strandbeest_linkage_validation

The task is "Wake up and do as you please." Based on the context, I'm in a batch mode where my purpose is to create cool Three.js demos in /space/demos/. The last execution created Demo 065 "Rosewindow". Now I should create Demo 066.

Let me first install shell tools and check the current state of the demos folder.

Let me check the current state of the demos folder to confirm what's there.

Good. The state is as expected: 65 demos exist, all indexed. I need to create Demo 066. Let me look at one recent demo briefly to see the general style/conventions used (import maps, etc.), then design a new demo.

Let me check Demo 065's structure briefly.

The demos use Three.js r160 from unpkg with import maps. Now I need to design Demo 066. Let me think of a fresh concept not covered by existing demos:

Existing demos include: spinning cube, nebula galaxy, mandelbrot, fluid dynamics, gravity sandbox, event horizon, sonic reactor, void runner, azure odyssey, abyssal bloom, physarum, powder, clockwork nebula, neon rain, aurora, skitter, coral, threshold, attractorium, murmuration, terraforge, cloudsea, frostline, koi pond, ferrofluid, synchrony, cymatics, teslasphere, pyrosymphony, morphogenesis, galton cascade, wavefront, gossamer, magnetosphere, cloud chamber, wavefunction, epicycle, sandpile, kinetic theory, lumen lab, squish lab, neon tilt, hyperfold, photon garden, critical point, bridge works, primordial, coasterworks, sakura grove, voxelia, neon district, supercell, caldera, domino rally, phantom jam, wavewalker, basin, microcosm, zoetrope, spume, klangwerk, echodeep, cinderforge, skyward, rosewindow.

Ideas for Demo 066:

1. Tidal Locked — an orbital mechanics piece with a planet/moon, tidal forces.
2. Origami / Paper folding — procedural origami crane folding animation.
3. Bioluminescent deep sea creature swarm — covered somewhat by abyssal bloom/echodeep.
4. Lightning storm / plasma — teslasphere covers some.
5. Mycelium network / fungi growth — somewhat physarum.
6. Clockwork / mechanical orrery with gears — clockwork nebula, epicycle exist.
7. Rain on a window with droplets shader — nice screensaver style. "Rainglass" — droplets on a window pane refracting a city bokeh behind. Very visual, doable with GLSL: procedural droplets that grow, merge, and slide down, refracting a blurred neon cityscape. That's a classic impressive shader demo. Interactive: mouse heat/fog, wipe with mouse.
8. Blacksmith forge — cinderforge covers fire/metal.
9. Sailing / ocean buoy sim — wavewalker/spume/cloudsea cover water.
10. Paper lantern festival at night — floating lanterns with flame flicker, heat physics, reflections on a lake. Gorgeous and fun: spawn lanterns by clicking, watch them rise with turbulence, glow via bloom-ish sprites. Lantern rise with realistic buoyancy + wind field, water reflection. That's fresh — no lantern demo yet. Call it "Skyharbour"? Or "Emberfall" (falling embers). Or "Gloaming" — dusk lantern festival.

Let me check what "Skyward" was (064) to avoid overlap — it was about...? Let me peek quickly at a couple recent demos to avoid duplicates.

Actually, from summaries in previous runs: 064 Skyward — probably about ascending/balloons? Let me check quickly.

I'll grep the meta description of a few recent demos.

Ah — 064 Skyward is already the lantern festival! So that idea is taken. I need something fresh.

Ideas not yet covered:

1. Rainglass — rain droplets on a window pane refracting a neon city bokeh at night, with fog/condensation the user can wipe with the mouse. Droplets grow, merge, wobble, and streak down. Classic gorgeous shader demo. Not covered yet (neon rain was rain falling through a city in 3D, presumably). This is a strong candidate: advanced GLSL (procedural droplet normal fields, refraction, blur-by-mipmap tricks), interactivity (wipe condensation, tap to add drops), audio (rain patter + thunder), adaptive quality.

2. Origami — procedural paper folding. Complex.

3. Mycelium / bioluminescent fungi forest — growth simulation. Somewhat overlaps physarum/morphogenesis.

4. Tide pools / ripples — overlaps water.

5. Astrolabe / orrery — overlaps epicycle/clockwork.

6. Fireflies in a jar / forest — bioluminescence overlaps abyssal bloom maybe. But firefly synchronization overlaps "synchrony" (which was probably about coupled oscillators).

7. Lightning forest / thunderstorm over plains — overlaps supercell probably.

8. Ink in water (3D fluid) — overlaps fluid dynamics.

9. Crystal growth / snowflakes — frostline might cover frost. Let me check frostline... "Frostline" likely frost crystals on glass. Hmm, that may overlap with the rainglass idea's condensation aspect but the droplet refraction city is distinct enough.

Let me check what 014-neon-rain and 023-frostline are about to be safe.

****************************************************************************************************************************************************************************fe.

Frostline is a "winter window" — that might be close to a condensation-window idea, though frost crystals ≠ rain droplets. Let me quickly peek at frostline's description/content to be sure there's enough differentiation. Actually, the difference between frost crystal growth (ice dendrites) and rain droplets with refraction of city bokeh is significant, and rain on glass is a distinct classic. But to be safe and maximally creative, maybe I should pick a different theme entirely.

Other ideas:

1. Deep-sea hydrothermal vent ecosystem — black smokers, tube worms, bioluminescent particles, sonar. Overlaps echodeep (sonar cavern) and abyssal bloom (deep sea creature).
2. Paper theater / shadow puppetry — silhouette cut-out art with layers (parallax), dynamic lighting. "Shadowbox" — a layered paper diorama with a movable light casting real shadows, silhouette mountains, animals. That's unique and artistic! Uses Three.js ortho or perspective, layers of extruded silhouettes, a draggable sun/moon that casts long shadows, flickering candle mode. Very pretty.
3. Trebuchet / siege physics — bridge works and domino rally cover physics.
4. Ant colony / termite cathedral builder — agent-based pheromone sim building structures. Physarum covers slime mold.
5. Star trail / long exposure night sky photographer — take long exposures, star trails form. Meh.
6. Glassblowing workshop — molten glass blob on a pipe that you shape by blowing (mic?) and spinning. Fun but hard to model well.
7. Dandelion / seed dispersal wind sim — thousands of fluffy seeds in the wind. Pretty but particle-heavy; somewhat like sakura grove (falling petals).
8. Bioluminescent plankton kayak — water glows when disturbed. Overlaps koi pond/water demos.
9. Origami folding animation — a flat sheet folds into a crane via animated fold sequences. Mathematically neat; hard to author a real crane sequence. Could do simpler: transformable "folding polyhedra" — like a kaleidocycle! A kaleidocycle is a ring of tetrahedra that rotates through itself — mesmerizing, mathematical, and doable: chain of 6/8 tetrahedra linked by hinges, animated folding. Combined with bloom, glassy materials, music. "Kaleidocycle" demo. But hyperfold (043) might already cover 4D polytope folding. Kaleidocycle is different but might feel similar.
10. Rainglass — I'll compare with frostline more carefully. Let me look at the frostline demo description and features quickly.

Frostline: winter window with frost crystals, breath, wipe. So a rain-on-window demo would be somewhat adjacent (window + wipe), but visually different (droplets refracting city bokeh vs frost dendrites). Hmm, there's decent overlap in concept ("window pane you wipe"). I'd rather do something totally fresh.

Let me go with the Shadowbox — layered paper diorama with dynamic light idea? Or something more physics/tech-flavored.

More ideas:

• Lissajous harmonograph table with sand — sand pendulum drawing on a plate. Harmonograph! A sand pendulum tracing beautiful decaying lissajous curves, with a real sand texture accumulation. Could be combined with physical simulation: two-pendulum harmonograph, adjustable frequencies/phases, sand grains accumulate on a black plate. Beautiful and fresh! But "synchrony" and "cymatics" cover pendulums/vibration plates. Hmm, cymatics = sand on vibrating plate (Chladni patterns). A harmonograph is quite different visually (fine line curves), but the "sand on plate" vibe overlaps.

• String art / cycloid drawing machine — Spirograph! "Epicycle" (037) already covers epicycles presumably (planetary or drawing?). Let me check epicycle... could be a spirograph-like demo. Probably planetary deferent-epicycle visualization. A spirograph drawing machine with glow trails would still be distinct, but meh.

• Mech/animal: procedural walking creatures — "Skitter" (016) likely procedural spiders. Yes, covered.

• Newton's cradle / kinetic sculpture — simple.

• Volumetric clouds flythrough — cloudsea (022) covers.

• Bioluminescent jellyfish — abyssal bloom likely jellyfish.

• Pottery wheel — shape clay on a spinning wheel with mouse, then glaze & fire. Interactive and fresh! Lathe geometry updated live by "hands" pushing the clay profile; spinning; wobble physics (if you push too hard off-center the clay collapses!). Glazing: choose glaze colors, then "fire" in kiln with crackle shader. That's a really fun creative demo — "Kilnfolk"? "Potter's wheel". Modeling: profile curve (array of radii) → LatheGeometry, updated per frame with smooth deformation via spring dynamics; clay wet sheen shader; hands represented by two glowing tools; collapse mechanic via center-of-mass offset; gallery shelf of finished pots. Nice, tactile, unique!

• Zen rake / sand garden — rake patterns in sand with stones, procedural sand normal map generated from strokes. Karesansui! Rake the sand (draw with mouse), generating ripples around rocks in real-time via a wave/SDF shader. Very calming, beautiful, and unique. Plus koi pond exists but sand garden is distinct. Implementation: a render target accumulates "rake strokes" (heightfield), shader computes normals + ambient occlusion; rocks placed by dragging; ripples automatically ring rocks. Audio: gentle rake scrape + shakuhachi/bamboo. This is very doable and gorgeous: "Sekitei — Zen Sand Garden".

• Stained glass — done (065).

• Paper lanterns — done (064).

• Rain window — adjacent to 023.

• Pinball — neon tilt (042) probably pinball. Yes "neon tilt" sounds like pinball.

• Mini-golf / marble run — coasterworks is roller coasters; galton cascade is a galton board; klangwerk is a ball music machine. Marble run adjacent.

• Tide clock / moon — meh.

• Ant farm cross-section — cute but complex.

• Glass prism / dispersion optics bench — lumen lab (040) probably optics. Yes, "Lumen Lab" sounds optics-y.

• Firefly forest — synchrony (026) is likely firefly synchronization (coupled oscillators). Let me not.

• Deep-sea anglerfish lure — dark, covered.

• Wind chimes / bamboo fountain — could pair with zen garden.

• Typewriter / printing press — meh.

• Cuckoo clock / automaton theater — clockwork nebula is space-clockwork. An automaton theater — wooden mechanical puppet show with cams and gears, a little ballerina... complex to author.

• Sushi/conveyor — lol.

• Glacier calving — caldera is volcanic; glacier: seracs, ice caves, calving chunks into water with buoyancy... "Boreal glacier". Could be cool but heavy.

• Mushroom / fairy ring — mycelium growth; adjacent physarum.

• Comet / icy body — space covered heavily.

• Hot spring / onsen with macaques — lol.

• Tea ceremony / matcha whisking — nah.

• Sumi-e ink painting — paint with flowing ink that bleeds into paper (GPU diffusion), generates mountains procedurally. Ink bleed sim: brush strokes deposit ink, ink diffuses with paper fiber noise, edges darken. Beautiful and interactive. But fluid-dynamics adjacent? It's 2D though presented on a scroll. Hmm, nice but maybe less "3D wow".

• Origami — still attractive: a sheet that folds into a flapping bird / jumping frog with a guided step-by-step. Interactive: scrub through folding steps with a slider! Each fold is a rotation of a subset of vertices around a crease line — computable! Actually doable: represent the paper as a grid of vertices; each fold step selects a crease line and rotates the appropriate region. For known models (paper plane, boat, crane is too hard) — a paper plane fold sequence is very manageable: ~6 folds. And a "fortune teller"? Paper plane: start square, fold diagonally, fold corners... Then launch it: fly it through hoops with aerodynamics-lite! That's a whole game: fold your plane, then throw it — flight sim with lift/drag/stall, thermals to catch. "Paperwing" — fold & fly. That's ambitious but super charming. Risk: fold animation bugs. Flight model for a paper plane: simple glider physics (gravity, lift ∝ v², drag, pitch control). Could skip fold interaction and just do folding animation sequence on a grid mesh with clean code.

Hmm. Which one gives the best "wow within a single HTML file written reliably"? The zen sand garden (Sekitei) is very robust: heightfield in RT + normal shading, rake strokes, rock ripples, soft lighting, audio. Tactile and gorgeous, low risk of bugs, and distinctive among 65 demos. The paper plane is more gameplay but higher risk.

Actually let me reconsider: does anything cover "raking/drawing into a surface"? "Sandpile" (038) is abelian sandpile automaton. "Cymatics" is sand on plates. A zen garden is different from both.

But hmm — the style guide says "games/experiences with wow factor". Zen garden is more of a calming toy. It can still be feature-rich: rake tools (fine/wide), rock placement, ripple generator (drop a pebble → expanding rings that interfere — wait, that's water-like; sand ripples could use the wave equation briefly then freeze... actually real sand gardens have static ripples; but a "living" one where ripples gently propagate and freeze looks magical). Add day/night cycle, moss, falling maple leaves (sakura grove has falling petals though... use maple leaves anyway, it's fine), wooden veranda frame, bonsai, shishi-odoshi (bamboo water feature) that periodically tips with a "tock" — that's a delightful audio element! Plus gentle wind chime. This becomes a rich diorama.

Alternatively "Karesansui" as an interactive toy:

• GPU heightfield sand (512² RT, ping-pong), raking writes parallel grooves; a smoothing pass slowly fades old strokes? No — keep persistent (real sand stays). Provide "erase all" (re-smooth sand).
• Wave pass: pebbles drop → propagating ripple rings in heightfield that decay and leave a subtle permanent ring (blend).
• Rocks: drag to reposition; sand shader auto-draws concentric "water" rings around rocks (analytic SDF rings baked into a separate accumulation channel? simpler: draw ring stamps into the height RT when a rock is placed/moved — each move stamps rings).
• Lighting: low sun with soft shadows from heightmap normals; warm paper-sky gradient; time-of-day slider.
• Tsuchi: wooden veranda at edge with subtle reflection; engawa platform you "sit" on (fixed camera mostly, orbit allowed).
• Shishi-odoshi: animated bamboo tube filling and tipping, water trickle particles, "tock" sound synthesized.
• Audio: ambient wind, distant temple bell occasionally, birdsong chirps synthesized, rake scrape noise (filtered noise burst while dragging).
• Tools: rake (3 sizes), smooth (eraser), pebble drop, rock place/move.
• Post: vignette + grain; soft bloom maybe minimal.

This is achievable and beautiful. But honestly, is it "advanced/wow" enough? It has: GPU sim (heightfield ping-pong), custom shaders (sand normal/AO, sky, water trickle), procedural animation (shishi-odoshi), synthesized audio, tools/interaction, day-night. Yes, comparable in richness to koi pond/frostline.

Let me also think about the paper plane flight more — "Paperwing: fold a plane, then fly it through a dusk archipelago catching thermals" — gameplay: throw with mouse flick, control pitch/bank, rings to fly through, thermals (rising columns visualized with particles), landing targets. Visuals: low-poly islands, sunset gradient, god rays-ish, clouds, ocean shader. That's a legit mini-game with wow. The folding part could be a scripted intro animation (a grid mesh folding into a plane over ~8 folds with a "skip" button), which doubles as the "wow, it folds!" moment. This is more impressive than the zen garden honestly, and gameplay adds replay value. Risk: flight feel might be janky; but a glider model is forgiving.

Hmm, both are good. Let me pick the one with the strongest visual identity and gameplay: Paperwing — Fold & Fly. Wait — check for overlap: "Void Runner" (008) is probably an endless runner flyer; "Wavewalker" (056)?; "Azure Odyssey" (009) probably a flying demo (fly over ocean?). Let me check azure odyssey & void runner quickly. If 009 is already a "fly a plane over the ocean" game, paper plane flight might be too close.

*********************************************************************************************************************************************************************re.

Azure Odyssey seems ocean/islands related (maybe sailing or flying over an archipelago). To avoid any overlap with a "fly over ocean islands" vibe, I'll go with the Zen Sand Garden (Karesansui) concept — it's distinct from all 65 demos: GPU sand heightfield you rake, rock placement with auto-rings, wave ripples from dropped pebbles, day/night cycle, shishi-odoshi bamboo fountain with water particles and "tock", synthesized ambient audio, wabi-sabi aesthetic.

Actually wait — let me reconsider one more option that's very "wow": a procedural walking mech / strandbeest — Theo Jansen strandbeest walking on a beach with wind-powered linkage animation! "Skitter" was procedural critters, but a Strandbeest with real Jansen linkage kinematics (solving the exact 11-bar linkage), driven by wind vanes, walking on wet sand at sunset with reflections... That's mechanically fascinating and visually striking. The Jansen linkage has known magic numbers, and I can implement the exact linkage solver analytically. Multiple legs offset in phase create the famous walking gait. Wind speed control, reverse, etc.

Hmm, strandbeest vs zen garden. The strandbeest is more "engineering wow", the zen garden is more "interactive toy wow". The style guide likes physics, procedural, shaders, interactivity.

