Skip to content
AI Pixel Wizard
Your sequence0 clips
Source

Dupin Cyclide

A smooth iridescent cyclide that breathes from a fat ring to a lopsided loop and back while it turns. Loops perfectly.

3D object, V2 Objects3DSeamless loop, verified122 lines of codev1.0.0

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

Next: Minimal SurfaceSurprise me

Dupin Cyclide preview
Starting live preview…
00:00:00:00 / 00:00:00:01

Live, running the real source at reduced resolution.

Your current settings go with it. Combine several clips and hand them over together from your sequence.

Effect controls

Presets

1
1
1

The preview runs the same code your AI receives. These settings travel with the hand-off.

View code Sample video (default settings, 1.5 MB)
Info

What it is

A Dupin cyclide: the smooth surface that bends, pinches and swells as its two shape numbers change, the generalisation of the torus. Here the numbers glide round a closed circle of values, so the surface breathes between a fat ring and a lopsided pear-shaped loop while it turns in space and an iridescent finish plays across it. Choose the finish (iridescent, chrome, pearl or gold), whether a net of curves lies on the surface, the mesh fineness, the turns per loop, how far the shape changes, the backdrop colour and whether the camera sways.

Reuse it in your own idea

  • Maths title: Iridescent, one turn.
  • Product-style loop: Chrome, bare.
  • Warm accent: Gold, big morph.

Which part is reusable

src/dupin-cyclide.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 is scaled to a steady size, so its horns and pinches change apparent proportions.
  • The ring cyclide has a singular point at its horn at the extreme of the morph, softened by the limited range.

Technical details

Technical details
Implementation
Three.js 0.185.1 (WebGL) · ES module src/dupin-cyclide.js
Exports
  • createCyclide({ finish?, lines?, detail?, turns?, morph? }) => { group, setProgress(progress), dispose() }
  • FINISHES: { iridescent, chrome, pearl, 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 cyclide is centred on the origin, scaled to a fixed root-mean-square radius of 2, hung 3.3 above the floor.

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

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

Output
1080×1080, 30 fps, 16 s · procedural (computed from the frame number) · seamless loop — The two shape numbers are sines of the loop, the surface turns a whole number of times per loop and the camera sway 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 11 000 vertices rewritten and re-normalised each frame: a few milliseconds a frame on an integrated Intel GPU. Software WebGL renders in about a second and a half a frame.
Export a video yourself
Download the source, then in the folder: npm install npm run render -- dupin-cyclide/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 · sha256:600a2db12eed3927…
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/dupin-cyclide (MIT) and rebuilt for AI Pixel Wizard in October 2026 as an original studio object: the ring cyclide's closed form with its two shape numbers on a closed loop, a size-steady mesh rewritten each frame and an iridescent finish on an exact loop.
BinMore like this

More like this

Play these full screen

Soap Film

3D object3DSeamless loop12 seconds

Ferrofluid

3D object3DSeamless loop16 seconds