop ≈ ∫sin... roughly 1.5·(rBot+rTop) ≈ 1.5·29 = 43m from base 10 → top at 53 > H=55?? marginal! v_top² = 856 − 2·9.81·43 ≈ 13 → v_top ≈ 3.6 m/s — nearly stalls, and top g ≈ v²/rTop − 1 ≈ 13/9 − 1 ≈ 0.44 — barely positive. Too tight. Make rBot = clamp(v2/(4.2G), 10, 15) and require H ≥ 50 for loop else skip; rTop = 0.45 rBot → top h ≈ 1.5·(1.45·rBot) ≈ 2.2·rBot... for rBot 13: top ≈ 10+28 = 38. v_top² = 856−2·9.81·28 = 306 → top g = 306/(0.45·13·9.81)... wait g_top = v²/r /G − 1 = (306/5.85)/9.81−1 = 5.3−1?? No: 306/5.85 = 52 m/s² = 5.3g +... that's wrong too. Hmm: 306/5.85 = 52.3 m/s² ≈ 5.3g at TOP?! That means way too fast at top → loop radius at top too small. rTop = 0.45·13 = 5.85m → κ=0.17 huge. Real loop tops ~ 1g. So rTop shouldn't be that small relative to speed. Classic clothoid: rTop ≈ rBot/2 with v_top² = v²/5 roughly... Let me instead size by top g: want top g ≈ 0.8-1.5: rTop = v_top²/(1.8·G). And v_top² = v² − 2G·loopH where loopH ≈ depends on shape... circular approx: loopH = 2·r̄ where r̄ = (rBot+rTop)/2·(adjust). Iterative: guess loopH = rBot + rTop... I'll do numeric: after building, measure actual top height and actual v from physics — but sizing needed BEFORE building. Do a two-pass: build loop with initial guess, measure top height from pts, compute v_top, check top g ∈ [0.5, 2.0] and bottom g ≤ 5.2; if out of range, adjust rTop/rBot and REBUILD the loop (builder can pop points: record pts length & state before loop, restore on retry). Implement b.mark() / b.restore(mark) then loop sizing loop (≤4 iterations). Deterministic, robust.

Let me implement:

• TrackBuilder.mark() returns {ptsLen, p, yaw, pitch}; restore(m) truncates pts and restores state.
• doLoop: v2 = 2G(H − h)·0.97 (design). Iteration: rBot given (from bottom g target 4.2: rBot = v2/(4.2G) clamp [11,17]); rTop guess 0.5 rBot. Build loop; find top height (max y in added range) → vTop2 = max(v2·0.94 − 2G·(topH − h), 4); topG = vTop2/rTop/G − 1 (approx, ignoring smoothing); if topG > 1.8 → rTop *= 1.15 retry; if topG < 0.5 → rTop *= 0.9 retry (but keep rTop ≥ 6 for κ limit... rTop 6 → κ 0.167 < 0.2 ✓). Max 4 tries then accept last.

Note: loop bottom g: v²/rBot/G + 1 with smoothing shrink ~ +15% → 4.2·1.15+1 ≈ 5.8 — borderline vs test limit 5.8. Use target 3.6: rBot = v2/(3.6G), clamp [12,18]. bottom g ≈ 1+3.6·1.15 ≈ 5.1 ✓. Loop taller though (rBot up to 18 → loopH ~ 40m) → require H − h ≥ 42 → only right after big drops when H ~ 55-62: H−10 = 45-52 ✓. Template guard: runningH() < 14 AND H ≥ 52 for loop; else skip loops. Hmm — but H = 46-62 random; for H < 52 no loops at all. Fine: loops only on tall coasters — realistic! Template 2 ("looper") forces H = R(56, 66) so loops fit.

Let me also reconsider: for rBot = 18, loop top ≈ base + 2.2·18 ≈ 10 + 40 = 50, H = 62 → vTop2 = 2·9.81·52·0.94 − 2·9.81·40 ≈ 958 − 785 = 173 → rTop = 173/(1.8·9.81) = 9.8. top g = 0.8 ✓.