Let me actually think about which one I can execute most flawlessly in a single file:

Strandbeest:

• Core: Jansen linkage math — known constants. Each leg: crank circle + linkage rods solved via circle-circle intersection per frame (cheap). 6-8 legs per side with phase offsets. Body frame, spine, windmill vanes on top driving the crank via gears.
• Feet produce the classic flat-bottom gait; body stays level; forward speed derived from foot contact — or cheat: speed ∝ crank speed; feet slide slightly. Good enough.
• Environment: beach at golden hour, wet sand with mirror-ish reflection (planar reflector or SSR-lite; could reuse simple reflection like demos before — Three.js Reflector), ocean waves shader, sky gradient with sun, clouds, gulls? footprints in sand (decal trail), wind particles (grass/sand streaks).
• Controls: wind speed slider, camera orbit, follow-cam, number of legs? maybe not. Sound: creaking wood, clicking gears, wind, surf.
• Wow factors: the hypnotic linkage motion, god rays, reflection, footprints.

That's very cool and unique among the demos. "Strandbeest" — a wind-walker on a beach.

Zen garden: more interactive (rake!).

Decision: go with the Strandbeest — "Windwalker". It's visually stunning (golden hour beach + mechanical creature), has real mechanical simulation (Jansen linkage — a fantastic math showcase), rich environment shaders, audio, footprints, wind physics. And it's unlike anything in the catalog. Rake interactions are nice but "a living machine walking a beach at dusk" has more wow.

Hmm, but hold on: implementation risk for the linkage. The Jansen linkage: I know the standard dimensions (a..m constants by Theo Jansen): a=38, b=41.5, c=39.3, d=40.1, e=55.8, f=39.4, g=36.7, h=65.7, i=49, j=50, k=61.9, l=7.8, m=15.

Geometry: fixed points: crank center M=(0,0) and fixed pivot A=(0,-38) (using a as the distance between the crank axle and the frame pivot). Crank pin B = M + m*(cos θ, sin θ). Then:

• C satisfies |C-A| = j? Let me recall the standard layout. There are 8 links. Points: A (fixed frame pivot below crank), M (crank axle). Joints: B (crank pin), C, D, E, F, G, H (foot). Constraints:
  • |B-C| = b
  • |C-A| = c?

I don't remember the exact incidence table reliably. But I don't need the exact Jansen constants — I can look up the standard setup from memory of having implemented it... risky. Alternative: derive linkage from a known configuration. Actually the standard description:

Jansen's linkage (from Wikipedia "Jansen's linkage"):

• a = 38.0 (distance M to A)
• b = 41.5
• c = 39.3
• d = 40.1
• e = 55.8
• f = 39.4
• g = 36.7
• h = 65.7
• i = 49.0
• j = 50.0
• k = 61.9
• l = 7.8
• m = 15.0 (crank radius)

Points: M is the crank center. A is the fixed point at distance a below M. B is the crank pin (radius m from M).

• Triangle from B: C with |BC| = b, |CA| = ... hmm.

From the Wikipedia diagram, the connections are:

• C: |BC| = c? Let me think of the labels in the typical diagram: The bars are labeled by letters. Joints: A (bottom fixed), B (crank pin), C (upper), D, E, F, G (left mid), H (foot).

I recall this exact table (it appears in many implementations):

• B = M + m·(cos θ, sin θ)
• C: |AC| = j, |BC| = b
• D: |CD| = d, |AD| = ... no wait.

Let me instead recall from a well-known JS implementation ("strandbeest" by ???). Common formulation:

Hmm. Actually I found it — the commonly cited assignment (e.g., from "Strandbeest simulation" blog posts):

• C from A (radius j) and B (radius b)
• D from C (radius d) and B (radius c) → triangle BCD
• E from D (radius e) and B (radius f)? no...

I'm not confident. Rather than risk wrong kinematics, safer approach: implement a generic circle-circle intersection solver and define the linkage with the table from Wikipedia, which I can reconstruct carefully:

Wikipedia's Jansen linkage diagram (I have decent memory of it): There are fixed points M (top, crank axle) and A (bottom). Crank M–B length m. From B, three rods: B–C (length b), B–D (length c), B–E? Hmm.

Actually, let me think about the known SVG animations. The classic one (by "Brion Vibber"? or the famous GIF) has:

• M at top center, crank going to B.
• A at bottom center.
• C top-left: connected to A by rod j? and to B by rod b?
• D left-mid
• E left-lower connected to A
• F mid
• G foot area
• H foot tip

I genuinely can't reconstruct the incidence table with certainty from memory. Risk of a broken-looking leg.

Mitigation: I can search for the data via web fetch — I have import_url_to_shell_environment! I can fetch the Wikipedia page or a known gist with the Jansen linkage constants and incidence table. Let me do that. If network access fails, fall back to the zen garden idea.

Actually, let me try fetching a compact reference — e.g., the Wikipedia article "Jansen's linkage". Let me try. If that fails (no internet), I'll design the demo around a linkage I can derive correctly myself.

Alternatively — I can design my own walking linkage whose correctness I can verify numerically: e.g., a Klann linkage (simpler, 6-bar) or a hoekens/chebyshev linkage (4-bar producing near-straight-line foot motion!). The Chebyshev lambda linkage is a 4-bar with exact known geometry that converts rotation to near-straight walking motion — used in walking machines, much simpler and fully correct from memory: base points O1, O2 distance 2a apart; crank r=a from O1; connecting rod length 2.5a... Chebyshev's lambda linkage: link lengths: base = 2, crank = 1, coupler = 2.5, rocker = 2.5, and the foot point is at the extension of the coupler by another 2.5. It produces the famous walking straight-line motion used in early walking machines and the "Mechanical Horse". A 4-bar is trivially solvable: crank pin known, then circle-circle intersection between rocker pivot and coupler. This I can implement with full confidence. But the Jansen linkage looks more organic/spidery with its many slender rods.

Plan: try to fetch Jansen linkage data from the web. Let me attempt a few URLs. If internet works, great — use exact Jansen geometry and verify by simulating the foot path (I can numerically check the foot's path has a flat bottom with a quick Node script!). Verification step: run the solver in Node for θ ∈ [0, 2π), print foot positions, check the bottom of the path is flat (y varies < a few % over the contact half). That makes it robust.

If no internet, use Chebyshev lambda linkage (or Klann), also verified numerically in Node.

Let me test internet access first.

Wikipedia gave 429. Let me try a different source — maybe a raw gist or another reference site. Let me try fetching from a couple of sources:

1. https://www.strandbeest.com/ — probably not technical.
2. Try Wikipedia again with different path (api?).
3. Try https://en.wikipedia.org/w/index.php?title=Jansen%27s_linkage&printable=yes
4. Or a known implementation on GitHub raw.

Let me try the Wikipedia REST API summary or the raw wikitext via api.php.

Wikipedia is rate-limited. Try GitHub raw content with known Jansen linkage implementations. Known repos: "jansen linkage" gists. Let me try a search-free guess at raw files... risky guesses. Alternatives:

• https://raw.githubusercontent.com/... need exact paths.
• Try "https://www.dummies.com"? no.
• Try "https://mechanicalspider.com"? unsure.
• Try Wolfram? no.
• Try "https://www.mechanical-toys.com"? no.

Better: GitHub code search requires auth. But raw file guessing: known project "strandbeest" by user "zalo"? There's a known JS demo: https://github.com/... hmm.

Alternative reference sites for Jansen linkage dimensions:

• https://www.strandbeest.com/beests_leg.php — actually the official site has leg geometry explanation? Not sure.
• https://www.mechanisms.??

Let me try fetching from a couple of plausible sources in parallel:

1. https://raw.githubusercontent.com/Vectorized/solady — no lol.
2. Known: "http://www.mechanicalpuppetry.com"? unknown.
3. Try "https://josephsdailywalkwithers.blogspot.com"? no.

Hmm. Let me try DuckDuckGo HTML search: https://html.duckduckgo.com/html/?q=jansen+linkage+simulation+github — then parse results. That may work.

Bing search worked. Let me grep the results for github links.

Bing returned a page but no useful organic results (probably a consent/redirect page). Rather than fighting search engines, I should rely on deriving the linkage myself and verifying numerically.

Actually, wait. I recall the Jansen linkage layout well enough to reconstruct it with careful reasoning, and then verify numerically in Node — if the foot path is wrong, I'll see it. But there's a risk I burn a lot of time tuning.

Alternative plan: Klann linkage — I remember it better: Klann's linkage has 6 bars: frame with two fixed pivots; crank; a rocker; two couplers; leg. Hmm, also don't remember exactly.

Chebyshev lambda linkage — I remember exactly:

• Fixed pivots: O1 = (0,0), O2 = (2, 0) (base length 2r where r is crank radius).
• Crank: O1 to P1, length r=1.
• Coupler: P1 to P2, length 2.5r... and rocker O2 to P2 length 2.5r? Chebyshev lambda: both the rocker and the coupler have length 2.5, base 2, crank 1. The tracing point is on the coupler extended past P2? For the lambda linkage, the coupler point M is such that P1–M is 2.5 and M–P2 is 2.5? No...

Chebyshev's lambda linkage specifics: O1=(0,0), O2=(2,0). Crank r=1 rotates around O1. Rocker of length 2.5 pivots at O2, connected at joint A to coupler of length 2.5 attached to crank pin B. The coupler extends past A to point M with AM = 2.5. M traces the lambda curve with a long straight segment at the bottom. Yes — I believe: B = crank pin; A = intersection of circle(O2, 2.5) and circle(B, 2.5); M = A + (A - B) normalized * 2.5 (extension of the coupler beyond A). When the crank rotates, M traces a "λ" shape: a flat-ish bottom half and an arched top. This is the mechanism used in the classic walking machines (e.g., the "Galloping Gertie"? no — it's used in Chebyshev's "plantigrade machine" — the first walking machine!).

So with Chebyshev lambda I get a 4-bar (plus extension) that I can implement correctly from memory and verify numerically. The mechanism looks simpler than Jansen (fewer rods), but I can build an artistic multi-leg walker with it, e.g., 6 legs total with phase offsets.

But honestly the Jansen linkage is the iconic "strandbeest" look — spidery, many thin rods, organic. Let me take one more stab at reconstructing Jansen from memory, and verify via simulation. I actually have decent recall of the Jansen incidence table because it's widely implemented:

From many implementations (e.g., the "rigid body" Strandbeest sims), the standard construction:

Fixed: A = (0, 0) [the frame pivot], M = (0, 38) [crank axle, since a=38 is the vertical distance]. Actually usually M above A.

Joints and rods (I'm fairly confident about this table — it matches the Wikipedia diagram where rods are labeled b..m and the drawing shows):

• B = crank pin: |MB| = m = 15
• C: |BC| = b = 41.5, |AC| = j = 50.0 → C is upper-left
• D: |CD| = c = 39.3? hmm.

Alternative well-known table (from "Strandbeest leg simulation" tutorials, e.g., the one by 'Wouter' or the openframeworks one):

I remember there are 8 rods b,c,d,e,f,g,h,i,j,k,l plus crank m. 12 named lengths. The foot is G or H.

Honestly, without a reference I have maybe 50% recall on the incidence table. Getting it wrong then debugging via foot-path flatness could take many iterations.

Different idea: fetch a known implementation via a different route. Options:

• GitHub raw guesses (need exact paths).
• Try Bing search RSS format (format=rss might return clean XML results!): "https://www.bing.com/search?format=rss&q=..." — the earlier page had an RSS link. Let me use that to find GitHub repos.

Search results are useless (wrong "Jansen"). I'll stop chasing web references. Decision: implement the walking machine with a linkage I can derive and verify from first principles.

Best choice: Jansen linkage reconstruction from memory + numerical verification, OR design my own linkage.

Actually — you know what? I recall the Jansen linkage table well enough to try, AND I can verify. Let me write the commonly cited table that I believe is correct (this appears in numerous JS/Python implementations, e.g., the well-known "strandbeest" p5.js coding-train-style sketches):

The widely-copied formulation (I'm now fairly sure, having seen many implementations) is:

Hmm no. Let me think about the shape: In the famous leg diagram, from crank pin B there are rods to C (top area) and to D and E. Let me think of the actual Wikipedia image: It's a stick figure: M top center with crank to B (right). B connects to: C (left upper), D (left mid), E? no...

OK here's another approach that is 100% reliable: I will fetch a page that is likely fetchable — e.g., a blog post or a university page. Let me try a few specific known URLs:

1. https://www.strandbeest.com/ — official site, probably no technical data.
2. http://www.mechanism101.com/? no.
3. "https://en.wikibooks.org"?
4. Try Wikipedia mobile mirror: https://en.m.wikipedia.org/wiki/Jansen%27s_linkage — maybe not rate limited? It's the same infra; 429 might be UA-based though. Worth one try with the REST endpoint: https://en.wikipedia.org/api/rest_v1/page/html/Jansen%27s_linkage

Let me try the REST endpoint once.

The Wikipedia REST endpoint worked! Let me extract the linkage dimensions and geometry description.

I have the official ratios: a=38, b=41.5, c=39.3, d=40.1, e=55.8, f=39.4, g=36.7, h=65.7, i=49, j=50, k=61.9, l=7.8, m=15. This matches my memory. The article mentions the circle intersection method, and the diagram "Length of the rods" (an SVG) defines the incidence. The incidence table isn't in the text, but the "Length of the rods" SVG illustration might be fetchable from Wikimedia. Let me try to get that SVG: it's likely "Jansen_linkage.svg" or similar. Let me search the HTML for image URLs.

There's "Strandbeest_Leg_Proportions.svg" — the "Length of the rods" illustration. Let me fetch the actual SVG (not the PNG thumb): https://upload.wikimedia.org/wikipedia/commons/2/23/Strandbeest_Leg_Proportions.svg — SVGs on Commons usually contain the geometry with labels, and since it's an SVG, the line coordinates + text labels will tell me exactly which segment has which length. Let me fetch it.

Excellent! This SVG contains the actual leg geometry drawn as lines/ellipses, plus a foot-path polyline. The key insight: I can extract the drawn line segments (the rods) and the joint positions (circles), and the labeled lengths. Even better: the SVG likely contains lines whose lengths correspond to the proportions (scaled by 10, given matrix(10,0,0,10,...)).

Let me extract all line elements, circle/ellipse centers, and text labels. Then I can reconstruct the linkage topology: which joints connect to which, and rod lengths. Let me parse the SVG fully.

This is a goldmine. The SVG has:

• 11 black lines (the rods!) with exact endpoint coordinates (in SVG units = 10× the proportion units, given matrix(10,...,...) on the polyline and ellipse).
• An ellipse (the crank circle) at cx=320, cy=240 with rx=15, transformed by matrix(10,0,0,10,-2287.2614,-1955.509). So crank circle center in SVG coords = (32010 - 2287.2614, 24010 - 1955.509) = (912.7386, 444.491), radius 15*10=150. Interesting — that matches line endpoint (912.73865, 444.49103) — the crank axle M! And radius 150 in SVG units = 15.0 in proportion units = m (crank radius).
• The polyline is the foot path trace (red), also in the 10x-scaled frame. In SVG coords, the foot path center would be around... The first polyline point (272.277, 331.78) transformed: x = 272.27710-2287.26 = 435.51, y = 331.7810-1955.51 = 1362.3 — matches the foot point (435.50964, 1362.322) from the last two lines! So the foot is at (435.5, 1362.3) in this pose.

So the joints in SVG coordinates (divide by 10 for proportion units):

• M (crank axle) = (912.73865, 444.49103)
• B (crank pin) = (1059.5565, 475.22424) [distance from M: dx=146.82, dy=30.73 → 150.0 ✓ crank radius m=15]
• C = (689.99451, 138.43954) [top]
• D = (532.73865, 522.49109)
• E = (172.31946, 346.70984) [left]
• F = (615.66541, 906.64215) [bottom mid]
• G = (299.99451, 719.44983) [left bottom]
• H (foot) = (435.50964, 1362.322)
• A (fixed pivot) — where is it? The dashed path goes from (530.0939, 521.07022) — that's basically D (532.7, 522.5) — horizontally 385.4237 to the right then up 79.32203 to M? The dashed path: m 530.0939,521.07022 l 385.4237,2.03389 → ends at (915.5176, 523.104), then l 0,-79.32203 → (915.5176, 443.78) ≈ M (912.7, 444.5). So the dashed lines show that D is 385.4 left of M and that A is 79.3 below... wait. Actually the dashed path indicates the horizontal distance D-to-M (385.4 = 38.5?) hmm, a=38. And vertical 79.32...

Wait, but where's the second fixed point A? In the standard linkage, A is the fixed pivot below M at distance a=38. The lines from A: Let me compute distances between all joints to identify rods and match them to the 12 lengths (×10):

Lengths available (proportion): a=38, b=41.5, c=39.3, d=40.1, e=55.8, f=39.4, g=36.7, h=65.7, i=49, j=50, k=61.9, l=7.8, m=15. In SVG units ×10.

Joints: M = (912.74, 444.49) B = (1059.56, 475.22) C = (689.99, 138.44) D = (532.74, 522.49) E = (172.32, 346.71) F = (615.67, 906.64) G = (300.00, 719.45) H = (435.51, 1362.32)

The 11 black lines (rods) given explicitly:

1. M→B: (912.74,444.49)-(1059.56,475.22): length √(146.82²+30.73²) = √(21555+944)=√22499≈150.0 → m ✓ (crank)
2. B→C: (1059.56,475.22)-(689.99,138.44): dx=369.56, dy=336.78 → √(136575+113401)=√249976≈499.98 ≈ 500 → j? j=50 ✓ — wait j is 50 → 500. Yes B→C = j=50!

Hmm wait, but I recall B→C as b. Let me not fight memory; use the data.

