Clyune Component GalleryPyramids & Spheres · How it works & code
Volume relationship between sphere and pyramid, layer-by-layer approximation
Runtime logic
Visiting `/math/area-volume`, DemoHost lazy-loads `demos/kits/kit-math.js` (registry `mod: 'kit-math'`) and calls `mount(host, { variant: 'area-volume' })`. mount resolves the variant to family `area-volume`; `withControls` builds the control panel (6 presets + sliders). `createInfoPanel` splits the stage into canvas + info panel; `makeCanvas` creates a HiDPI canvas. Every `requestAnimationFrame`: read controls, `drawFamily` runs this demo’s branch, and the info panel readout refreshes. Pointer down/drag/move updates the interaction (drag handles, hover readouts); when untouched and auto-demo is on, the pointer follows a Lissajous path. 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; 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
Dependencies
react 18.3.1
Imported APIs
makeCanvas — Creates an auto-sized canvas; loop — requestAnimationFrame loop (stoppable); bar — Demo control bar; paramsFromSpec — Turns the spec (colour/speed/size/count/extras) into control-panel parameter definitions; readLiveControls — Reads live control values (CSS-variable fallback); localPoint — Event → canvas-local coordinates; withControls — Wraps the demo in the shared control panel (presets, sliders, reset); hot-updates or remounts on change; createInfoPanel — Side/bottom info panel: live readout + formula/notes/params/steps; alignDocParams — Aligns the documented parameters with the actual controls; MATH_DOCS — Formula/notes/params text table for math demos; ctx.fillRect() — Fills a rectangle; ctx.beginPath() — Starts a new path; ctx.arc() — Adds a circular arc (center, radius, start/end angle); ctx.fill() — Fills the current path; ctx.fillText() — Draws filled text; ctx.lineTo() — Adds a straight line to a point; ctx.moveTo() — Moves the pen without drawing; ctx.closePath() — Closes the current sub-path; ctx.stroke() — Strokes the current path; ctx.createRadialGradient() — Creates a radial gradient; ctx.ellipse() — Adds an elliptical arc; ctx.strokeRect() — Strokes a rectangle
Source code
frontend/src/demos/kits/kit-math.js: FAMILY_CONTROLS['area-volume'] (L80-L80), drawFamily() · case 'area-volume' (L600-L600), MATH_DOCS['area-volume'] (L41-L50)
Code walkthrough
L80-80: This demo's entry in the `FAMILY_CONTROLS` table (control config). L600-600: `case` branch in `drawFamily()`: this demo's per-frame drawing. L41-50: This demo's entry in the `MATH_DOCS` table (info-panel text: formula/notes/params/steps).
Principles
V 球 = 4 3 πr³ S 球 = 4πr² V 锥 = 1 3 ·S 底 ·h Cone size is a 1-by-bottom column / 3;Cyan transliterate the cone into multi-layered thin sheets in the figure (the principle of ancestorism) / The idea of points. The volume of the ball increases three times with the radius.