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Minimal Surface

A soap-film surface that bends from a catenoid into a helicoid and back without stretching. Loops perfectly.

3D object, V2 Objects3DSeamless loop, verified101 lines of codev1.0.0

In Science & maths, Light, glass & shine, Liquids, Patterns & illusions

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Minimal Surface preview
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Info

What it is

A soap film's shape, and its famous disguise. The catenoid (the film between two rings) and the helicoid (a spiral ramp) look nothing alike, yet one bends into the other without stretching and without ever leaving the family of minimal surfaces: the Bonnet transformation. A single angle runs once round the circle, so the surface passes from catenoid to helicoid to the catenoid's mirror image and back, in iridescent glass with a net of curves. Choose the finish (iridescent, chrome, soap or gold), whether the net of curves is drawn, the mesh fineness, how far the surface reaches, the turns per loop, the backdrop colour and whether the camera sways.

Reuse it in your own idea

  • Maths explainer: Iridescent, one turn.
  • Delicate: Soap film, wide.
  • Product-style: Chrome, bare.

Which part is reusable

src/minimal-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

  • Only a patch of the surface is drawn, so it has open edges (a cut at u = ±π shows when it is a helicoid).
  • The soap finish is transparent without true refraction.

Technical details

Technical details
Implementation
Three.js 0.185.1 (WebGL) · ES module src/minimal-surface.js
Exports
  • createMinimalSurface({ finish?, lines?, detail?, reach?, turns? }) => { group, setProgress(progress), dispose() }
  • FINISHES: { iridescent, chrome, soap, gold }
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's axis is vertical through the origin; the group hangs 3.3 above the floor; the surface is the Bonnet family x = cos α sinh v sin u + sin α cosh v cos u and so on, u over −π … π.

Lighting: A warm key light with a shadow map and the studio environment.

Timing: setProgress(progress) rewrites the mesh from the family's closed form; frames render in any order.

Output
1080×1080, 30 fps, 16 s · procedural (computed from the frame number) · seamless loop — The Bonnet angle runs once round the circle over the loop, which returns the surface to itself, the group turns a whole number of times and its tilt 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
About 7 400 vertices rewritten and re-normalised each frame plus a net of lines: a couple of milliseconds a frame on an integrated Intel GPU. Software WebGL renders in about two seconds a frame.
Export a video yourself
Download the source, then in the folder: npm install npm run render -- minimal-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:d35837a5f9082b24…
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/minimal-surface (MIT) and rebuilt for AI Pixel Wizard in October 2026 as an original studio object: the Bonnet associate family of the catenoid and helicoid evaluated each frame with one trip round the family per loop, on an exact loop.
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