3. C→D: (689.99,138.44)-(532.74,522.49): dx=157.26, dy=384.05 → √(24731+147494)=√172225≈415.0 → b=41.5 ✓

4. C→E: (689.99,138.44)-(172.32,346.71): dx=517.68, dy=208.27 → √(267992+43376)=√311368≈558.0 → e=55.8 ✓

5. D→E: (532.74,522.49)-(172.32,346.71): dx=360.42, dy=175.78 → √(129902+30899)=√160801≈401.0 → d=40.1 ✓

6. B→F: (1059.56,475.22)-(615.67,906.64): dx=443.89, dy=431.42 → √(197038+186123)=√383161≈619.0 → k=61.9 ✓

7. D→F: (532.74,522.49)-(615.67,906.64): dx=82.93, dy=384.15 → √(6877+147571)=√154448≈393.0 → f=39.4? computed 393.0 vs f=39.4 → 394. Hmm, 0.25% off — rounding in the drawing. Let me recompute: dx = 615.66541-532.73865 = 82.92676, dy = 906.64215-522.49109 = 384.15106. √(6876.85+147572.0) = √154448.9 ≈ 393.0. f=39.4 gives 394. Or c=39.3 → 393 ✓. Hmm c=39.3! So D→F might be c. But then which is b vs c? We already assigned C→D = b=41.5 (computed 415.0, exact). So D→F = c=39.3 ✓ (393.0 matches 39.3 well).

8. F→G: (615.67,906.64)-(300.00,719.45): dx=315.67, dy=187.19 → √(99648+35040)=√134688≈367.0 → g=36.7 ✓

9. E→G: (172.32,346.71)-(300.00,719.45): dx=127.68, dy=372.74 → √(16302+138935)=√155237≈394.0 → f=39.4 ✓ (this one is f!)

10. F→H: (615.67,906.64)-(435.51,1362.32): dx=180.16, dy=455.68 → √(32458+207644)=√240102≈490.0 → i=49.0 ✓

11. G→H: (300.00,719.45)-(435.51,1362.32): dx=135.51, dy=642.87 → √(18363+413282)=√431645≈657.0 → h=65.7 ✓

That's 11 rods: m, j, b, e, d, k, c, g, f, i, h. Missing from the 13: a=38 (frame M→A), l=7.8.

So where's A and l? A is the fixed point at distance a=38 below M. In the diagram, the dashed path went from D right 385.4 and up 79.3. Hmm: M.x - D.x = 912.74-532.74 = 380.0 = a×10 ✓!! So A coincides... wait no. The dashed line shows D is 380 left of M, and 79.3... M.y-D.y = 444.49-522.49 = -78.0. Hmm close to l=7.8 → 78.0! Interesting: D is directly below A? Let's hypothesize: A = (532.74, 444.49)? Then M→A = 380 ✓ (a=38, horizontal). And A→D = 78.0 = l ✓!!

So the fixed frame: M = (912.74, 444.49), A = M + (-380, 0) = (532.74, 444.49). And rod l connects A→D. In the diagram the crank is at the right, A is to the LEFT of M by 380 units, at the same height, and D is 78 below A.

Wait, but conventionally A is below M. Here A is left of M. Fine — orientation is arbitrary; what matters is the topology:

• Frame: M, A with |MA| = a = 38.
• Crank: B around M, radius m = 15.
• j: B→C = 50
• b: C→D = 41.5
• e: C→E = 55.8
• d: D→E = 40.1
• k: B→F = 61.9
• c: D→F = 39.3
• g: F→G = 36.7
• f: E→G = 39.4
• i: F→H = 49.0
• h: G→H = 65.7
• l: A→D = 7.8

So solving order given crank angle θ:

1. B = M + m(cosθ, sinθ)
2. C = circle-intersection(center B, radius j=50; center D? no—) hmm. C connects to B (j), D (b), E (e). D connects to A (l), C (b), E (d), F (c).

D is known first: D = circle intersection(A, l; ...) — D connects to A via l only as its "anchor" — but a point connected by a single rod isn't determined. Need to reconsider: D is determined by... D connects to A(l), C(b), E(d), F(c). In a 1-DOF mechanism, each new point must be pinned by two known distances.

Chain: known initially: M, A, B(θ).

• C: needs two connections to known points. C connects to B (j). Only one... unless C also connects to A? In my distance table, is there a rod C→A? |C→A| = |(689.99-532.74, 138.44-444.49)| = |(157.25, -306.05)| = √(24768+93667)=√168435≈410.4 — not one of the lengths (would be 41.0; closest is b=41.5 but C→D is exactly 415.0 and there's no 41.0 rod). So C does not connect to A.

Hmm, so how is the mechanism solved? The mechanism is an 8-bar: the standard solution solves it in two stages using the fact that C, D, E form a rigid triangle? No wait — C, D, E connect to each other (C→D: b, D→E: d, C→E: e) — so CDE is a RIGID TRIANGLE! And D connects to A via l... still D on a circle around A. And C connects to B via j.

So the sub-assembly: rigid triangle CDE, with D constrained to circle around A (radius l), and C constrained to circle around B (radius j). That's a 4-bar: A→D is the rocker (l), B→C is a coupler link (j) attached to crank pin B, and the triangle CDE is the coupler body. Solution: D lies on circle(A, l); C lies on circle(B, j); and |CD| = b. Solve: parametrize D = A + l(cosφ, sinφ), then C must satisfy |C-B|=j and |C-D|=b → C is circle-intersection of (B,j) and (D,b). Substituting gives constraint on φ — solvable numerically (1D root find) or via the standard trick: this is a 4-bar (A, B, C, D) with ground link |AB|... but B moves on the crank circle, so overall it's a 5-bar? no...

Standard 4-bar: ground pivots A and M. Crank M→B (m). Rocker A→D (l). Coupler B→...— the coupler is the rigid body containing B's rod-end and D's rod-end: i.e., the rigid body consisting of triangle BCD? B→C = j, C→D = b, and B→D? B→D is not a rod, but B, C, D form a rigid triangle IF B→D distance is fixed. Is it? |B→D| in the drawing: dx=1059.56-532.74=526.82, dy=475.22-522.49=-47.27 → √(277539+2234)=√279773≈528.9 — not in the length list (closest 52.9? no). So BCD is not rigid.

OK so the mechanism must be solved as: 4-bar with ground (A,M): crank MB, rocker AD, coupler BD where the coupler point C is attached via triangle... but BD isn't a physical rod. Hmm, but kinematically: consider the 4-bar M-B-?-A: we need a rigid connection between B's joint and D's joint. C provides it through two rods: B→C→D with C free — that's NOT rigid (it's a dyad with a free hinge).

Wait — actually it IS determined: the chain from B to D through C (two rods j, b) plus... no, a two-rod chain between B and D has one internal freedom (C can swing). Unless C is additionally constrained by E: C→E (e) and D→E (d): E completes triangle CDE. But E itself only connects C and D — so triangle CDE is rigid but still has the freedom of rotating as a whole... The rigid body CDE connects to B (via j at C) and to A (via l at D). So the rigid body CDE has point C constrained to circle around B, point D constrained to circle around A. That's exactly a 4-bar: ground link B→A?? B is moving though. Ugh.

Let me re-think: The whole mechanism has 1 DOF (crank angle). Fixed: M, A. Crank: B(θ) — known given θ. Now solve for C, D given B, M, A:

• D: |D−A| = l
• C: |C−B| = j
• |C−D| = b (E is then rigidly attached: |E−C|=e, |E−D|=d → E determined. Similarly F, G, H determined by subsequent dyads: F from B(k) and D(c); G from F(g) and E(f); H from F(i) and G(h). All simple circle-circle intersections!)

So the only hard part is solving (C, D) with three constraints: |D−A|=l, |C−B|=j, |C−D|=b. Two unknowns (each 2D = 4 DOF) minus 3 constraints = 1 DOF?? That can't be — the mechanism is 1-DOF total and the crank supplies it, so (C,D) must be fully determined. Count again: unknowns C(2), D(2) = 4. Constraints: |D−A|=l (1), |C−B|=j (1), |C−D|=b (1) = 3 constraints. 4−3 = 1 DOF remaining! So something's missing — there must be another constraint: probably |B−D| IS fixed by an actual rod that I mislabeled, OR C also connects to A or M.

Recheck my rod assignments. I assigned based on distances from ONE drawn pose. Let me recheck B→C: computed 499.98 ≈ j=50 (500). Alternatively could be exactly 500 for j. C→D = 415.0 = b. D→E = 401.0 = d. C→E = 558.0 = e. B→F = 619.0 = k. D→F = 393.0 = c. F→G = 367.0 = g. E→G = 394.0 = f. F→H = 490.0 = i. G→H = 657.0 = h. M→B = 150 = m. Remaining lengths: a=38 (M→A frame), l=7.8 (A→D?).

Check |A→D| with A=(532.74,444.49): A→D = (0, 78.0) → 78.0 = l ✓.

Hmm so with this topology: count DOF using Grübler: links: ground(M,A), crank MB, rod j (BC), rod l (AD), triangle CDE (one rigid link with 3 joints), rod k (BF), rod c (DF), rod g (FG), rod f (EG), rod i (FH), rod h (GH). Total links n = 11 (including ground). Joints (revolute, 1 DOF each): M-B (crank hinge), B-C? wait B is a multiple joint: crank, j, and k all meet at B (that's 2 joints in Grübler counting: k joints at one pin of multiplicity m count as m−1). Let me count pins: M (crank+ground: 1), A (rocker l + ground: 1), B (crank, BC rod, BF rod: multiplicity 3 → 2), C (BC + triangle: 1), D (AD rocker, triangle, DF rod: multiplicity 3 → 2), E (triangle, EG: 1), F (BF, DF, FG, FH: multiplicity 4 → 3), G (FG, EG, GH: multiplicity 3 → 2), H (FH, GH: 1). Total joints j1 = 1+1+2+1+2+1+3+2+1 = 14. Grübler: F = 3(n−1) − 2·j1 = 3(11−1) − 2·14 = 30 − 28 = 2. That gives 2 DOF — wrong! So my topology is off by one constraint. Something else connects.

The drawing has exactly 11 black lines + 1 crank ellipse + dashed construction lines. Maybe I missed a line — there might be a 12th line. Let me list again: lines 1423..1433 = 11 lines. Plus the dashed path (construction). Hmm.

Maybe A also connects to E? |A→E| = |(172.32-532.74, 346.71-444.49)| = |(-360.42, -97.78)| = √(129902+9561) = √139463 ≈ 373.4 → 37.3? Not in list (g=36.7=367, no). Close but not matching.

Maybe A connects to C? computed 410.4 → not in list.

Hmm, wait — maybe I misidentified which point is A. What if A is NOT at (532.74, 444.49)? The dashed line from D goes RIGHT 385.42 and then UP 79.32 to M. The dashed path likely indicates that D is at (M.x − 385.42, ...) hmm, M.x − D.x = 912.74 − 532.74 = 380.0, not 385.4. And the path length was 385.4237 horizontal from x=530.09 → 915.52; then up 79.32 from y=523.10 → 443.78. Endpoint (915.52, 443.78) vs M (912.74, 444.49): dx≈2.8, dy≈−0.7 — close but not exact. Hmm, so the dashed construction goes from approximately-D to approximately-M with legs 385.4 and 79.3. What's 385.4? And 79.3? Hmm: a=38 → 380, l=7.8 → 78. The dashed legs 385.4/79.3 don't exactly match 380/78. Odd. Maybe the dashed path shows the foot... no.

Wait, maybe the dashed path is from D to B?? D=(532.74,522.49): to B=(1059.56,475.22): dx=526.8, dy=-47.3. No.

Hmm, whatever the dashed path means, I have a DOF problem. Let me recount Grübler — maybe I miscounted links. Links:

1. ground (M, A)
2. crank (M-B)
3. rod B-C (j)
4. rocker A-D (l)
5. triangle C-D-E (b, d, e)
6. rod B-F (k)
7. rod D-F (c)
8. rod F-G (g)
9. rod E-G (f)
10. rod F-H (i)
11. rod G-H (h) n = 11. Joints: M: ground-crank (1). A: ground-rocker (1). B: crank + rod3 + rod6 → 3 links at one pin = 2 joints. C: rod3 + triangle = 1. D: rocker + triangle + rod7 = 3 links = 2 joints. E: triangle + rod9 = 1. F: rod6 + rod7 + rod8 + rod10 = 4 links = 3 joints. G: rod8 + rod9 + rod11 = 3 links = 2 joints. H: rod10 + rod11 = 1. Total = 1+1+2+1+2+1+3+2+1 = 14. F = 3(10) − 28 = 2. So 2 DOF with this topology — but the real Jansen linkage is 1 DOF. So I'm missing a rod.

The real linkage must have one more constraint. Candidates from the standard diagrams I remember: there might be a rod from A to E or B to D... Let me check distances in the drawing for ALL pairs and see if any pair matches a remaining named length... All 13 lengths are assigned: a (frame), b,c,d,e,f,g,h,i,j,k,l,m — all matched to pairs I found. Unless one of my assignments is wrong and one pair actually uses a different length, freeing a length for another pair.

Wait, actually, let me recheck: is it possible that B-C is not j=50 but rather C connects to A with j, and B-C uses... |B→C|=499.98 must be j=50 (no other 50). Hmm what if instead of B→C the rod is B→D=528.9? Not in list.

Let me recount the DOF differently — maybe I misidentified a joint multiplicity. At F: rods k(B-F), c(D-F), g(F-G), i(F-H) — 4 rods = 3 joints ✓. Total 14 joints, 11 links → 2 DOF. The real Jansen linkage: n=11? The classic count: Jansen linkage has 8 moving links? Hmm, Wikipedia says "one-degree-of-freedom eight-bar". EIGHT-bar: 8 links total including ground? So 7 moving + ground. But I count 10 moving links. Contradiction → my topology is definitely wrong somewhere.

Let me reconsider. Maybe the triangle CDE is wrong: maybe C, D, E are not all interconnected. The lines from the drawing: C→D (line1425: 689.99,138.44 → 532.74,522.49 ✓), C→E (line1426: 689.99,138.44 → 172.32,346.71 ✓), D→E (line1427: 532.74,522.49 → 172.32,346.71 ✓). Yes triangle.

Hmm wait, actually let me recheck line 1426: x1=689.99451 y1=138.43954, x2=172.31946 y2=346.70984. Yes C→E.

So with the drawn 11 rods, the mechanism has 2 DOF — impossible for the real thing. Unless... one of the "lines" I see is doubled: line1428: B→F (1059.5565,475.22424 → 615.66541,906.64215). line1429: D→F (532.73865,522.49109 → 615.66541,906.64215). Both present.

Hmm, let me recount Grübler yet again. Actually wait — I should double check joint count at B: crank(M-B), rod j(B-C), rod k(B-F). Three links meeting → 2 joints ✓. At D: rocker l(A-D), triangle(CDE), rod c(D-F) → 2 joints ✓.

Links n=11 → 3×(11−1)=30. Joints 14 → 28. DOF=2.

Real Jansen = 1 DOF. Missing one joint/rod. In the real mechanism, I'm now quite sure there's ALSO a rod from A to somewhere. What if l connects A to E instead of A to D? |A→E| computed 373.4 ≠ 78. No. What if there's a rod A→F? |A→F| = |(615.67-532.74, 906.64-444.49)| = |(82.93, 462.15)| = √(6877+213583)=√220460≈469.5 → not in list. A→G? |(300-532.74, 719.45-444.49)| = |(-232.74,274.96)| = √(54168+75603)=√129771≈360.2 → not in list. A→B? that's a, but a is M→A. A→C = 410.4 no.

Alternatively maybe M connects to something else: M→C? |(689.99-912.74, 138.44-444.49)| = |(-222.75,-306.05)| = √(49618+93667)=√173285≈416.3 → close to b (41.5=415) but not exact... suspicious! Hmm: 416.3 vs 415.0. And C→D measured exactly 415.0. Both can't be b. If M→C = b and C→D = ??? then C→D would need another length... all are used. Hmm, but what if the drawing has slight inaccuracies and M→C is not a rod at all (there's no line M→C in the SVG — the lines are explicit, and none goes M→C).

OK here's the thing: the SVG lines are EXPLICIT. 11 rods drawn. That's the actual geometry the artist drew, and the polyline foot path was clearly computed from a working simulation (it shows the classic flat-bottomed D-shaped foot path). So the artist's simulation worked with... hmm, or the artist drew it as a schematic.

Wait — actually, maybe I should recount. Is the triangle CDE really rigid (3 lines)? Lines 1425 (C→D), 1426 (C→E), 1427 (D→E). Yes 3 lines.

Hmm OK, let me look at this from the "eight-bar" description: 8 links. Ground + crank + 6 = 8? The Jansen linkage is often called an 8-bar: links = ground, crank, and 6 others, with the rods forming a chain: crank BC?, ... Let me look up "eight-bar" counting: n=8 (incl. ground), j1=10 → F = 3×7 − 2×10 = 1 ✓. So 10 joints, 8 links. But the drawing shows 11 rods + frame + crank = 13 links and ~16 joints → F = 3×12 − 2×16 = 36−32 = 4?? That's way off. Hmm, that can't be right either. Let me recount drawn lines: 1423 M→B? wait!

Hold on. Line 1423: (912.73865, 444.49103) → (1059.5565, 475.22424) = M→B. That's the crank drawn as a line. So the 11 lines INCLUDE the crank. Rods beyond crank: 10. Plus frame M-A (not drawn as solid, shown dashed?) and rocker l (not drawn?). Hmm — so the drawing omits the frame link and rocker l, and shows them as dashed construction lines! The dashed path: from D (530.09, 521.07 ≈ D) right 385.42 then up 79.32 to ≈M. If the dashed path represents the frame (a) and rocker (l): horizontal leg = a? 385.4 vs 380. And vertical leg = l? 79.3 vs 78. Both off by ~1.4%. Hmm, weird but plausible for a hand-drawn dashed line (the artist dragged a connector). Actually Inkscape connector tool... the numbers would be exact. 385.4237 and 79.32203. Hmm.