5. Banking clamp: allow up to 100° but ALSO the smoothing window ±8 samples (~7m) over a 25m turn smears edges — acceptable. The 9.36 lateral was probably the ground bug. Re-test after fixes.

6. Also minGv −1.6: over hills (airtime) — fine (target −1.9 limit). Real ejector air −1.5 is intense but demo-ok. Actually −1.6 with design... fine, keep limit −1.9.

7. maxGlat sim = 9.36 — after fixes re-measure. If still high in turns, it means banking ψ lags reality because vDes² differs from actual v². I used 0.95 factor; sim friction μ=0.0035 gives more loss... vDes slightly overestimates → over-banking → small residual. 9g is structural though — likely the h≈0 spot. Fix and see.

Also fix: the sim's g sampling included 'dispatch' mode (v<3.6, minor). fine.

Also potential problem: homeTo overrides y of integrated points but the SMOOTHING + resample then shift things slightly; closure at (−26,Y0,0)→(0,Y0,0) ✓.

And the zone mapping for 'station' span from b.station: anchors a=(0,Y0,0), b=(26,Y0,0); plus extra span from iHome(−26) to iStatEnd+2 — iStatEnd = nearest to (26,Y0,0) — same as zone b. OK redundant but fine.

One more: tryLayout templates call doLoop guarded by runningH() < 26 — replace with the smarter guard. Also remove helixSmooth/helix/_helixRest dead/broken code and the duplicate helix2 definitions (keep the correct one). Clean up.

Let me rewrite the layout section of core.mjs with these fixes:

• TrackBuilder: add mark/restore.
• Replace loop() to accept rTop and return metrics {topH}.
• doLoop with retry sizing.
• doHelix with height cap.
• doTurn flat, no pitch hacks.
• templates with guards.
• burn loop cap.

I'll rewrite core.mjs sections via targeted replacements. Actually given the number of edits, rewrite the whole file cleanly. Faster to write fresh with fixes incorporated.

CRITICAL: I'm at 92% of time budget! I need to wrap up NOW. The demo isn't finished — core isn't passing tests and I haven't built the HTML template.

I need to make an emergency decision. Options:

1. Rush to finish the coaster (risky — core still fails all seeds, no time to debug + build template + deploy).
2. Pivot: deploy a SIMPLER but still impressive coaster demo quickly — skip the node test iteration, hand-craft ONE fixed good coaster layout (predefined element sequence with known-good parameters), build the Three.js renderer, deploy.

Actually — wait. Let me reconsider time. 92% used. I have maybe a few minutes. The task says "Wake up and do as you please" — the previous turn was 048-coasterworks which ended "idle/success" but never deployed anything. The demos folder has no 048.

Priority NOW: get SOMETHING deployed, or at least leave the space in a consistent state. If I can't finish the coaster, I shouldn't leave a broken demo.

Emergency plan (fastest path to a complete, impressive demo):

• Write a single self-contained index.html for 048-coasterworks with a HAND-DESIGNED track: I can define a coaster via a closed Catmull-Rom curve with control points I design inline, compute parallel transport frames, rails/ties/supports, a train animated along the curve with simple energy physics (v from height: v = sqrt(2g(hmax−h)·k) + min speed), POV/orbit/follow cameras, terrain, bloom. No procedural generation, no node tests — deterministic and achievable in one shot.

But honestly writing a full polished 1000-line HTML file plus debugging takes longer than the remaining time. Still, I must try — a simpler-but-complete demo is the goal. I'll write a compact but still impressive version: ~600 lines.

Actually, let me be even more pragmatic: the biggest risk is running out of time mid-write leaving NOTHING deployed. Strategy: write the demo HTML directly to /space in ONE write operation (complete file), then update index.html quickly. Skip testing except a node syntax check of the script portion if time permits.

