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Boy's Surface

The three-lobed, self-crossing Boy's surface turning in studio light under an iridescent, oil-slick skin. Loops perfectly.

3D object, V2 Objects3DSeamless loop, verified106 lines of codev1.0.0

In Science & maths, Light, glass & shine

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Boy's Surface preview
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Info

What it is

Boy's surface, the strange self-crossing sheet that is the projective plane immersed in ordinary space, drawn from the Bryant–Kusner formula and turning slowly in the studio light. Its skin is iridescent, shifting colour like an oil film or soap bubble as it turns; a fine net of curves runs along it; a clear-coated sheen catches the softboxes. Choose the finish (iridescent, chrome, pearl or dark), whether the net of curves shows, the fineness of the mesh, how many turns it makes about each axis, the backdrop and whether the camera drifts.

Reuse it in your own idea

  • Maths or topology explainer: Iridescent, with curves.
  • Design-studio showpiece: Chrome, bare.
  • Luxury abstract loop: Pearl.

Which part is reusable

src/boy-surface.js is the ingredient your AI reuses. demo.js is only the example scene around it, and uses chrome-material only for the demo.

Good to know

  • The surface crosses itself, so its inside and outside are both visible; the iridescence is the standard thin-film model, not a simulation.
  • The mesh near the centre of the disc (the surface's tip) is slightly coarse.

Technical details

Technical details
Implementation
Three.js 0.185.1 (WebGL) · ES module src/boy-surface.js
Exports
  • createBoySurface({ finish?, lines?, detail?, turnsX?, turnsY? }) => { group, setProgress(progress), dispose() }
  • boyPoint(r, theta) => [x, y, z]
  • FINISHES: { iridescent, chrome, pearl, dark }
Dependencies (exact)
  • three@0.185.1 (source) — Renderer, geometry and shader materials.
  • chrome-material@1.1.0 (demo) — Studio environment light, backdrop and contact shadow.
  • apw-runtime@1.0.0 (demo) — Demo harness.
How it fits a scene

Coordinates: The surface is centred on the origin, about 2 across before scaling; the demo scales it by 1.45.

Lighting: A warm key light with a shadow map and the studio environment on the clear-coated, thin-film surface.

Timing: setProgress(progress) sets the rotation; frames render in any order.

Output
1080×1080, 30 fps, 16 s · procedural (computed from the frame number) · seamless loop — The surface turns a whole number of times about x and y per loop and the camera drift is a sine of the loop, so the last frame meets the first.
Tested
Rendered 480 frames on 2026-10-05 in Chrome 154.0.8037.97 headless on Linux 7.0.0-38-generic (x64), Node 22.14.0 (WebGL 2 via SwiftShader (software)). Same frame twice from fresh pages: identical. Loop: Frame 0 vs end state (progress 1): mean |Δ| 0.0000, max |Δ| 0 of 255.
Performance
One mesh of about 22 000 vertices and a few thousand line segments, one shadow map. A few milliseconds a frame on an integrated Intel GPU. Software WebGL renders in about a second a frame.
Export a video yourself
Download the source, then in the folder: npm install npm run render -- boy-surface/1.0.0 --out my-video.mp4Needs Node 18+, ffmpeg and Chrome/Chromium. Add --params my-settings.json (from Copy settings) for your own settings.
Version
1.0.0 · sha256:793e94f99601df6d…
Files
License
MIT. Copyright (c) 2026 AI Pixel Wizard. Released under the MIT License. See LICENSE in this folder. License details
Provenance
Adapted from the owner's threejs-sketches/geometry-math/boy-surface (MIT) and rebuilt for AI Pixel Wizard in October 2026 as an original object: the Bryant–Kusner parametrisation evaluated on a welded grid, an iridescent clear-coated skin and whole-turn rotation for an exact loop.
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