Actually wait: maybe the dashed path starts not exactly at D: it starts at (530.0939, 521.07022); D = (532.73865, 522.49109). dx=2.64, dy=1.42. And ends at (915.5176, 443.78216) vs M=(912.73865, 444.49103): dx=2.78, dy=0.71. The offsets are similar (~2.7, ~1) — so the dashed path endpoints are D and M shifted by roughly (2.7, 1) — maybe the artist drew it slightly off the points, or the points D/M I computed are slightly off because the drawn pose isn't perfectly consistent. So dashed = frame a (M to A horizontal) + rocker l (A to D vertical), implying A is at (532.7, 444.5) — directly left of M by ~a and directly above D by ~l. ✓ consistent with my hypothesis.

So topology stands: 2 DOF?! But the artist computed a foot-path polyline... which traces a perfect flat-bottomed path. How? If the artist's model had 2 DOF, the foot path wouldn't be a closed curve. So the artist's model DID have another constraint that isn't drawn as a line... OR my Grübler count is wrong. Let me recount very carefully.

Moving links (n_mov): crank, rodBC(j), rockerAD(l), triangleCDE, rodBF(k), rodDF(c), rodFG(g), rodEG(f), rodFH(i), rodGH(h) = 10 moving links. n = 11 with ground.

Joints:

1. M pin: ground–crank.
2. A pin: ground–rocker.
3. B pin: crank–rodBC–rodBF (2 joints).
4. C pin: rodBC–triangle.
5. D pin: rocker–triangle–rodDF (2 joints).
6. E pin: triangle–rodEG.
7. F pin: rodBF–rodDF–rodFG–rodFH (3 joints).
8. G pin: rodFG–rodEG–rodGH (2 joints).
9. H pin: rodFH–rodGH. j1 = 1+1+2+1+2+1+3+2+1 = 14. F = 3(11−1) − 2(14) = 30 − 28 = 2.

Yeah, 2 DOF. The real Jansen linkage has 1 DOF. So the drawing is missing a rod... OR one of the "rods" I identified is actually part of a rigid multi-vertex link. E.g., if rods BF(k), DF(c) and B?? — no. Hmm, what if BDF is a rigid triangle (one link, like CDE)? It would need a third side B–D, not drawn.

Wait, wait. Let me reconsider: maybe there's no rocker l, and instead A connects differently. What if the missing constraint is that the dashed line means D is rigidly connected to the frame in a different way...

Alternatively, maybe I mis-mapped a rod: what if rod k isn't B→F but M→F? |M→F| = |(615.67-912.74, 906.64-444.49)| = |(-297.07, 462.15)| = √(88251+213583)=√301834≈549.4 — no. The line clearly goes from B's coordinates to F.

Hmm, let me look at it from a different angle — maybe CDE isn't a triangle but there's an extra constraint I'm missing because TWO of my identified "rods" are actually a single rigid bent link (a bell crank!). E.g., if EG(f) and ED(d) are one rigid bent piece... they're part of triangle CDE anyway.

Let me try: what if the intended mechanism is the classic one and the drawing's rod set is: m(crank), a(frame), l(rocker), j, b, e, d, k, c, g, f, i, h = 13 named lengths, 12 rods + frame. Moving links: crank, j-rod, l-rocker, CDE-triangle(b,e,d), k-rod, c-rod, g-rod, f-rod, i-rod, h-rod = 10 moving, 11 total, joints 14 → 2 DOF. There's genuinely one constraint missing for 1 DOF.

Unless... the foot H is constrained?? No.

Let me question the triangle: what if C, D, E is NOT a rigid triangle because the lines represent: C→D (b), C→E (e), D→E (d) — hmm those are 3 lines, rigid. Yes.

Alternatively — maybe I have the wrong Grübler formula application because of a passive DOF... no, passive DOF would INCREASE the count.

Let me just count DOF by sequential construction: Given θ: B known. Now, C must satisfy |C−B|=j. D must satisfy |D−A|=l. |C−D|=b. Unknowns: C(x,y), D(x,y): 4 unknowns, 3 equations → 1-dimensional solution set. To pin it, we need one more equation. In the REAL Jansen linkage, what is it??

Let me recall the real Jansen linkage structure from the famous animation: Looking at the Wikipedia animation description: "When the blue line at the right end of the picture is driven in a clockwise rotary motion..." — the blue line is the crank at the right.

I found it — I remember now! In the standard Jansen linkage, the point I called C (top) connects via rod to BOTH the crank pin B AND... hmm.

Let me try to just fetch the actual first SVG "Jansen's_Linkage.svg" (the animated one at the top of the article, file b/b4). If it's an animated SVG with the linkage drawn, I can extract the rod endpoints at some frame and cross-check which pairs are connected — and importantly it might have MORE lines (12 or 13). Let me fetch https://upload.wikimedia.org/wikipedia/commons/b/b4/Jansen%27s_Linkage.svg.

Very interesting!! Look: C-M: 378.53 ≈ a (380). So C connects to M with a rod of length a=38! And A-M = 380 is the frame... wait, but then what connects A? A-D = 78 = l.

Hmm, now I have TWO candidate pairs for 'a': A-M (exactly 380) and C-M (378.53). And the topology might be:

• M is crank axle (fixed), A is fixed pivot, |MA| = a.
• C connects to M? Hmm, but 378.53 isn't exactly 380 (0.4% off — the drawing is a snapshot of one pose; if it were a real rod it would be exact like the others).

Alternatively, maybe the artist's drawn pose isn't from a perfect simulation and C-M is coincidentally near a. The other matches are all exact to 0.1. So C-M=378.5 is probably coincidence.

The real question remains: what pins down the (C,D) dyad? Let me think about the actual published Jansen linkage structure once more.

I now recall with higher confidence the standard incidence (from the Wikipedia "Length of the rods" diagram which I have in front of me as data): the rods drawn as solid lines are the 11 lines I extracted; plus dashed a and l. That's 13 segments for 13 letters. So the drawing's topology is:

Frame: M-A (a, dashed) Crank: M-B (m) B-C (j), B-F (k) C-D (b), C-E (e), D-E (d) D-F (c or f), F-G (g), E-G (f or c), F-H (i), G-H (h) A-D (l, dashed)

And Grübler says 2 DOF. Yet this is THE diagram from Wikipedia... The DOF count must actually be 1, so let me recount Grübler once more, very carefully, considering that C, D, E with rods b, e, d form ONE rigid link (triangle) — I did count it as one link. Hmm.

Links (including ground):

1. ground {M, A}
2. crank {M, B}
3. rod {B, C} (j)
4. rod {B, F} (k)
5. triangle {C, D, E} (b, d, e)
6. rocker {A, D} (l)
7. rod {D, F} (c)
8. rod {E, G} (f)
9. rod {F, G} (g)
10. rod {F, H} (i)
11. rod {G, H} (h) n = 11

Revolute joints: J1: ground–crank at M J2: ground–rocker at A J3: crank–rod3 at B J4: crank–rod4 at B (two joints at same location, counted separately) — WAIT. Hmm, actually in Grübler counting, when 3 links meet at one pin you count 2 joints. But here — do rod j (B-C) and rod k (B-F) both hinge on the crank pin independently? Yes. So 2 joints at B. ✓ J5: rod3–triangle at C J6: triangle–rocker at D J7: triangle–rod7 at D J8: rod4–rod7 at F?? NO WAIT. At F: rods k(4), c(7), g(9), i(10) meet = 4 links → 3 joints. J9: triangle–rod8 at E J10: rod8–rod9 at G (plus rod11 h → 3 links → 2 joints at G) J11: rod10–rod11 at H

Count: M:1, A:1, B:2, C:1, D:2, E:1, F:3, G:2, H:1 = 14 joints. F = 3·10 − 2·14 = 2.

Hmm OK so it IS 2 DOF by Grübler. But the actual Jansen linkage is 1 DOF. So one of my rod identifications must be wrong — i.e., maybe there's no separate rocker A-D and instead l is used somewhere else, OR the triangle isn't CDE.

What if D-E isn't a rod, and instead the third side of the triangle is elsewhere? Line 1427: (532.73865, 522.49109)→(172.31946, 346.70984) = D→E exactly. It's drawn. Hmm.

Let me approach from the other side: simulate! Assume topology as extracted, crank B rotates around M. Constraints for (C, D): |C−B| = j, |C−D| = b, |D−A| = l, |D−E|... no wait E depends on C,D. Let me just do the forward kinematics as a constraint system and see if there's a residual DOF: solve for C, D given B: equations: |C−B|=j, |D−A|=l, |C−D|=b. 3 equations, 4 unknowns → 1-param family. So indeed underdetermined → the drawing as-is is NOT a mechanism. So I'm definitely missing a rod.

The C-M ≈ 380 ≈ a observation: what if the frame isn't M-A but the mechanism has rod C-M of length... hmm but then A-M=380 exactly would be the coincidence (frame could be any length — it's just ground, its length is a=38 by definition).

New hypothesis: the actual linkage:

• C connects to M via rod (length a=38)? No wait — hmm, that would make a both the frame M-A AND rod C-M? Each letter is one segment.

Let me look at it again: what if A is NOT a separate fixed point, and the frame pivot is just M, with the dashed lines meaning something else (like the foot's bounding box)? And the real constraint set is:

• |C−M| = a? (378.53 measured — 0.4% off)
• |D−A| with A = left-of-M...

Hmm hmm. Let me test the hypothesis that the linkage is: frame M only; C pins to M (rod a); D pins to C (rod b); E: triangle CDE; D also pins to... we'd still need A for l.

What if BOTH: A exists with |MA|=a (frame) and |AD|=l (rocker), AND C connects to M with... no, every letter used once.

Honestly, the cleanest resolution: look at the ANIMATED svg (Jansen's_Linkage.svg, the b/b4 file) — it's the main illustration and likely has the rods drawn as an animation where each rod is a line with animate transforms, or it might be a SMIL-animated SVG with several frames. Its geometry would resolve ambiguity. Let me fetch it.

I'm at 50% of max time already?! Wait, timeProgress 0.506 — that's concerning. Hmm, "maxTime" threshold at 50%. I need to be efficient now. But iterationProgress is only 0.025. Let me move fast.

Actually wait, this might just be a time checkpoint. I should hurry: decide the linkage topology NOW.

Let me quickly parse the animated SVG — it's small (6.6KB), so let me just cat it.

PERFECT. This animated SVG has the linkage drawn with colored rods at two poses (one normal-width, one with thicker stroke-width=10 — two animation frames baked in). Let me extract the topology:

Fixed points: M = (790, 342) [crank axle, circle r=150 dashed around it], A = (410, 420) [circled white].

Frame: dashed path8771: "m410 420 h380 v-78" → from A=(410,420) right 380 to (790,420), up 78 to (790,342)=M. So A→(790,420) is a=380 horizontal... wait: A=(410,420), M=(790,342). The dashed construction: right 380, up 78. So |AM|² = 380² + 78²?? Hmm no — the dashed path shows the horizontal offset 380 (=a) and vertical offset 78 (=l)?? That would make |AM| = √(380²+78²) = √157684 ≈ 397.1.

Hmm interesting — so in THIS diagram, a=38 and l=7.8 are the horizontal/vertical OFFSETS between the two fixed pivots A and M! Not separate rods!

Now the rods (pose 1, normal stroke):

• path8598 (blue): "m790 342 l74.59 -130" → M=(790,342) to B=(864.59, 212). |MB| = √(74.59²+130²) = √(5563+16900)=√22463≈149.9 = m ✓ crank.
• path8596 (green): "m864.59 212 l-454.59 -207" → B=(864.59,212) to (410, 5) = C? Endpoint (864.59-454.59, 212-207) = (410, 5). Length = √(454.59²+207²) = √(206652+42849) = √249501 ≈ 499.5 ≈ j=500 ✓. So B→C = j, with C=(410,5).
• path8600 (orange): "m593.13 767.45 l271.46 -555.45" → from F=(593.13,767.45) to (864.59, 212) = B. Length = √(271.46²+555.45²) = √(73690+308525)=√382215≈618.2 ≈ k=619 ✓. So B→F = k. F=(593.13, 767.45).
• path8602 (blue triangle): "m229.39 721.38 l363.74 46.07 l15.463 489.45 z" → vertices: P1=(229.39,721.38)=E?, P2=(593.13,767.45)=F, P3=(608.59,1256.9)=H(foot). So E→F→H→E triangle?? Wait: side E→F: √(363.74²+46.07²)=√(132307+2122)=√134429≈366.6 ≈ g=367 ✓. Side F→H: √(15.463²+489.45²)=√(239+239561)=√239800≈489.7 ≈ i=490 ✓. Side H→E: from (608.59,1256.9) to (229.39,721.38): dx=379.2, dy=535.52 → √(143793+286782)=√430575≈656.2 ≈ h=657 ✓. So E, F, H form a RIGID TRIANGLE with sides g, i, h!!

That's the missing constraint! E-F-H is a rigid triangle, not just point-to-point rods. My earlier topology treated g, f, i, h as forming a 4-bar E-G-F-H... but actually:

• path8604 (olive): "m410 420 l183.13 347.45" → A=(410,420) to D=(593.13, 767.45)?? wait that ends at F's coordinates. Hmm: (410+183.13, 420+347.45) = (593.13, 767.45) = F. Length = √(183.13²+347.45²) = √(33537+120761)=√154298≈392.8 ≈ c=393 ✓. So A→F = c=39.3!! Not D→F!

• path8606 (purple): "m10.287 394.3 l219.1 327.08" → from (10.287,394.3)=D? to (229.39,721.38)=E. Length = √(219.1²+327.08²) = √(48005+106981)=√154986≈393.7 ≈ f=394 ✓. So D→E = f, D=(10.287, 394.3), E=(229.39, 721.38).

• path8705 (red, thick — pose 2): "m410 420 l-377.38 134.39 l213.74 -515.25 z" → from A=(410,420): to (32.62, 554.39)=D2, then to (246.36, 39.14)=C2, back to A. So triangle A-D2-C2: side A→D2: √(377.38²+134.39²)=√(142416+18061)=√160477≈400.6 ≈ d=401 ✓. Side D2→C2: √(213.74²+515.25²)=√(45685+265483)=√311168≈557.8 ≈ e=558 ✓. Side C2→A: √( (410-246.36)² + (420-39.14)² ) = √(163.64²+380.86²)=√(26778+145054)=√171832≈414.5 ≈ b=415 ✓!!

So A, D, C form a RIGID TRIANGLE with sides d (A-D), e (D-C), b (C-A)!!! THE TRIANGLE IS A-D-C, attached to the fixed pivot A!

• path8590 (red, opacity .4 — pose 1): "m410 420 l-399.71 -25.7 l399.71 -389.3 z" → A=(410,420) to D=(10.287,394.3) to C=(410,5) back to A. ✓ Confirms triangle ADC in pose 1: A-D=d, D-C=e, C-A=b.

Now C also connects to B via rod j (green, path8596/8703). So:

MECHANISM (correct topology!):

• Fixed: A=(0,0) [let's relocalize], M with offset (a=38 right, l=7.8 up) from A. I.e., M = A + (a, -l) in y-up convention (in SVG y-down: M = A + (a, -l)).
• Crank: B = M + m·(cosθ, sinθ).
• Rigid triangle T1 = ACD: |AD|=d, |DC|=e, |CA|=b — rotates about A. ONE unknown angle φ.
• Rod j connects C to B → constraint |C−B|=j determines φ. ✓ (4-bar: ground A-M, crank M-B, coupler B-C rod j, rocker = triangle ACD rotating about A.)
• Rigid triangle T2 = EFH with sides g(EF), i(FH), h(HE).
• Rod k: B→F. Rod c: A→F! So F is determined by circle-intersection(B, k; A, c). ✓
• Rod f: D→E. E determined by circle-intersection(D, f; F, g) [since |EF|=g from triangle T2]. Then H from triangle T2 geometry (rigid: H = E + R·(H_local) using F as the other anchor: H = circle-intersection(F, i; E, h) with correct branch). ✓
• Foot = H.

Grübler check: links: ground, crank, rod j, triangle ACD, rod k, rod c, triangle EFH, rod f = 8 links! EIGHT-BAR ✓✓ ("one-degree-of-freedom eight-bar" — matches!). Joints: A: ground-triangle-ground... A: ground, triangle ACD, rod c → 2 joints. M: ground-crank: 1. B: crank, rod j, rod k → 2. C: rod j, triangle: 1. D: triangle, rod f: 1. F: rod k, rod c, triangle EFH: 2. E: rod f, triangle EFH: 1. Total = 2+1+2+1+1+2+1 = 10. F = 3(8−1) − 2·10 = 21 − 20 = 1 ✓ ONE DOF.

So the FIRST SVG (leg proportions) had a different topology?? It doesn't matter — it was misleading (or I misread which points the lines connected: e.g., "D→F" line there might have been A→F where their "A" point = my D... their labels differ). The ANIMATED svg gives a clean, DOF-verified topology.

FINAL JANSEN LINKAGE SPEC (y-up convention, units = the proportion numbers):

Fixed:

• A = (0, 0) — main frame pivot
• M = (a, l) = (38, 7.8) — crank axle [in y-up: SVG had M up-right of A: A=(410,420), M=(790,342): dx=+380=a×10, dy=-78=-l×10 → in y-up, M = A + (38, +7.8)]

Crank:

• B = M + m·(cosθ, sinθ), m = 15

Triangle 1 (about A): C, D with |AC| = b=41.5, |AD| = d=40.1, |CD| = e=55.8. Solve: C = circle-intersection(A, b; B, j) — with j=50, |BC|=j. Then D = point of triangle: D = circle-intersection(A, d; C, e), choosing branch opposite to B side (mirror of C across...). Actually D is on the opposite side of AC from... in the SVG pose 1: A=(410,420), C=(410,5) (above A), D=(10.287,394.3) (left of A). B=(864.59,212) (right). So D is on the opposite side of line A→C from B. I'll compute both intersection points and pick the one opposite B relative to line AC. Better: precompute the rigid triangle's local coordinates and apply rotation: φ = angle of C around A: C = b·(cosφ, sinφ). D = d·(cos(φ−α), sin(φ−α)) or (φ+α) where α = angle DAC in the triangle: cosα = (b²+d²−e²)/(2bd). Sign: choose so D is on opposite side of AC from B. From the pose: A=(410,420), C=(410,5) → direction A→C is straight up (in y-down svg; angle −90°). D is to the left. In y-up convention: A=(0,0), C=(0, b)... let me just determine sign numerically at init and keep it fixed (branch selection once, track continuity).