Design a fixed track: I'll generate control points procedurally in the browser (simple closed loop: lift hill, drop, 2 hills, turnaround, helix, brake run — laid out as ~40 control points computed from a small parametric script), CatmullRomCurve3 closed, sample 800 points, parallel transport frames, banked by curvature·speed heuristic, two rail tubes + instanced ties + supports to ground, train of 5 cars, physics = energy-based speed profile with chain lift on the lift section (identify lift as the rising section before max height — simpler: define speed profile v(s) = max over closure... just compute v² = vmax² − 2g(h − hmin)... v = sqrt(max(vmin², 2g(hmax−h)·0.92)); that gives plausible pacing; on lift section force v=2.5. Identify lift samples by zone: from station end index to index of max height. I'll parametrize by index fraction since I generate the points myself: I know which control points are the lift. Track cumulative arc length at control points to define zones.

Simplify further: physics profile v(s) computed once (with lift clamp), train moves with v varying along s: ds/dt = v(s) — smooth, plausible, no integration needed. G-force estimate for HUD: v²κ vertical ±.

Cameras: ride POV / follow / orbit. Bloom + vignette. Terrain with corridor flattening (simple: flatten near track samples via distance to coarse track grid — or skip flattening, keep terrain gentle amp 2.5 and track min height 8 with supports; visual overlap risk low). Golden-hour sky, fog, water plane, instanced trees avoiding track (distance check to track samples, coarse loop), station platform + canopy, UI with stats + g-meter + speed, camera buttons, audio: wind noise ∝ v + lift clack — minimal WebAudio.

This is doable in one big file. Let me write it NOW, fast, directly to /space. Then update the index, then finish.

Track layout (control points, y=height, ground≈2-4): Let me design in XZ with heights, a loop roughly 260m x 160m:

station: (0,8,0) → (30,8,0) heading +X lift: (55,14,0), (85,30,0), (110,48,0) crest first drop w/ right turn: (135,20,8), (150,10,25) hill 1: (165,22,45) over... let me lay out a rough circuit clockwise: (0,8,0),(30,8,0) station (55,15,0),(85,32,0),(110,50,0) lift crest (135,18,10) drop (155,9,28) pullout (178,20,52) hill crest (camelback) (200,9,80) dive (215,8,110) low straight (205,10,145) turn left 180 start... turnaround: (180,12,165),(150,14,150),(135,16,120) sweeping left zero-g-ish straight: (120,12,90) with roll applied over it (flag in code) hill: (100,24,60) dive: (80,9,40) helix down left: (55,9,60),(35,8,85),(45,8,115) hmm helix = 360+ turn: (60,14,95),(45,9,120),(20,8,110),(15,8,80),(40,8,65) — a full circle roughly centered (35,90) r~25. brakes: (10,8,40),(-10,8,15) back to station: (-20,8,-5) → close to (0,8,0).

Closed Catmull-Rom through these ~30 points. Curvature might be tight in spots — acceptable visually; banking computed from curvature will handle. Since v(s) is design-profile-based, no stall issues: v = sqrt(max(9, 2·9.81·(50−h)·0.9)) and lift zone clamp v=2.5 between station end and crest.

Heights: min 8 > terrain max ~5 ✓ no flattening needed if terrain amp small. Terrain: h = 2.5 + 2.5·fbm ∈ [0,5] with water at 0.8. Track min 8 → supports 3-8m tall. ✓

Roll element: pick s-range on the straight after turnaround: apply banking roll 0→2π there explicitly.

Banking elsewhere: ψ = atan2(v²·κ_h, g) computed per sample from frames, smoothed.

Train: 6 cars spaced 2.2m, each oriented by frame at its s; simple car mesh (box + nose + wheels skip). POV at car 0 front.

g-meter: vertical g = (v²·κ_vert + g·cos(pitch-ish))/g approx via frames: gv = dot(v²K−G, U)/g.

Audio: white noise → lowpass, gain ∝ v²; clack timer in lift zone. Start overlay unlocks audio. Keep tiny.

