Clyune Component GalleryDerivatives & Tangents · How it works & code
Secant line approaches tangent.
Runtime logic
Visiting `/math/derivative`, DemoHost lazy-loads `demos/kits/kit-math.js` (registry `mod: 'kit-math'`) and calls `mount(host, { variant: 'derivative' })`. mount resolves the variant to family `derivative`; `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.fillText() — Draws filled text; ctx.beginPath() — Starts a new path; ctx.moveTo() — Moves the pen without drawing; ctx.lineTo() — Adds a straight line to a point; ctx.stroke() — Strokes the current path; ctx.setLineDash() — Sets the dash pattern for strokes
Source code
frontend/src/demos/kits/kit-math.js: FAMILY_CONTROLS['derivative'] (L94-L94), hitTargets() · if (family === 'derivative') (L495-L499), applyDrag() · if (family === 'derivative') (L580-L585), drawFamily() · case 'derivative' (L614-L614), MATH_DOCS['derivative'] (L180-L189)
Code walkthrough
L94-94: This demo's entry in the `FAMILY_CONTROLS` table (control config). L495-499: Branch for this demo inside `hitTargets()`: math via `Math.sin`. L580-585: Branch for this demo inside `applyDrag()`. L614-614: `case` branch in `drawFamily()`: this demo's per-frame drawing. L180-189: This demo's entry in the `MATH_DOCS` table (info-panel text: formula/notes/params/steps).
Principles
f'(x) = lim h→0 f(x+h) − f(x) h (sin x)' = cos x Tangent: y = f'(x₀)(x − x₀) + f(x₀) The slope of the cutting line is in h→0 This is the index.