F: circle-intersection(B, k=61.9; A, c=39.3). Branch: from pose 1, F=(593.13,767.45) in svg y-down → y-up: F below A (y-up negative). Pick branch accordingly (the intersection point farther from M? or with y < A.y in y-up). I'll pick the one "below" A.

E: circle-intersection(D, f=39.4; F, g=36.7). Branch: from pose, E is to the left of D... in y-up, E=(-399.7+?...) A=(410,420) so E relative to A: (229.39-410, 721.38-420) = (-180.6, +301.4) in y-down → y-up: (-180.6, -301.4). So E is left-down of A. Pick intersection branch with smaller x.

H: circle-intersection(F, i=49; E, h=65.7). Branch: foot should be below: pick the one with smaller y (y-up). From pose: H relative to A: (608.59-410, 1256.9-420)=(198.59, 836.9) y-down → y-up (198.59, -836.9): below ✓.

All branch choices can be made deterministically at each frame by picking the intersection closest to the previous frame's position (continuity) — robust. Or fixed geometric rule. I'll use continuity tracking per leg.

The foot path (from the first SVG polyline): spans x from ~248 to ~316 (svg units /10 → 24.8..31.6 relative to that drawing's origin), height ~331.8 flat bottom for a good stretch. In the animated SVG coordinates, foot H at pose1 = (608.59, 1256.9), pose2 = (753.9, 1226.4?) — pose2 triangle path8711: "m171.73 922.83 l344.83 -124.63 l237.33 428.1 z" → E2=(171.73,922.83), F2=(516.56,798.2), H2=(753.89,1226.3). OK.

Foot relative to A: pose1: (198.59, -836.9) y-up → so the foot reaches ~84 units below A when scaled /10. Leg height ~85 units; foot stroke width ~7 units in x.

SCALE: proportion units; total leg ~85 tall. For a creature ~3.5 m tall at the hip, scale = 3.5/85 ≈ 0.041 m/unit. Or just make it big: hip height 3.2m.

WALK GAIT: multiple legs per side with phase offsets. Classic strandbeest: legs paired mirrored; phase offsets of crank by 2π/nLegs per side; sides mirrored (the triangle ADC mirrors → crank direction reversed? In practice: mirror the whole leg in the z-plane? No — the legs are planar; a multi-leg beast has legs arranged along the body axis (z), each leg in its own x-y plane, with crank phases offset. Pairs: left side and right side legs are the same planar mechanism (not mirrored) — on real strandbeesten the legs on opposite sides are identical, just phase-shifted (the crankshaft has throws at different angles). Actually on real ones, opposite-side legs are mirrored? Let me think: the crankshaft runs along the body axis (z). Each leg is in a plane ⊥ z. The mechanism is planar; all legs identical orientation; phases staggered around the shaft. Mirroring isn't needed for walking — identical legs with phase offsets work (like a centipede). The Wikipedia note said "two legs are in pair and are mirrored, where they share the same crank" — mirrored pair sharing one crank: one leg's plane at z=+w, the mirrored one at z=−w, same crank pin → mirrored geometry. Mirroring = flip x → and reverse crank direction (θ → −θ) to keep gait consistent? If you mirror a planar mechanism (x → −x) and run the same crank angle, the foot path mirrors too — the flat part stays flat, direction of travel reverses?? The foot path mirrored has the same flat bottom; the horizontal motion during contact reverses?? No: mirroring x flips the sign of horizontal foot velocity — so a mirrored leg with the same crank rotation would push the wrong way during stance. Fix: mirrored leg runs θ → −θ (crank rotates opposite) — on a shared crankshaft that's achieved by mounting the crank throw mirrored... whatever — in simulation I can just set crank angle per leg: θ_leg = θ_shaft + phase, and for mirrored legs θ_leg = −θ_shaft + phase.

Simplest robust approach: N legs per side (say 4 per side, 8 total), phases equally spaced 2π/8... Real beasts use specific phasing. With 4 legs/side and phase step π/4 across all 8 legs, you always have ~half the feet in stance. I'll verify stance pattern numerically in Node (compute foot y for each leg over cycle) — but quick: I'll trust equally spaced phases, it works (that's what most sims do).

Forward motion: derive speed from foot kinematics: during stance, foot moves backward relative to hip at rate v(θ); set body forward speed = average |dx_foot/dt| during stance × direction. Compute numerically at init: for a leg, find stance phase (foot near bottom), measure average horizontal foot speed during stance → set that as body speed so feet don't slide.

Also body bob: real strandbeest hip height varies slightly as legs cycle. I can compute hip height = max over legs of (support height)... simpler: keep hip at fixed height with tiny sinusoidal bob. Feet planted: with equally spaced phases and flat-ish stance, fixed hip height ~ works if stance bottom is flat (it is: polyline showed y=331.78±0.05 over a wide x range!). The foot path flat bottom: y from 331.78 to 330.5 → flatness ±0.6 svg units = ±0.06 units over x from 272 to 248 (24 units!) — extremely flat.

So: hip height H_hip such that foot bottom touches ground: H_hip = −min(footY_rel_hip). With hip above A by some amount. Actually define leg coordinate: A at origin; hip bone connects A and M — the leg's frame attaches to body at A and M. Foot min y = y_min (about −83.7 relative to A in y-up). So place A at height 83.7·s above ground (s = scale) → feet touch exactly.

Now — THE DEMO. Time check: I'm at ~50% time. I need to write ~800 lines of HTML/JS/GLSL efficiently, validate, deploy. Let me design compactly but with wow:

Demo 066: "Strandbeest — Windwalker of the Infinite Beach"

Scene:

• Golden-hour beach: huge sky dome (gradient shader w/ sun glow, a few procedural clouds), ocean plane on one side with animated waves shader + foam line, wet sand plane with subtle ripples + the beast's reflection (cheap: mirrored geometry render or just a fake blurred reflection via a second rendered copy with scale y=-1 and opacity — Three.js Reflector is easiest and reliable: import from examples? Reflector is in examples/jsm/objects/Reflector.js — with importmap "three/addons/" → unpkg three@0.160.0/examples/jsm/. That works (I've presumably used addons before; risky but standard). Alternatively skip reflector; do "wet sand darkening + footstep decals". Reflection adds huge wow on wet sand though. Alternative cheap reflection: clone the beast mesh group with matrix scale(1,-1,1), material with low opacity + fog — renders under sand plane drawn with transparency... complexity. Let me use a simpler trick: sand is a big plane with a custom shader that includes FAKE planar reflection of a procedural sky + darkens; and the beast gets a soft blob shadow... Meh.

Actually — simplest high-wow: render the beast twice: once normal, once mirrored below the sand with a fade-out shader (clip by distance), and make the sand semi-transparent glossy where wet near the water line. This is very controllable, no addons needed. Mirrored clone: group.scale.y = -1 flips winding → set material.side = THREE.BackSide for the clone... or DoubleSide. With flat-ish shading and fresnel fade, looks like wet-mirror sand. I'll do that.

• The beast: frame built from rods: I'll build each leg as 3D extruded rods (boxes or cylinders between joints, computed per frame). 8 legs (4/side... actually classic look: 6-8 pairs? Animaris has ~12+ legs). Performance: each leg has ~11 rods; 12 legs = 132 rods + frame + spine. Update per frame: set rod positions/orientations via quaternion from joint vectors. Use InstancedMesh? Rods differ in length per leg but same set per leg type — all legs identical geometry; per-frame each rod scales in y (length fixed though! rods are rigid — only position/orientation change!). So: each rod = a cylinder/box mesh of fixed length, re-posed each frame. 12 legs × 11 rods = 132 meshes — fine as regular meshes, or use one InstancedMesh with per-instance matrix (matrix update per frame on CPU, 132 matrices — cheap). I'll use individual meshes grouped per leg for clarity (132 draw calls — ok, or merge materials to keep state changes low). Actually simpler: ONE InstancedMesh for ALL rods (unit cylinder along Y, scaled per instance: length from joint pairs, radius by rod type), plus InstancedMesh for joint spheres, plus crankshaft, spine, "sails"/windvanes. That's 3-4 draw calls for the whole beast.

Wind drive: the crankshaft is driven by a big rotor with blades (like real ones have wind sails / fan blades on top... actually real ones use sails; many have a windmill-like rotor). I'll add a gorgeous rotor: 8 curved sails (canvas-textured blades) spinning on top, driving the crankshaft via visible gears (two meshing gear discs with teeth — procedural geometry). Wind speed slider controls rotor RPM → walk speed. Auto gusts: wind noise varies.

• Footprints: decal rings/dimples on sand — implement as a canvas texture (2048²) on the sand plane where each foot plants (stamp an ellipse with darken + rim). Manageable: map world x/z → uv, draw ellipse. Feet leave prints that fade over ~60s (redraw with fading via semi-transparent erase... canvas fade: periodically draw translucent sand-colored rect? that would lighten prints uniformly — fine, prints fade).

Hmm wait — sand is one big plane with shader. If I use a CanvasTexture for the near field (say 120m × 30m strip along the walk path) with prints + procedural sand noise baked... The beast walks in a straight line along the beach; camera follows. Endless: when beast reaches texture edge, wrap/jump: shift the world (move everything back) — standard endless-runner trick. Or simpler: the beast walks in place?? No — walking along the beach is the dream shot. Let me do: beast walks +x; camera follows; footprint canvas follows with offset wrapping (teleport canvas region when beast moves 60m, fade out old prints quickly before jump). Simpler alternative: beach curves — the beast walks along a huge CIRCLE (radius 500m)! Then footprints canvas can be a ring texture... complexity again.

Simplest robust: beast walks straight; world "endless" via repositioning: every time beast advances 100m, shift beast, camera, and footprint-texture offset back by 100m, fading prints during the shift (they're 100m behind anyway, mostly off-screen). Also ocean/sky are infinite shaders (no reposition issues). Distant props (dunes, rocks, wrecked older beests!) positioned procedurally and recycled modulo 400m — nice parallax and no emptiness. Gulls! A few simple gulls (two-triangle wings flapping) circling — cheap and adds life.

• Audio (WebAudio, synthesized): wind noise (filtered noise, gusts via LFO), rhythmic wooden clunks synced to foot plants (filtered noise burst + low sine thump), gear creaks (occasional short bandpass sweep), surf (slow-modulated filtered noise, stereo), distant gull cries (rare, FM swoops). Master mute toggle, starts muted until user interacts (autoplay policy) — but previous demos init on first interaction; follow that pattern.

• UI: HUD title, wind speed slider, camera mode (orbit/follow/side-chase), leg count toggle? (keep fixed 8 or 12), time-of-day slider? Golden hour default; maybe day/dusk presets. Buttons: Pause walker, Snapshot PNG. Stats: rotor RPM, speed m/s, steps count.

• Post: keep simple — ACES tone mapping, vignette via CSS? Use renderer tonemapping + fog; skip EffectComposer (avoid addon imports entirely!). Actually bloom adds a lot of wow for sun glints... but addon import via importmap "three/addons/" is standard and I've likely used it. Let me check a previous demo to see if addons were imported successfully — e.g., 064 or 065 used only "three". To minimize risk, I'll skip EffectComposer and get glow via shader tricks (sun halo in sky shader, speculars). Fine.

Sky: big inverted sphere with gradient + sun disc + halo + procedural cloud bands (fbm, domain-warped, in shader) — done many times.

Ocean: plane (or part of sand shader?) — separate plane on the left (z<0 side), vertex waves in shader (gerstner-lite) + fresnel sky reflection + foam near shoreline based on world z + time. Shoreline: water edge undulates (z_offset = sin bands) — the classic lapping waves: in ocean shader, alpha fades near shore line which oscillates with slow sine → waves creep up the sand.

Sand: plane with shader: procedural sand noise (grain + larger ripples via stretched noise), wetness darkening near water line (z-based + the same oscillating shoreline so it stays wet after waves recede — use smoothstep with offset), sparkle glints (view-dependent noise glints), footprint CanvasTexture multiplied in near field, and the mirrored-beast fake reflection: instead of true reflection, sample reflection only via... hmm the mirrored clone approach: draw mirrored beast BELOW sand; sand alpha ~0.85 in wet zone so mirror shows through slightly?? True wet-sand mirror look: I'll do the mirrored-clone + sand with alpha blending where wet: alpha = mix(1.0, 0.55, wetness) — the mirror beast visible through. But order/transparency sorting: sand transparent → renders after opaque mirror beast. Mirrored beast material = clone of main materials with darker tint + fog. It's doable: I'll create the beast twice from a builder function (shared geometries, cloned materials with color multiplied 0.35, roughness 1... using MeshStandardMaterial? For stylized look, MeshLambert/Standard with flat shading). Mirror group: scale.y = -1 → normals flip; set material.side = BackSide? With flat shading and simple lighting it still reads okay; I'll set mirrored materials side=DoubleSide and accept slight lighting inaccuracy (it's a dark reflection anyway). Winding: mirrored geometry renders inside-out with FrontSide → use side: THREE.BackSide for mirror clone materials... but then lighting normals... MeshStandardMaterial with BackSide flips normals automatically in the shader? In three.js, for BackSide the normals are negated in the fragment shader (flipNormal). Actually normal = normalize( vNormal ) * ( float( gl_FrontFacing ) * 2.0 - 1.0 ) in normal_fragment_begin when double-sided... For BackSide, geometry winding appears reversed so gl_FrontFacing is false → normals flipped → correct-ish lighting. OK: mirror clone materials = side: BackSide, color darker.

Foot contact detection for prints & sounds: per leg, track foot y; when foot crosses below ground+ε while moving down → plant event: stamp footprint at (x,z), play clunk (volume ∝ speed), small sand puff particle (Points with velocity+fade; a pool).

Particles: sand puffs on foot plants + wind-blown sand streaks (a Points field streaming near ground, speed ∝ wind). Seagulls: 5 gulls, simple.

Beast construction details:

• Legs: 12 total (6 per side)? Phase: 12 legs × 30° offsets. On real beasts the two sides' cranks are often in anti-phase arrangement such that pairs alternate. I'll compute per-leg crank phase = i * (2π/12), mirrored side: negate direction (θ_m = −(θ + φ_i)). Verify stance coverage numerically in Node before finalizing (count legs in stance over a cycle; want ≥ 4 always... with flat-bottom half-cycle stance, ~6 of 12 in stance at any time — great).
• Frame: central spine box along z connecting hip plates; each leg's A and M pivots attach to an axle housing: crankshaft = long cylinder along z at M positions of all legs; crank throws (crank disks) visible per leg; A-frame struts to spine. Gears: crankshaft gear → up to rotor shaft via two gears (ratio ~1:12?) Actually rotor spins FASTER than legs? On real beests the rotor spins fast, legs slow: gear reduction rotor→crankshaft, e.g., rotor rpm = 6× crank rpm. Visual: big gear on crankshaft (r=0.5), small on rotor shaft (r=0.12): ratio ~4.2. Gears with procedural teeth (extruded boxes around a disc — or just cylinders with tooth boxes; ~24 teeth big gear, 8 small: keep meshing plausible: place centers at distance r1+r2, teeth counts proportional to radii, animate rotations θ1·r1 = −θ2·r2).
• Rotor: vertical mast from spine to ~2.2m, rotor hub + 6 blades: each blade a slightly tapered box with cloth texture? Keep stylized: wooden spars + canvas panels (semi-transparent, flapping slightly via vertex... keep rigid, rotate whole rotor). Add slight blade flex via rotation lag? Skip — keep rigid, add whole-mast sway.

Materials: wood (procedural canvas texture: grain stripes), brass/steel for shafts, canvas cloth (subtle checker weave). Keep palette: warm wood #8a6b46, dark joints, brass #c9a227.

Lighting: directional sun (warm, low angle ~10°), hemisphere sky/ground, soft shadows: use PCFSoft shadowmap, only beast casts (rods instanced castShadow = true — 132 instances fine), sand receives. Shadow camera follows beast.

Camera modes:

1. "Track": cinematic side tracking at beach level, slight dolly bob.
2. "Orbit": OrbitControls — need addons for OrbitControls... I could implement minimal orbit myself (spherical coords + damping, ~30 lines) to avoid addon import. Previous demos (065) had "orbit look" — did they import OrbitControls from addons? Let me check quickly how 065 imported controls — if unpkg addons worked before, I can use OrbitControls safely. I'll grep.

Let me also verify with Node: (a) linkage solver produces the classic foot path (flat bottom), (b) stance-phase count with 12 legs, (c) foot speed during stance → body speed constant. Quick node script with the math.

Then write the HTML (~900 lines), validate module JS with node --check, deploy to /space, update index.

Time is tight (50%+ used). GO.

First: check OrbitControls usage in prior demos + node availability.

**************************************************************************************************************************************************************************************************************************************************ce.

Excellent! The solver WORKS:

• Foot path: x range -33.5 to +34.4 (68 units wide), y range -84.0 to -61.6 (22.5 tall) — classic Jansen proportions ✓
• Stance: 390/721 = 54% of cycle in stance ✓ (Jansen ~50%+)
• Bottom flatness: 2.24 units over 66 units span — hmm, that's 2.2 units of vertical variation during stance, which is more than the ideal Jansen (~0.5). Hmm. Actually the "bottom" here includes the entry/exit transitions (my 10% threshold is generous). The truly flat part is flatter. With 12 legs and 6-7 always in stance, body height variation will average out — 2.2 units at scale 0.04 = 9cm bounce — actually that would look like natural bobbing! Fine.
• Mean foot speed during stance: 19.38 units/rad. So body speed = 19.38 × ω × scale.
• 12 legs: always 6-7 in stance ✓ perfect.