UI: title, stats (length, height, max speed), live speed + g, buttons: camera mode (RIDE/FOLLOW/ORBIT), regenerate? NO — fixed layout (skip seed). Actually "new layout" button could re-run with different control-point jitter — risky; skip, fixed masterpiece + it's fine for the demo. Hmm the demo is named coasterworks — procedural was the point, but given time, a beautiful fixed-layout coaster is acceptable. I can add small seed jitter to control points (±3m horizontal, ±2m vertical) with a few seeds — low risk since Catmull-Rom stays smooth. I'll add jitter seeded regenerate — but must ensure no craziness; jitter small → safe.

Supports: every ~7m sample, if track y − terrain > 2.5: cylinder from track to terrain + footer box. Also station/lift structure fine.

Ties: every ~0.8m instanced box 1.6×0.06×0.14 oriented with S direction, positioned slightly below rail center (−0.12 along U).

Rails: offset ±0.55·S, CatmullRom through offset pts (closed), TubeGeometry radius 0.07, 8 radial segs, tubularSegments ~1200. Two tubes ~ 1200·8·2 = manageable. Plus center spine tube radius 0.12? skip.

Trees: 500 attempts, accept if terrain h > 1.4 and min dist to track samples (stride 4) > 12. Instanced cones + trunks.

Rocks: 120, h<1.5 or slopes, instanced dodecahedron, gray.

Water: plane y=0.75, MeshStandardMaterial color #2a5a7a transparent 0.8 roughness 0.15 metalness 0.6.

Sky: big sphere ShaderMaterial gradient (top #2b3a67 → horizon #ff9a56 warm sunset), sun sprite glow. Fog #d9a06b-ish exp2 0.0035.

Lights: DirectionalLight warm (#ffd9a0, 2.2) low angle with shadows (map 2048, camera box 260), hemisphere light (#8fb4ff/#5a4632, 0.5).

Post: EffectComposer, bloom 0.35/0.7/0.85, vignette.

Train position update: sHead advances by v(s)·dt; per car k: sCar = sHead − k·2.3; set pos = pt + U·0.9? car sits ON track: pos = pt + Uf·0.5, orient via Matrix4.makeBasis(S, U, Tneg?) — build basis (right S, up U, forward T) → quaternion.

POV: pos = car0pos + U·1.1 + T·0.4; lookAt pos + T·10 + U·(banked up) — set camera.up = Uf, lookAt ahead. Add slight shake ∝ v²κ.

FOLLOW: camera lerps to pos = trainCenter − T·14 + U·7 (use smoothed), lookAt train.

ORBIT: OrbitControls target (60,10,70)-ish center.

HUD: speed km/h big, g vertical with color, layout stats top-right, camera buttons bottom-right, hint bottom. Overlay start: "COASTERWORKS — click to ride". Also g-meter canvas bar? Keep DOM simple: vertical bar div.

Time scale: buttons ×1 ×2 ×4.

OK writing the file NOW — one shot, careful with syntax. Then quick node --check by extracting module script (strip import lines via a stub? node --check parses ESM if file .mjs with imports — but imports of 'three' fine for parse). I'll extract script → /tmp/x.mjs → node --check. Then deploy + update index. GO.

Still 93%. I have maybe ~5-6 min of wall clock budget. The HTML file is big (~700 lines). A single write operation is atomic, so writing it takes one call. Then index update + a syntax check. Let me write it as compact as possible while still complete and working. I must be extremely careful with syntax — no time for debugging iterations.

Let me write the file now. I'll keep it tight but complete. Careful points:

• import map + module script
• All three.js API usage must be r160-correct: THREE.CatmullRomCurve3(points, closed), TubeGeometry(curve, tubularSegments, radius, radialSegments, closed), InstancedMesh, EffectComposer/RenderPass/UnrealBloomPass/OutputPass, OrbitControls.
• makeBasis: Matrix4().makeBasis(xAxis, yAxis, zAxis) sets rotation columns.
• For quaternion from basis: obj.quaternion.setFromRotationMatrix(m).

Write it.