Clyune Component GalleryTorus Knot · How it works & code
Wind p turns around the major circle and q turns around the tube to get the (p, q) torus knot.
Runtime logic
Visiting `/threejs/knots`, DemoHost lazy-loads `demos/kits/kit-three.js` (registry `mod: 'kit-three'`) and calls `mount(host, { variant: 'knots' })`. mount resolves the variant to family `knots`; `withControls` builds the control panel (6 presets + sliders). `createThreeStage` sets up WebGLRenderer, Scene, PerspectiveCamera and OrbitControls, plus the info panel. The family’s `build(S)` initialises state and returns the per-frame callback. Every `requestAnimationFrame`: read controls, advance a speed-scaled clock (dt ≤ 50 ms), run the frame callback; returned readouts go to the info panel. Changing parameters: colour/speed/size apply live; structural ones remount; leaving the page cancels rAF, removes listeners and frees resources.
Environment
Canvas 2D: 2D canvas drawing; WebGL (three.js): WebGL through three.js WebGLRenderer; requestAnimationFrame: Display-synced animation loop; ResizeObserver: Canvas follows container size; Pointer Events: Unified mouse/touch/pen events; devicePixelRatio: Crisp HiDPI rendering (capped at 2×) · react 18.3.1, react-router-dom 6.30.6, vite 5.4.21, three 0.170.0
Dependencies
three 0.170.0, three/addons/controls/OrbitControls.js 0.170.0, react 18.3.1
Imported APIs
withControls — Wraps the demo in the shared control panel (presets, sliders, reset); hot-updates or remounts on change; paramsFromSpec — Turns the spec (colour/speed/size/count/extras) into control-panel parameter definitions; createThreeStage — Shared three.js stage: WebGLRenderer, scene, perspective camera, OrbitControls, auto framing and render loop; addLights — Adds ambient + key + fill lights; THREE — three.js namespace; fmt — Number formatting (fixed decimals); deg — Radians → degrees text; triCount — Counts triangles in a geometry; F — Formula block HTML; S.get — Reads current control values; S.onFrame — Registers a per-frame callback; its return value feeds the info panel; THREE.TorusKnotGeometry — Torus-knot geometry; THREE.Mesh — Mesh (geometry + material); THREE.MeshStandardMaterial — PBR standard material
Source code
frontend/src/demos/kits/kit-three.js: FAM.knots (L344-L367)
Code walkthrough
L345-345: Control definitions (colour/speed/size/count/extras): Color, Zoom, Number of turns around central axis p, Number of turns around tube q, Wireframe. L346-346: Preset buttons: name → parameter overrides (6). L347-347: 3D framing radius. L348-356: Info-panel content: live rows(v), formula, notes, params, steps. L357-366: Init function: sets up state and returns the per-frame callback: creates three.js objects `TorusKnotGeometry`, `Mesh`, `MeshStandardMaterial`; math via `Math.round`; returns readouts `th`, `p`, `q`, `g`, `tris` to the info panel.
Principles
r = cos(q·u) + 2 x = r·cos(p·u)，y = r·sin(p·u)，z = −sin(q·u)，u∈[0, 2π] Imagine a line entangled on the surface of a donut: orbiting the big circle p Circles, along the pipes q Circle, you get it (p, q) Ring knot . (2,3) The most famous“Miha!”. If p 和 q Greater number of conventions 1，线会提前首尾相接，实际是几条互相扣在一起的环。