Direction: mean dx/dθ = +19.38 during stance. So as crank angle increases, foot moves +x relative to hip during stance → the body moves −x relative to the foot... wait: during stance the foot is planted on the ground (world-fixed); body moves relative to foot opposite to foot's motion relative to body: body velocity = −dx/dθ × ω in x. So with ω > 0 (increasing θ), body moves in −x at 19.38 units/rad. To walk toward +x, use ω < 0 (crank rotates clockwise when viewed from +z). Fine — I'll just set the sign empirically: body velocity = +19.38·(−ω)... I'll compute body speed = stanceSpeed × crankRate with a sign chosen so feet don't slide: v_body = −(dx/dθ)·ω·scale. With dx/dθ=+19.38: v_body = −19.38·ω·scale. Set crankRate sign by wind direction button (forward/reverse).

Also hip height: foot min y = −84.03 rel A. So place A at height 84.03·s. With s = 0.042: hip A at 3.53m, foot reach x ±2.86m, step length... x-span 68·0.042 = 2.86m stance span. Creature ~3.5m tall hip, body maybe 5m long (12 legs over ~4m). Speed: choose crank rate ~0.8 rad/s → v = 19.38·0.8·0.042 = 0.65 m/s leisurely. Wind slider scales crank rate 0..1.6 rad/s → up to 1.3 m/s. Rotor spins at ratio ~5× crank.

For mirrored legs (other side of body): mirror x → −x, and to keep foot kinematics consistent use θ' = −θ + phase... Mirroring the x-coordinate of the whole mechanism and negating crank angle: foot path mirrors; during stance dx/dθ relation flips appropriately so with the SAME shaft rotation direction the beast still walks the same direction. Actually simplest: compute leg joints in local frame, then for left-side legs scale x by −1 on the joint positions when building meshes, and run their crank angle as −θ+φ. Let me verify quickly: mirrored leg with θ' = −θ: position x_m(θ) = −x(−θ). During stance, original dx/dθ=+19.4. x_m derivative: dx_m/dθ = −(dx/dθ)|_{−θ}·(−1) = +19.4·... wait: d/dθ[−x(−θ)] = −(−1)·x'(−θ) = x'(−θ) = +19.4 during stance ✓ same sign. So body velocity for the mirrored leg is still −19.4·ω. Consistent ✓. So: left legs: θ_leg = −(θ_shaft) + φ_i, geometry x mirrored. Equivalent: θ_leg = θ_shaft + φ_i with geometry mirrored AND crank circle direction... I'll just implement per-leg: solve(legSign * theta + phase) and mirror x by legSign in mesh placement (legSign=+1 right side, −1 left). Wait but careful: if I both mirror geometry x AND feed −θ, that's the consistent pair. If I mirror x but feed +θ, the stance motion flips → feet slide. So: right legs (z=+w): sign=+1: solve(+θ+φ), no mirror. Left legs (z=−w): sign=−1: solve(−θ+φ), mirror x. ✓

Phase arrangement for 12 legs (6/side): real beasts stagger so footfalls are evenly spaced: total 12 legs, phases φ_i = i·(2π/12) assigned alternating sides... simplest: legs indexed 0..11 around the crankshaft positions along z; phase = i·π/6. Assign z positions: interleave sides: leg i at z = (i%2==0? +1 : −1)·w_row... hmm, but legs on the same side can't overlap in z; legs along the body: 6 z-slots × 2 sides = 12 legs. Phase assignment: within one side, phases spread by 2π/6; opposite side offset by π. Pair (z-slot n): right φ = n·π/3, left φ = n·π/3 + π. This gives alternating footfalls L/R like walking ✓.

But wait — legs in adjacent z-slots on the SAME side will collide visually if their linkages overlap... leg planes are at distinct z (spacing ~0.7m), mechanism width ~2.9m in x but flat in z (rod thickness ~0.1m) — no inter-leg collision in z. But DO adjacent legs' rods cross each other's planes? Each leg is planar at its own z; rods never leave their plane ✓. However the crankshaft (along z) passes through all M pivots — cranks at different phases on the same shaft ✓ exactly like the real thing.

Also the real strandbeest has the two legs of a "pair" sharing a crank throw but mirrored — mirrored leg runs θ'=−θ: a shared crank throw can't drive both +θ and −θ... real beasts: mirrored legs use the same throw and the mechanism is mirror-symmetric about the yz-plane?? If the left leg is mirrored in x AND driven by the same crank pin position (θ same), then its foot motion mirrors: stance dx/dθ flips → slides! UNLESS the mirror is about the xy-plane (z→−z), i.e., the left leg is the SAME planar mechanism translated in z (not mirrored), and "mirrored" in the thesis quote refers to something else. Hmm — but if both sides are identical orientation, the beast's feet on both sides move the same way — fine for walking (like a centipede), and looks symmetric from the side. But then the linkages are not mirror images — from the front, both sides lean the same way. Real strandbeest legs: looking at photos/videos, the legs on both sides appear as mirror images (the knee bends point outward... actually they point backward on both sides).

Let me think again: a planar leg in the x−y plane at z=+w. Another at z=−w. If both are identical (same orientation), viewed from the front they look identical (both lean right, say). If left one is mirrored (x→−x) AND crank phase adjusted (θ→−θ+φ), it walks consistently and looks mirrored. Which do real beests do? From videos of Animaris: the crankshaft is one long shaft with crank throws; adjacent legs are often mirrored pairs (the linkage planes lean symmetric). I recall the legs come in mirrored pairs sharing throw orientation... With θ→−θ on a shared throw: the throw is a crank pin rotating in the x−y plane; both the right leg (uses pin at angle θ) and mirrored left leg (needs pin at −θ+φ) can attach to the SAME physical pin only if θ ≡ −θ+φ → 2θ = φ: not generally true. So mirrored pairs CAN'T share a throw — they need separate throws at different phases. The thesis said "two legs are in pair and are mirrored, where they share the same crank" — hmm, maybe "share the same crankSHAFT". Whatever — in MY sim I have full freedom: crank throws at arbitrary phases per leg. I'll do mirrored left legs with θ' = −θ + φ (verified consistent above), phases assigned so footfalls alternate.

But visual: crank throws (disks/pins) per leg on the shaft — fine.

Hmm, actually hold on — let me reconsider whether mirrored+negated is even needed aesthetically. Simplest correct: all 12 legs IDENTICAL orientation (no mirroring), phases staggered. From videos this looks totally fine (many walking-machine toys do this). But real strandbeest silhouette has the beautiful symmetric "spider" look from the front... I'll go with mirrored left legs since I verified the math — it's just a sign flip on x and θ.

Now — footprint orientation: foot is a flat-ish "shoe"? In my mechanism the foot is point H (the real beasts have a flat foot plate attached at the triangle EFH... the foot in the drawing IS the point H; real ones add a small flat pad). I'll add a small pad mesh at H aligned with body (stays roughly level during stance — attach pad with orientation from segment E→H? During stance the triangle's orientation w.r.t. ground: keep pad level for simplicity — pads stay horizontal, like snowshoes ✓ looks right).

Rod rendering: rods as cylinders between joint points (in 3D, at each leg's z-plane). For the mirrored side, joint x negated. Crank pin B also needs a small axle stub connecting to the crankshaft (from z_shaft surface to leg plane). The crank THROW: the pin at B rotates around M on the shaft: draw a crank arm (box from M to B at leg z) or crank disk. Crank disks per leg (12 disks on the shaft, each with offset pin) — chunky and mechanical ✓.

Frame: A and M pivots connect to body: M = crankshaft axis (shared). A = a fixed rod along z at A positions (an "axle" rod the rockers pivot on — the triangle ACD pivots around the A-rod). So the frame: two long parallel shafts along z: crankshaft (at M height) and A-rod (below-left... A=(0,0), M=(a,l)=(38,7.8): M is 38 right, 7.8 up from A in local frame; in walking direction... note walking direction: body moves −x when ω>0 (from v=−19.4ω). Hmm — which way is "forward"? If the beast walks toward −x_local, then the foot path's x-extent is symmetric anyway. I'll orient local frame so forward = +z_world and rotate the whole leg group: legs' local x → world forward. Simplest: build the beast in a group where legs lie in x−y planes (z = body axis), walking direction = local x; then rotate group −90° about y so local x → world +z? or just keep walking along world x and place the ocean at z<0, camera looking at the side (z>0 view). Walk along +x world: set crankRate sign negative (since v_body=−19.4·ω·s, want v>0 → ω<0). Fine.

Spine/frame above: connect M-shaft and A-shaft with triangular trusses at each z slot (vertical plates), plus a raised mast holding the rotor, plus two diagonal braces. Gears near center: big gear on crankshaft, small gear on rotor shaft, plus an intermediate? Keep: crankshaft big gear (r 0.42m) ↔ layshaft... rotor shaft vertical? Wind rotors on beests: horizontal axis facing the wind (like windmill). Wind blows along... to walk INTO the wind, rotor faces forward (axis along x, at front of beast, up high). Rotor drives via bevel gear down a vertical shaft to the crankshaft?? Real beests: the rotor is at the back/top with bicycle-like hub, driving the crankshaft via gears/belts in the spine. Simplify visually: rotor on top (axis along x, facing forward), a vertical drive shaft with two bevel gears connecting to crankshaft... bevel gears are visually complex; use a chain/belt: two pulleys + a belt (torus segments?) — a simple belt: two pulley discs + two thin box "belt" runs between them, no animation of belt texture needed (or animate dashed texture offset). Belt drive: rotor pulley (r=0.25) at top, crank pulley (r=0.5) at bottom, belt as 2 stretched boxes + end caps... use a flat torus stretched? Simplest: draw belt as a thin elongated rounded box (capsule) around both pulleys: a RingGeometry extruded... I'll build belt from 2 cylinders (straight runs) + 2 half-tori at pulleys — doable: path as rounded rectangle in a plane; use TubeGeometry along a closed curve (CatmullRom or custom path) — TubeGeometry with a custom closed curve class... simpler: LinePath... honestly, simplest reliable: two pulleys + belt = ExtrudeGeometry from a rounded-slot 2D shape (Shape with absarc) in the x−y plane, thin extrusion in z. One mesh, static, done. Animate pulley rotation only.

Gear ratio visual: rotor rpm = crank rpm × (0.5/0.25) = 2× … wind rotors spin much faster: ratio 4: pulley top r=0.18, bottom r=0.72? Bottom pulley r 0.72 on crankshaft between legs — z-space is tight (legs at z spacing 0.7m; put drive at center z=0 where no leg... 12 legs at 6 slots × 2 sides; center slot gap available. Pulleys in the vertical mid-plane z=0 ✓.

Rotor blades: 6 blades, each: spar (thin box) + triangular canvas sail (custom BufferGeometry or PlaneGeometry skewed, DoubleSide, slight curl via vertex bend baked in geometry). Rotor hub + nose cone. Rotor axis slightly above spine at front? Real ones: rotor at the top rear... place at top center, mast from spine. Rotor faces +x (forward into wind) — the beast walks into the wind ✓ poetic.

Canvas texture: procedural via Canvas API: weave noise + seams + patches. Wood texture: canvas stripes. Sand texture: shader noise (no texture needed) + footprint canvas.

Numbers: scale s=0.042 m/unit. Leg geometry local coordinates × s.

• A height = 84.03·s = 3.53m. Hmm big beast. s=0.038 → 3.19m hip, stance span 2.58m. Let's s=0.04: hip 3.36m.
• z slots: 6 slots each side at z = ±(0.55 + n·0.62)m? Body length ~ 2·(0.55+5·0.62)+... = slots at |z| from 0.55 to 3.65 → body ~7.3m long. Big majestic beast ✓. Spine length ~7.5m.
• Rotor: mast top at ~5.2m, rotor radius 1.6m.

Performance: 12 legs × 11 rods = 132 cylinders + 12 crank disks + 8 joint spheres per leg (96)... use InstancedMesh: rods (cylinder unit, per-instance matrix compose from endpoints), joints (sphere, per-instance position, two sizes), crank disks (instanced cylinders, pose from θ_i), pads (instanced boxes at H). Frame meshes: few boxes/cylinders individually. Rotor: group. Total draw calls ~25 ✓.

Rod instancing: matrix per rod per frame: position=midpoint, quaternion from +Y to direction, scale=(r, len, r). 12 legs × 11 rods: compute per frame — cheap. Rods list per leg (endpoints in joint set): MB(crank arm? drawn as disk instead — skip MB rod), rods: BC(j), BF(k), AC(b: rocker side), AD(d), CD(e), DE(f)... wait careful with triangle rods: triangle ACD sides: b=AC, d=AD, e=CD. triangle EFH sides: g=EF, i=FH, h=EH. plus rods j=BC, k=BF, c=AF, f=DE. Total drawn rods per leg: b,d,e,g,i,h,j,k,c,f = 10 rods + crank disk. Hmm count: 4 (j,k,c,f) + 3 + 3 = 10. ✓ plus pads. So 120 rod instances + 12 disks + pads 12 + joints: A,B,C,D,E,F,H ×12 = 84 + M stubs... ~90.

Joints: small cylinders along z (pins) — instanced cylinders oriented along z (constant orientation!), scale z... just small spheres or z-cylinders: cylinders along z: quaternion fixed, position from joint ✓.

Sand puff particles: THREE.Points ~600 particles pool with per-particle velocity/gravity/fade in shader — standard.

Wind sand streaks: Points ~800 streaming +x near ground with noise sway, wrap in a 60m box around beast. ✓

Gulls: 6 gulls = cone body + 2 wing planes flapping (rotation.z = sin(t·6+i)·0.5), circling above water. Cheap meshes. ✓

Sky: shader dome (fbm clouds, sun disc+halo, warm gradient, stars none at golden hour). Fog: THREE.Fog matching horizon color.

Ocean: plane 800×300 at z from −15 to −300 (water line around z=−12±2m with slow oscillation), custom shader: gerstner-ish vertex waves (3 sine/octaves + fbm normal detail), fresnel reflection of sky gradient (approximate with same gradient function inline), sun glint (specular streak), foam: shoreline band + wave-crest foam via noise threshold. Alpha blend at shoreline. Also secondary "wet sand" darkening band on sand shader synced with same shoreline phase. ✓

Sand: big plane (800×120, z from −15 to +105): shader with: base sand color, fbm grain (2 octaves value noise), large ripple bumps (anisotropic noise along x), footprint CanvasTexture (covers 200×40 region centered near beast x, updated on plants), wetness band (darken + slight blue reflection tint), sparkle glints (hash sparkles ∝ view angle). Receives shadows (ShadowMaterial? custom shader + shadows = need lights_fragment... using onBeforeCompile on MeshStandardMaterial to inject noise/footprint/wetness into map/color — keeps shadows+fog for free. I'll do MeshStandardMaterial + onBeforeCompile injecting into diffuseColor via vUv/world pos. Need world position varying: add in vertex. ✓ This is the pragmatic path for both sand and ocean? Ocean with MeshStandardMaterial + onBeforeCompile for waves... vertex displacement + custom normals: inject into begin_vertex and beginnormal_vertex. Doable but fiddly; ocean as pure ShaderMaterial with manual fog + no shadow receive (nothing casts on it) — simpler: ShaderMaterial with fog: true and include fog chunks manually... I'll write fog manually (mix by distance) — fine.

For time: keep ocean ShaderMaterial straightforward.

Beast reflection (wet mirror): clone group approach with scale.y=−1 — but beast is animated via per-frame rod matrices; cloning = duplicating the whole beast update (2× instanced meshes, matrices computed once, applied to two InstancedMeshes with extra y-flip matrix multiply). Actually simplest: reflection InstancedMeshes get matrix = flipM × rodM. flipM = scale(1,−1,1). Then ALSO multiply instance matrix... order: flip∘rodM: mirror across y=0 plane AFTER rod transform in world → correct mirrored pose ✓. So second set of instanced meshes (rods2, joints2, disks2, pads2) with same counts; plus frame/rotor reflection: add those few static meshes mirrored (static except rotor spin — rotor is dynamic... reflect rotor too: parent mirror group? I'll put ALL beast meshes (main + rotor + frame) under beastGroup; reflection = new THREE.Group with cloned instanced meshes + cloned frame meshes + cloned rotor group, updated by copying matrices with flip. Hmm, rotor reflection: clone rotor group, per frame: rotorClone.position = (x, −y, z) of rotor, quaternion mirrored... mirroring rotation across y=0 plane: q' = (qx, −qy, −qz, qw)? For reflection across xz-plane (y→−y), rotation conjugate: R' = M R M⁻¹ where M=diag(1,−1,1): quaternion transforms as (w, x, y, z) → (w, x, −y, −z). ✓ easy.

Simpler: reflectionGroup = beastGroup.clone()? Cloning InstancedMesh shares instanceMatrix buffer?? .clone() of InstancedMesh shares the same instanceMatrix attribute?? In three.js, InstancedMesh.clone() copies... it calls copy() which copies instanceMatrix reference? InstancedMesh.copy copies this.instanceMatrix = source.instanceMatrix.clone()? Let me not rely on it. Cleanest: build beast twice via builder (two full sets), and in the update loop write matrices to both sets (second = flip×first). Double memory, trivial CPU overhead (12×11 matrix writes). ✓ Materials for reflection: same geometries, darker materials (color×0.3, transparent? no—opaque under sand which is alpha-blended in wet band). Sand alpha in wet band ~0.75 → reflection shows at 25% → subtle ✓. BUT: sand is a MeshStandardMaterial with transparent=false... enabling transparent on the whole sand plane = sorting issues with ocean (also transparent)... Manageable: sand.transparent=true, renderOrder: reflection-beast renders in opaque pass (it's opaque, drawn first among opaques by depth), then sand (transparent) draws over it ✓, ocean transparent drawn after (further)... Ocean and sand overlap region: ocean renderOrder > sand renderOrder, both transparent → sorted by depth anyway; set ocean.renderOrder=2, sand.renderOrder=1 to be safe. Reflection only visible where sand alpha < 1 (wet band near water + faintly overall? make dry sand alpha=1 opaque so reflection only in wet mirror zone ✓).

Wait — but if sand is transparent with alpha=1 in dry zone, it still goes in transparent pass → main beast (opaque) drawn before ✓ fine. Footprints canvas texture with alpha... footprint darkening multiplies diffuse; keep alpha channel for wetness only.

Hmm, one more consideration: the reflection clone also appears ABOVE ground if sand alpha<1? No: reflection is BELOW y=0; sand plane at y=0 occludes... transparent sand lets below-plane pixels show through ✓ that's the point. In dry areas alpha=1 → no reflection ✓. Wet band near water alpha 0.72 → mirror-ish ✓. Between: subtle fade. Also add a blur illusion: reflection materials darker + fog — reads as wet sheen ✓.

Shadows: main beast castShadow; reflection set castShadow=false ✓.

Footprint stamping: track each foot's planted position; stamp ellipse (dark, soft edge, ~0.35×0.5m) into canvas at world→uv mapping; canvas 2048×512 covering 200m×50m around... feet are within |z|≤4m of beast center; sand strip for prints: x∈[beastX−120, beastX+80], z∈[−14(water edge),+14]. Canvas follows beast: when beast moves, shift uv offset (uniform) instead of redrawing: keep canvas fixed to WORLD (not beast): world is endless though... canvas covers fixed world window [x0, x0+200]; when beast x > x0+140 → x0 += 140, clear canvas (prints behind are gone). Teleport visible? The window edge would be 60m ahead of beast — at fog distance ~... make window 260m, jump when beast within 100m of edge, jump distance 120m: old prints in overlapped region... overlap region [x0+120..x0+260] maps to different uv → prints would jump/duplicate. Accept: fade prints continuously (global fade: every second, ctx.fillStyle='rgba(255,255,255,0.02)' with 'destination-out'? that erases alpha... my footprint texture uses rgb multiply; fading = draw translucent base-color rect over entire canvas every few seconds → prints lighten toward base → then region jumps are invisible since prints faded in ~30s. ✓ good enough.

Base color of footprint canvas: white (multiply neutral); prints = dark brown-gray multiply.

Gull audio: skip gull cries maybe; keep: wind, surf, foot clunks, gear creak, rotor whoosh (filtered noise amplitude ∝ rotor speed... nice: blade-pass frequency pulse). All synthesized.

UI:

• Title HUD "STRANDBEEST · Windwalker Nº66"
• Wind slider (0–12 m/s), auto-gusting toggle.
• Camera: Cycle button [Track | Orbit | Low tide (close side) | Rotor cam]? Keep: Track / Orbit / Free-orbit target beast. OrbitControls with target following beast + damping; "Track" = auto cinematic path (lerp between preset offsets slowly); user drag switches to orbit.
• Buttons: Pause, stride direction (Walk ↔ reverse: flip crankRate sign — fun: beast walks backward!), Snapshot, Mute.
• Stats: wind m/s, rotor rpm, speed, distance walked, steps.
• Toast on actions. Keyboard: arrows/WASD = wind up/down, camera.

Post: UnrealBloom? The sun in sky shader + glints... bloom would make sun glints on water gorgeous. 064 used EffectComposer+UnrealBloom from addons successfully → I'll include bloom (threshold ~0.85, strength 0.35) + maybe Vignette via ShaderPass... keep bloom only, plus renderer ACESFilmic. OutputColorSpace handling r160: with composer, use OutputPass? In r160: composer.addPass(new OutputPass()) handles tonemapping+srgb. Import OutputPass from addons ✓ (exists since r152ish).

Adaptive quality: if fps < 45 for a while: reduce pixelRatio & disable bloom. ✓ (pattern from 065).

Alright — also import map: {"three": ".../three.module.js", "three/addons/": ".../examples/jsm/"}.

Now, quick numerical decisions to lock via Node (fast):

1. Branch picks per frame with continuity (pick closest to prev) — verified working ✓ (already ran full revolution).
2. Pad orientation: pad at H; angle = angle of segment F→H? or keep pads world-level. I'll compute pad yaw from... keep level.
3. Body vertical bob: hip height constant + small bob = mean of stance feet deviation... skip bob (flat bottom) — add tiny procedural sway of spine roll (0.5°, slow) for organic feel.

One more numerical check I should do: continuity branch-picking when legs run BACKWARD (θ decreasing) — pick-closest works both ways ✓. And at startup prev=pose from svg ✓ hardcode that initial guess per leg (with phase: solve stepping from θ0 to target phase in small increments to move branches smoothly to the phase config). At init for each leg: start prev from svg pose, step crank from θ0 to φ_i in 60 steps ✓ robust.

Rod endpoints local: rods connect joint→joint in leg's x−y plane, then to world: (x·s, y·s, z_leg) + beast pos, mirrored legs: x→−x AND their crank disk rotation mirrored.

Wait, mirrored legs: geometry x_m = −x, and θ_m = −θ+φ. In local coordinates I compute joints with solve(θ_m) then negate x ✓ (equivalent, as shown). Crank disk for mirrored leg: disk is symmetric; pin at B_m = (−Bx, By) with θ_m ✓ automatically from joints. ✓

Walk direction & ocean placement: beast walks +x. Ocean at z<0 (waves come from −z toward +z shore). Wind blows from +x toward −x?? Beast walks INTO the wind → wind from +x: sand streaks blow toward −x; rotor faces +x ✓. Gulls circle over water z∈[−80,−20]. Sun: low in sky at... put sun ahead-left over the ocean (toward +x,−z) for rim light + glints ✓ gorgeous: beast silhouette against sun-glittered sea, walking toward the sun. Sun elevation ~7°.

Camera track mode: default offset behind-right-above looking forward-ish... classic shot: from the beach side (+z), slightly behind, low height 2m, looking at beast mid; sun ahead → backlit rim ✓. Slow dolly around presets.

OK. Time to write the file. ~1000 lines. Let me write it in one careful pass, then node --check the module script, then quick sanity greps, deploy, update index.

File: /space/demos/066-strandbeest/index.html

Let me carefully draft the JS architecture:

Constants: Jansen lengths, S=0.04 scale, NL=12 legs, ZSLOTS.

Linkage solver (as tested), per-leg state prev joints.

Beast build:

• materials: wood, woodDark, brass, cloth, padMat (dark rubber-ish), reflect materials (cloned darker, BackSide).
• geometries: unit cylinder (open-ended along Y, 8 radial), unit sphere low, crank disk cylinder (r=0.30m? crank radius m·S=0.6m — disk r=0.34 < crank throw 0.6: pin at edge... crank pin at 0.6m from center: disk r 0.62 with counterweight look: make disk r=0.62, pin at edge ✓ chunky), pad box (0.55×0.08×0.4), rods cylinder.
• InstancedMesh rods: count NL10; joints: NL7 pins (A,B,C,D,E,F,H) cylinders along Z + NL2 (M stub + foot axle?) keep NL7.
• Per-frame update: for each leg: solve, write rod matrices (mid, quat, scale), joint matrices, disk matrix (rotZ by crank angle... disk at M with rotation θ_leg about z-axis (in local leg plane) — disk orientation: cylinder axis along Z; plus rotor/pulleys/spine static.

Wait — coordinate mapping: leg plane = world x−y at z=z_leg ✓ so cylinders for joints along Z axis: quaternion = rotX(90°) (unit cylinder Y→Z) ✓ fixed.

Frame: spine = box along z at (x_M·S·0.5-ish? Actually spine should sit above A/M line... M=(38,7.8)·S=(1.52,0.312) rel A; A at hip height 3.36. The body trunk: connect A-rod (long cylinder along z at A) and crankshaft (along z at M) with vertical plates at each slot (triangle plates A-M-spine top). Add top deck box along z at y=+0.5 above M, mast at center to rotor, diagonal braces. Keep simple but layered: A-shaft (r 0.06), M-crankshaft (r 0.05), deck (box 1.2×0.12×7.6) at y = M.y+0.45, struts at slots: box from A to deck (angled) ×6, mast (cylinder) center 1.8 tall, braces.

Rotor: group at mast top (x = M.x (local), y ≈ M.y+2.3, z=0): hub sphere + 6 blades (group per blade: spar cylinder along radius + sail plane (custom geometry: triangle-ish trapezoid with slight bend) attached at angle of attack ~18°), nose cone. Rotor rotates about local X (facing +x wind) ✓ blades sweep in y−z plane.

Belt drive: bottom pulley on crankshaft (r 0.55, z=0 plane, i.e., pulley disc in x−y plane at z=0), top pulley on a jackshaft at mast mid... rotor axis is along x; belt to jackshaft then bevel to rotor? Simplify: drive shaft along z at deck level?? Ugh. Alternative real-beest homage: the rotor shaft goes down the mast diagonally and connects via two bevel gears to the crankshaft — too complex. PRAGMATIC: belt from crankshaft pulley (vertical plane x−y, z=+0.2) up to a pulley on the ROTOR shaft?? rotor shaft axis along x → its pulley would be in y−z plane — belt twist 90° = weird.

New simplification: rotor axis VERTICAL?? Some strandbeests have vertical-axis wind rotors?? No — real ones have horizontal-axis propellers facing the wind driving a vertical mast shaft down via bevel gear... Actually many beests use the "windmill" on top with a vertical crankshaft down... You know what, visual fidelity of transmission is not critical: I'll do: rotor (axis along x) → on the rotor shaft a small gear; a vertical drive shaft inside the mast with a bevel gear pair (two cones with teeth hint: just two cone gears meeting at 90° — visually reads as bevel gear!) at top; at bottom another bevel pair to the crankshaft. Gears = cylinders with box teeth around. Bevel gear meshing at 90°: rotations: rotor ω about x → shaft ω about y (sign/ratio via cone radii) → crankshaft ω about z... wait crankshaft axis is along z (body axis)? NO — crankshaft: the cranks rotate in the x−y leg planes → crankshaft axis along Z ✓. So: rotor (x-axis) → bevel → vertical shaft (y-axis) → bevel → crankshaft (z-axis) ✓ 90° turns each ✓✓ mechanically plausible and looks amazing with 4 bevel gears + a shaft. Gear ratios: rotor:crank = 5:1 (rotor faster) — visual only: rotate accordingly. Teeth: instanced small boxes on gear rims (24 big/12 small ×4 gears = ~72 instances static) — or skip individual teeth on bevel gears; use grooved cones (ridged texture via normal-ish stripes in material? meh) — just make bevel gears as two truncated cones (CylinderGeometry with different top/bottom radius) with tooth boxes: small count, do it: static teeth placed once around each cone rim — 4 gears × 14 teeth = 56 boxes, merge into one geometry? Just create meshes; static scene objects, 60 draw calls extra... hmm. Use InstancedMesh for teeth (unit box, 56 instances set once) ✓ 1 draw call.

Spur vs bevel: cones at 45° meeting — good enough silhouette.

Rotor spins by wind; crank = rotor/5.

Leg speed linkage: crankRate ω = windSpeed mapped: wind 0..12 m/s → rotor 0..~4 rad/s with spool-up lag (inertia!) → ω_crank = rotor/5 → walk speed = 19.38·S·ω_crank ≈ 0.775·ω_crank m/s: at wind 8 → rotor 2.7 → crank 0.53 → v 0.41 m/s... bit slow; ratio 4: crank 0.67 → 0.52 m/s; wind 12: rotor 4, crank 1, v 0.78 m/s ✓ stately. Add idle creep? At wind 0: rotor→0, beast stops ✓ (with spool down).

Foot plant detection: per leg track H world y; plant when y crosses S-adjusted ground (~0.02m) downward... with hip fixed, min foot y = 0 by construction (hip = 84.03·S exactly): foot min y ≈ 0.00 — bottom flatness 2.2 units → foot dips to 0 but most of stance at ~+0.05?? Hmm: y range −84.03..−61.58; hip at 84.03·S → lowest point exactly 0; during most of stance foot hovers up to +0.09?? flatness 2.24 units×0.04 = 0.09m: feet would float up to 9cm above ground during much of stance — visible! Fix: hip = (yMin + 0.35·flatness)·S?? Let me instead compute hip so that the MEAN stance bottom = 0.012m: then max dip = −0.07 (foot sinks 7cm into sand — FINE, it's sand! feet sink ✓ natural). Compute numerically: hip_offset = −(mean stance y) + 0.012. I'll compute at init from sampled path. Actually simpler: set hip = −yMin·S − 0.045 (sink 4.5cm at lowest) → most of stance foot at 0..4.5cm above ground, touching at extremes... plant detection: foot y < 0.03 && descending → plant event at contact... prints appear slightly before actual touch, ok at 60fps. Let me just set hip so min y = −0.03 (3cm sink) and plant threshold y<0.02.

Body pitch/roll: slight roll = sin(t·ω_step)·0.6°, pitch constant −1°, plus bob y += sin(2·stridePhase)·0.02. Subtle ✓.

Stride phase for sounds: footsteps from plant events ✓ real ones drive audio.

Camera presets (Track mode cycles every ~14s with smooth blend):

1. Side dolly: pos = beast + (0, 1.6, +9.5), look at beast+ (3,2.2,0)
2. Front 3/4 low: beast + (+10, 1.2, +6), look +2 ahead
3. Rear rotor: beast + (−7, 4.5, −4) looking at rotor/beast
4. Water side silhouette: beast + (+4, 1.0, −10) — from ocean side, beast against sky?? camera over water looking back ✓ gorgeous with sun glints OrbitControls: enabled always; Track mode = auto-updates camera unless user interacts (pointerdown → switch to Orbit mode). Modes via button: Auto / Orbit.

Sun position: azimuth ahead-left: dir from beast: (60, 9, −80) normalized → sun over ocean ahead. Golden: color 0xffd9a8, intensity 2.6; hemi: sky 0x9db8d9 ground 0x8a7358, 0.5; ambient small. Fog: color horizon #e8b98a... scene.fog = new THREE.Fog(0xe9c39a, 60, 420). Sky shader handles sun disc.

Bloom threshold 0.8 strength 0.45 radius 0.6.

Ocean shader plane: 900×400 at y=−0.15 (mean waterline), centered z=−200, x following beast? make ocean HUGE (2000) centered origin; waves vertex: 4 gerstner waves along +z (toward shore) + chop; normal from analytic derivative + fbm detail normal in fragment; color: deep #0b3d5c → shallow #3fa7a0 by depth fake (z distance from shore + wave height); fresnel → sky reflect color (mix horizonWarm/zenith); specular sun glint (blinn pow 600 × sun color) + sparkle noise; foam: crest foam (smoothstep on wave height × noise) + shoreline foam band: shoreZ(x,t) = −12 + sin bands (t, x) → foam where worldZ near shoreZ within 2m with lapping stripes (sin(worldZ·2 − t·1.5)·noise). Alpha: 1 deep → fade at shoreZ − 1.5... wet band on sand: darken where z < shoreZ+4 + hysteresis via another sine (slow) → implement matching formula in sand shader with same uniforms (uShore = f(x,t) needs x-dependence: shore line curves: shoreZ(x) = −12 + 3·sin(x·0.01+t·0.05) + lapping: + 2·sin(t·0.35 + x·0.05)). Pass uTime; both shaders compute identical shoreZ ✓.

Sand plane 2000×130: z from −16 to +114 (overlap under ocean 2m), y=0. onBeforeCompile MeshStandardMaterial: inject uniforms uTime, uPrintTex, uPrintRegion(vec4), varyings vWorldPos; diffuse modifications: grain noise, ripples (normal perturb? skip normal — use diffuse shading trick: lighten/darken by ripple derivative), wet band (darken + saturate), prints multiply, glints (hash sparkle × sun-facing). roughness 0.93 dry → 0.55 wet (inject into roughnessFactor). ✓ keeps shadows & fog.

prints canvas: 2048×512, region 220×55m: uv = ((wx−rx0)/220, (wz−rz0)/55). update uPrintRegion on jumps. feet z ∈ ±4 → z strip [−16..+14]... make region z [−18, +12]: 30m → canvas 2048×384. eh fine: region z0=−18, depth 30.

Distant scenery: dune ridge at z=+70 (long box ridge with dune shader color... simple: 2-3 long low ridges (extruded triangles) with sand color + fog does the work), some rocks (icosahedrons flattened, gray-brown) scattered z∈[10,60], recycled mod 500m; driftwood logs (cylinders) few; a wrecked older beest skeleton far behind?? (a few arcs: torus segments + rods) — cute storytelling, cheap: place 2 wrecks at fixed world x recycled with the mod system. Keep: dunes, rocks, driftwood, gulls. ✓

Recycling: props[] with worldX = base + n·spacing; each frame: prop.position.x = baseX + floor((beastX−baseX)/spacing... simpler: prop.x = mod(baseX − beastX, 600) + beastX − 150 → wraps within [beastX−150, beastX+450] ✓.

Sand streak particles: Points 700, positions in shader: x = mod(seedX − t·windSpeed·3, 60)+beastX−30, y=0.05+hash·0.5+sin, z=hash·40−10, size 1-3px, alpha by edge fade — do CPU-less: custom shader with uniforms uTime, uWind, uBeastX; per-particle attributes seed. ✓ cheap.

Puffs: pool 400, CPU update (fine): spawn 6 per plant at foot pos, vel random up/out, gravity −2, life 0.9s, size attenuation, soft round sprite (canvas radial), additive-ish alpha 0.35 tan color. ✓

Audio engine (all synth, no assets):

• master: ctx, gain (muted until toggle), compressor.
• wind: bufferSource loop white noise → bandpass 400Hz Q0.4 → gain ∝ wind + gust LFO (slow random). stereo: second noise delayed panned.
• surf: noise → lowpass 500 → gain modulated by shore lap phase (use same lap sine value from JS: gain = base + lap·0.5) + foam hiss bandpass 2000 × lap spike.
• footstep clunk: on plant: noise burst (0.06s, lowpass 300) + sine 70Hz decay 0.12 + tiny knock 180Hz. velocity ∝ crank speed. slight random detune ✓.
• creak: every few strides: short bandpass sweep 300→500 on sawtooth 0.15s quiet + ratchet clicks for gears (tiny highpass bursts at gear tooth frequency ∝ crank speed, very quiet).
• rotor whoosh: noise → bandpass at blade freq (rotor·6 blades)·gain ∝ rotor² — amplitude pulsed: gain *= (0.5+0.5·sin(t·rotor·6)) — do with setTargetAtTime per frame? cheaper: LFO oscillator → gain.gain via GainNode automation from JS each frame (smooth). ok.
• gull cry (rare random): two descending sine glides 1200→700 with vibrato, echo via delay. nice. Mute toggle + volumes. Init on first pointerdown/key (policy).

HUD: styled like 065 (serif? this is industrial/poetic: use letterspaced small caps sans). Bottom bar: Wind slider, gusts btn, Walk◀▶ btn, pause, camera mode, mute, snapshot. Stats right-top. Hint left-bottom. Toast.

Title: "Strandbeest — Windwalker Nº LXVI"? Demo folder 066-strandbeest. Title: "Strandbeest — a wind-walker on an endless shore".

Snapshot: renderer.domElement.toDataURL after render (preserveDrawingBuffer or render-on-demand before capture: composer.render(); then toDataURL — need preserveDrawingBuffer:true OR capture immediately in same frame — call snapshot within rAF after render: standard trick: set flag, in loop after composer.render() if flag → toDataURL → download ✓ no preserveDrawingBuffer needed).

Adaptive quality: track EMA fps; if <45 for 3s: pixelRatio→1 (from min(dpr,2)), bloom off; if still <40: disable reflection set visible=false + reduce ocean segments?? ocean static geometry — skip; just pixelRatio 0.85. Show toast "Quality adjusted".

Resize handler ✓.

Pause: stops crank/wind integration (rotor spools down), camera still live.

Direction toggle: crankTarget sign flip (beast walks −x: camera offsets flip? keep simple: allow reverse; world wraps handle ±x; sun stays — walking away from sun, still pretty). ✓

Also — IMPORTANT — OrbitControls import: target = beast position (lerp follow). In Auto mode: disable controls.enable? Set controls.enabled=false in Auto; on pointerdown while Auto → switch to Orbit + enable. In Orbit mode: controls.target lerps to beast+look offset each frame ✓.

Edge case: beast walks +x forever → float precision: after hours x huge; wrap beastX mod 10000? At 0.7m/s, 10000m = 4h — ignore, but do reset at 5000: shift beast −5000 & prints reset (fog hides). Add silently.

Let me now write the code. I'll write it as one big file via write tool. Estimated 1000-1100 lines. Then extract the module script → node --check.

Some shader details:

Sky dome (ShaderMaterial, BackSide sphere r=1500, fog:false, depthWrite:false, renderOrder=-1... draw first): uniforms: uSunDir, uTime. frag:

• base gradient: mix(horizon #ffd9a8, zenith #7fa8d8, pow(max(dir.y,0),0.55)); below horizon: duskier.
• sun: d=dot(dir,sunDir); disc smoothstep(cos(0.9993..)) + halo pow(max(d,0),180)·1.2 + wide glow pow(,8)·0.35.
• clouds: 2D fbm in dir.xz/dir.y plane (project dir onto plane y=1: p = dir.xz/(dir.y+0.15)·1.5 + wind offset t·0.006): fbm 4 octaves value noise; cloud mask smoothstep(0.55,0.75,fbm) × horizon fade; cloud color lit warm on sun side: mix(#fff4e2, #ffb98a, sunward) ; thin high streaks: another fbm stretched (p.x*0.3) subtle.
• output color, keep <1 mostly except sun disc >1.2 for bloom.

Ocean ShaderMaterial: uniforms uTime, uSunDir, colors, fog uniforms (color, near, far), transparent:true. vertex: gerstner 3 waves (dir +z mostly): pos.z += A_i·... keep simple sum-of-sines displacement y + slight x/z shift; compute normal analytically via derivatives accumulation. varying vN, vWorld, vWaveH. frag: viewDir; fresnel = pow(1−max(dot(N,V),0),3); base = mix(deep, shallow, shoreFactor+w·crest); reflect = mix(horizonC, zenithC, reflectDir.y)... approximate sky(refl): grad function; col = mix(base, skyRef, fresnel·0.85); spec = pow(max(dot(reflect(-sunDir... blinn: h=normalize(V+sunDir), pow(max(dot(N,h),0), 700)·3·sunColor + sparkle: hash(floor(w.xz7)+floor(t3))>0.997 → +0.8; foam: crest: smoothstep(0.55,0.8,vWaveH)·noise(w.xz·0.8+t)·0.6 + shore: band near shoreZ: smoothstep(2.2,0.4,|wz−shoreZ|)·(0.5+0.5·sin(wz3.1−t2.2+noise2))·0.9; col+=foam·#fff8ec·(1-fresnel); alpha: deep 0.96 → near shoreZ-1: 0; fog mix; shoreZ shared formula: float shoreZ(float x){ return -12.0 + 2.5sin(x0.011 + uTime0.045) + 1.6sin(uTime0.33 + x*0.045); } — second term = lapping surf ✓ sync in sand shader.

Sand onBeforeCompile injections on MeshStandardMaterial({color:0xd9bc8e... white since we tint in shader, roughness:1, metalness:0}): vertex: add varying vWorld; #include <worldpos_vertex> append vWorld = (modelMatrix·vec4(position,1)).xyz... modelMatrix available ✓. fragment: uniforms uTime, uPrints, uPrintReg(vec4 x0,z0,w,d), plus shoreZ fn.

• after #include <color_fragment>: grain: n1=fbm(w.xz3.0); ripples: r=sin(w.x1.9 + fbm(w.xz0.5)4.0)·... anisotropic dune ripples along wind (x): ripple=sin(w.x2.2+w.z0.3+noise3)0.5+0.5; col = base #e0c39a(0.92+0.08·n1) darken ripple troughs ×(0.96+0.05·ripple); wet: shore=shoreZ(w.x); wet=smoothstep(shore+5.5, shore+1.0, w.z)... wait z toward ocean = negative: wet where w.z < shore+... smoothstep(edge0=shore+6, edge1=shore+0.5, w.z)?? smoothstep needs edge0<edge1... use 1−smoothstep(shore+0.5, shore+6.0, w.z): w.z near shore →1, far (+6 inland)→0 ✓ plus permanent damp band: extra = smoothstep(shore+1.0, shore−1.5, w.z)... keep one band. col = mix(1.0, 0.62, wet); col = mix(col, col·vec3(0.85,0.95,1.05), wet·0.5); prints: uv=(w.xz−reg.xy)/reg.zw; if inside: tex=texture2D(uPrints,uv).r; col=mix(1.0, tex, 0.9); glint: sp=hash(floor(w.xz14.0)); glint where sp>0.995 && dot(N,V)... approximate: col += step(0.997,sp)·wet?·sunGlint·... keep tiny: + step(0.998, hash)·0.25·(1−wet);
• roughness: after #include <roughnessmap_fragment>: roughnessFactor = mix(0.95, 0.35, wet);
• alpha: need transparent for wet-mirror: material.transparent=true; inject at end (after opaque output?) — set diffuseColor.a in color_fragment injection: alpha = mix(1.0, 0.78, wetMirror) where wetMirror = 1−smoothstep(shore+0.2, shore+3.5, w.z) (narrower, closer to water than the darkening) ✓.

Footprints stamp: ctx on canvas 2048×384 fill #ffffff initially; stamp: radial gradient ellipse rgba(60,48,36,0.55)→transparent, scale (0.4,0.28)m→px: px/m = 2048/220 = 9.3; ellipse rx 1.9px?? 0.4m=3.7px — small; make prints bigger: foot pad 0.55m → stamp 5px dark + sand displacement rim: draw twice: dark center + light rim offset. Fade: every 2.5s: ctx.globalAlpha=0.03; fillStyle #fff; fillRect → exponential lighten ✓ (prints last ~40s).

needsUpdate on texture per stamp & fade tick ✓ (mark texture.needsUpdate).

Gulls: 5; each: body = small white capsule (sphere scaled), wings = 2 planes (0.5×0.16) hinged at body, flap rotZ = ±(0.2+sin(t·7+i·1.7)·0.55); path: circle center over water (beastX+off, 6+2·i, −35−8·i) radius 12+3i, angular speed 0.15+; bank into turn (rotZ body = 0.3·dir). Mesh lambert white. 15 draw calls — merge wings+body into one group per gull (3 meshes ×5 = 15 small calls, fine).

Wrecks: skip (time). Rocks: 14 icosahedra scaled flat, recycled; driftwood: 8 logs; dunes: 3 long ridges static at z 60-90 spanning x ±1000 (just long boxes with dunes color, fogged) ✓.

Stats DOM update 4×/s.

Audio graph code ~120 lines. Toast helper.

Alright, also the linkage per-frame solve: 12 legs × (5 circle-intersections) = trivial.

Also crank disks: orientation: cylinder axis default Y; need axis Z: quaternion rotX(π/2) then rotate about Z by θ_i: q = qz(θ_i)·qx90 ✓ position M_leg. Pin visual: small cylinder at B along z (part of joints set: B pin ✓).

Pads at H: orientation level: pad matrix = translation(H)·small yaw = angle of F→H projected? keep identity (level) ✓ scale (0.55,0.07,0.34).

Wait — pads should be at foot bottom: H is the bottom point already (foot tip). Pad centered at H + tiny y offset +0.035 ✓ sinks into sand at plant — good.

Reflection set: reflectGroup same structure; per-frame after writing main instance matrices: m2 = flip·m1 (flip=scale(1,−1,1)): m2.copy(flipM).multiply(m1) ✓ for instanced meshes setMatrixAt same index. Static frame meshes reflected: build them twice with scale.y=−1 group? Static frame: put frame meshes in frameGroup; frameReflection = frameGroup.clone(true)?? clone shares geometry ✓ materials — need darker: traverse clone, replace materials with reflect versions, set side=BackSide, then frameRefl.scale.y=−1, done (static — set once ✓). Rotor reflection: rotorRefl = rotor group rebuilt? rotor spins dynamically: rotorRefl = rotor.clone(true) with materials replaced; per frame: rotorRefl.position.set(rx, −ry, rz); quaternion: (qx,−qy,−qz,qw)... for reflection across y=0: q' = (qx, −qy, −qz, qw) — verify: reflection M=diag(1,−1,1); R' = M·R·M. For quaternion q=(x,y,z,w): conjugating by reflection isn't a rotation unless det>0: M·R·M has det = (+1)(+1)... det M = −1, so MRM has det +1 ✓ rotation; its quaternion: q' = (x, −y, −z, w) ✓ (reflection conjugation negates the components perpendicular... rule: for mirror along axis n, q' = (w, x−2(n·q)... for n=ŷ: (x,y,z,w)→(x,−y,−z,w) ✓).

Gulls/rocks/props: no reflection (they're away from wet band mostly) ✓.

InstancedMesh castShadow = true for rods/joints/disks/pads ✓ (shadow of marching legs = WOW ✓). Reflection set: castShadow false, receiveShadow false.

DirectionalLight shadow: camera box ~30m around beast, target follows beast; bias −0.0005, mapSize 2048.

One risk: InstancedMesh + shadows + many instances: fine.

Let me also compute exact hip height & stance speed & phase stepping in JS at init (reuse tested code). For phase-stepped init: for leg i with target crank angle φ_i: solve from θ0 stepping 80 steps to φ_i (continuous branch following) ✓ then per frame step from current leg θ to new θ in 1 step (small Δ per frame ✓ continuity holds; at 60fps Δθ = ω/60 ≈ 0.017 rad tiny ✓; when paused→resumed no jump since θ state persists ✓; direction change: continuous ✓).

Leg z positions: 6 per side: slots n=0..5: z = side·(0.62 + n·0.66) → from 0.62 to 3.92; spine length ±4.3. Phases: pair n: right φ=n·(2π/6), left φ=n·(2π/6)+π. All 12 distinct half-cycle... stance 54% → average 6.5 feet down ✓.

Hmm wait — right legs and left legs (mirrored) with the phase scheme: footfall timing spacing 2π/12 across all legs ✓ (left offset π interleaves).

Body x position: beastX += v·dt; v = −stanceSlope·S·ω_shaft... sign: measured dx/dθ=+19.38 during stance ⇒ foot moves +x rel hip ⇒ body −x rel ground ⇒ v_body_x = −19.38·S·ω. For walk +x: ω negative. I'll define walkDir=+1 (forward=+x) and shaftSpeed = −walkDir·ω_mag. Rotor sign: rotor faces +x; spinning direction either way visually; tie rotor ω_rotor = −shaftSpeed·RATIO·(rotorFacesForward?1:−1)... rotor direction should match "pulling into wind": any — link rotor ω = −5·shaftSpeed so reverse walking reverses rotor ✓ (wind would never do that but meh — better: rotor always spins same way by wind; when reversing (user button), rotor keeps wind direction while crank reverses = gears would break in reality lol — but visually nobody checks; still, tie them: reverse = whole machine reverses ✓ simpler story: "the beast turns its sails and walks back").

Actually simpler UI: forget reverse button; wind slider 0..12, gusts toggle; beast always walks +x into the wind... Add "Turn around" button? That requires rotating the whole beast 180° (yaw) — actually trivial: beastGroup.rotation.y = π!! Then it walks −x (its local forward flips)... but legs' local x maps... walking direction is derived from local kinematics; rotating the group rotates everything: world v = R·(local v) ✓ consistent automatically if I apply group yaw and compute v_world from group quaternion ✓. Turn-around = animate yaw 0→π over 3s while pausing stride (lift... it'd look like a smooth pivot on sand — acceptable & fun!). Hmm — time. Skip turn-around (scope!). Beast walks +x toward the sun forever. Poetic ✓. (Reverse = not needed.)

Camera Auto presets (relative to beast, beast faces +x):

1. (0, 1.7, 10.5) look (+2.5, 2.6, 0)
2. (+11, 1.1, 5.5) look (+2, 2.8, 0)
3. (−9, 5.0, −5.5) look (+1, 3.2, 0)
4. (+5, 0.9, −11) look (+1, 3.0, 0) [from sea side] Blend every 16s, ease; slight noise sway handheld.

Write it all now. Also add , HUD styling consistent w/ collection vibes (dark glass + brass accent since machine+beach: brass #d8a86a).

Fog: 0xe6c9a2, near 80 far 500; sky dome radius 1200 (inside fog far? sky material fog:false ✓).

Bloom: threshold 0.85, strength 0.5, radius 0.5.

Also renderer.toneMapping = ACESFilmic, exposure 1.05; outputColorSpace default srgb in r160 ✓; with composer: RenderPass→Bloom→OutputPass ✓.

Let me write the file now. I'll be disciplined. After writing: extract content → node --check; grep balance of braces in GLSL; then cp to /space (write via staging /tmp then cp to /space for s3fs safety per previous run's lesson); update index.html card.

Length estimate: ~1150 lines. GO.

Key numeric constants from verification:

• stance slope dx/dθ = +19.38 units/rad (I'll recompute at init anyway from sampled path — robust to sign).
• Actually do compute at init: sample one revolution (720 steps), get path, yMin, mean stance bottom, slope. Use those for hip height & speed constant. This self-calibrates ✓.

Rod list per leg (endpoints by joint name): rods = [ [A,C,b],[A,D,d],[C,D,e],[B,C,j],[B,F,k],[A,F,c],[D,E,f],[E,F,g],[F,H,i],[E,H,h] ] — 10 ✓ (A is a joint per leg: A = (0,0) local ✓ include as joint pin positions too.) Joints pins: A,B,C,D,E,F,H = 7 ✓ (M gets crank disk + shaft.)

Rod radii: j,k,e,f,g,h,i: 0.045m; b,d,c: 0.04; crank disk r=0.30?? crank throw m·S=0.6m: disk radius 0.34, pin at 0.6: pin sticks beyond disk → crank as ARM instead: box from M to B (rounded) + counterweight opposite: two boxes per leg?? Add rods entry [M,B] with radius 0.09 + counterweight box at −B dir... counterweight: skip (beests don't have them). So rods per leg = 11 (incl. crank arm M→B radius 0.07 thicker + brass). ✓ 132 instances total.

OK writing now. One more: mirrored left legs: I compute joints in local frame (x toward walk dir +x... hmm wait: local frame of beast group: legs in x−y plane; walking dir local −x or +x? v_body_local = −slope·ω·S. I'll set ω_shaft = −ω_mag (ω_mag>0 when wind) → v_local = +19.38·ω_mag·S → +x local ✓. Beast group yaw=0 → world +x ✓. Mirrored leg (left): θ_leg = −θ_shaft + φ = +ω_mag·t + φ; geometry x→−x ✓ stance slope: as computed earlier stays consistent (v local still +x) ✓.

Sun direction: toward (+0.55, 0.14, −0.75) normalized-ish; elevation ~8°.

Now write.