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BiasHysteresis — a level/capacity gauge rendered as an analog tape deck's // own AC-bias hysteresis loop instead of a bar or dial. // // SOURCE: AC-bias magnetic tape recording linearizes an inherently nonlinear // medium by superimposing a high-frequency bias signal on the audio; the // tape's flux density B vs. drive field H traces a hysteresis loop, not a // straight line (Jiles-Atherton hysteresis model; documented on any pro // reel-to-reel service manual, e.g. Studer A80 / Ampex ATR bias alignment // procedures). As input climbs toward and past 0dB the loop widens and its // corners round off toward saturation — the mechanism behind analog tape's // "soft clip" character, colloquially "tape saturation". // // A bright marker rides the loop's edge, one full lobe traversal every 8.3s. // The loop itself is recomputed every frame from B = Bsat*tanh(k*(H -+ Hc)) // (sign set by sweep direction — ascending vs. descending branch — which is // what opens the two straight tanh curves into a closed lobed loop rather // than a single line), so its own envelope amplitude breathes on an // independent 21s cycle: the loop is visibly narrower/sharper at low drive // and wider/rounder at high drive across a single 5-second sample, not just // a dot moving on a fixed shape. The real bias frequency this represents // (~150kHz on a pro deck) is documented here only — rendering it 1:1 against // a ~60Hz paint rate would alias into a strobe, so the rendered rate is a // decoupled, deliberately slow drive sweep instead (round-9 legibility rule). // --------------------------------------------------------------------------- const DRIVE_PERIOD_S = 8.3; // one full lobe traversal (0.12Hz) const DRIVE_PHASE_OFFSET = 0.12; // cycle fraction offset — see freeze-frame note below const ENVELOPE_PERIOD_S = 21; // saturation-amount breathing cycle const ENVELOPE_MIN = 0.6; // peak H amplitude at envelope trough const ENVELOPE_MAX = 1.4; // peak H amplitude at envelope peak const COERCIVITY_HC = 0.18; const B_SAT = 0.92; const K_STEEPNESS = 2.4; // tanh steepness — controls corner rounding const LOOP_POINTS = 240; // 120 ascending + 120 descending branch samples const SQUARE_FRACTION = 0.7; // loop region side = min(w,h) * this const H_DOMAIN = 1.5; // H-axis half-range shown — tight enough that the trough-amplitude // loop (amp 0.6) still reads as a lens with real horizontal width, not a // tall sliver dominated by the fixed ~0.75 vertical coercivity gap const B_DOMAIN = 1.05; // B-axis half-range shown, padding beyond Bsat const MARKER_RADIUS_PX = 3.5; const AREA_FILL_ALPHA = 0.05; // FREEZE FRAME: reduced-motion locks at drive-cycle phase 0.62 — chosen so // that with DRIVE_PHASE_OFFSET applied, H is descending through zero right // as the 21s envelope sits within a hair of its own peak (0.62 * 8.3s = // 5.146s; 5.146s / 21s ~= 0.245 of the envelope's own sine, ~=0.9993 of its // peak). At H=0 the marker sits at the widest vertical separation between // the two branches (the coercivity gap, ~0.75 of the B range) with the loop // itself at peak envelope amplitude — the single frame that shows the full // open loop at its widest, rather than a thin near-origin sliver at a small // envelope amplitude. const FREEZE_PHASE_FRAC = 0.62; const FREEZE_T = FREEZE_PHASE_FRAC * DRIVE_PERIOD_S; function envelopeAmplitude(t: number): number { const center = (ENVELOPE_MIN + ENVELOPE_MAX) / 2; const halfRange = (ENVELOPE_MAX - ENVELOPE_MIN) / 2; return center + halfRange * Math.sin((2 * Math.PI * t) / ENVELOPE_PERIOD_S); } function driveAngle(t: number): number { return 2 * Math.PI * (t / DRIVE_PERIOD_S - DRIVE_PHASE_OFFSET); } /** ascending branch: H rising, B lags "behind" toward +Hc */ function bAscending(h: number): number { return B_SAT * Math.tanh(K_STEEPNESS * (h - COERCIVITY_HC)); } /** descending branch: H falling, B lags "behind" toward -Hc */ function bDescending(h: number): number { return B_SAT * Math.tanh(K_STEEPNESS * (h + COERCIVITY_HC)); } /** Full closed loop, LOOP_POINTS samples, for the current envelope amplitude. */ function buildLoop(amp: number): { h: number; b: number }[] { const half = LOOP_POINTS / 2; const pts: { h: number; b: number }[] = []; for (let i = 0; i <= half; i++) { const h = -amp + (2 * amp * i) / half; pts.push({ h, b: bAscending(h) }); } for (let i = 0; i <= half; i++) { const h = amp - (2 * amp * i) / half; pts.push({ h, b: bDescending(h) }); } return pts; } /** Current marker position: same math as the loop branches, evaluated * directly at the drive's current H and sweep direction. */ function markerPoint(t: number, amp: number): { h: number; b: number } { const angle = driveAngle(t); const h = amp * Math.sin(angle); const rising = Math.cos(angle) >= 0; const b = rising ? bAscending(h) : bDescending(h); return { h, b }; } export interface BiasHysteresisProps { /** accessible name for the reading, e.g. "Input drive" */ label?: string; /** canvas panel height in px. Default 220. */ height?: number; /** extra classes merged onto the rendered root element */ className?: string; } export function BiasHysteresis({ label = "Bias saturation", height = 220, className = "", }: BiasHysteresisProps) { const canvasRef = useRef(null); useEffect(() => { const canvas = canvasRef.current; if (!canvas) return; const ctx = canvas.getContext("2d"); if (!ctx) return; const reduced = window.matchMedia("(prefers-reduced-motion: reduce)").matches; let fg = ""; let border = ""; // fallbacks are CSS keywords, never literal colour values const readTokens = () => { const root = getComputedStyle(document.documentElement); fg = root.getPropertyValue("--foreground").trim() || "currentColor"; border = root.getPropertyValue("--border").trim() || "currentColor"; }; let w = 0; let h = 0; let sized = false; const resize = () => { const rect = canvas.getBoundingClientRect(); if (rect.width < 2 || rect.height < 2) { sized = false; return; } const dpr = Math.min(window.devicePixelRatio || 1, 2); w = rect.width; h = rect.height; canvas.width = Math.max(1, Math.round(w * dpr)); canvas.height = Math.max(1, Math.round(h * dpr)); ctx.setTransform(dpr, 0, 0, dpr, 0, 0); sized = true; }; const draw = (t: number) => { if (!sized) return; ctx.clearRect(0, 0, w, h); const side = Math.min(w, h) * SQUARE_FRACTION; const cx = w / 2; const cy = h / 2; const xFor = (hVal: number) => cx + (hVal / H_DOMAIN) * (side / 2); const yFor = (bVal: number) => cy - (bVal / B_DOMAIN) * (side / 2); // axis crosshair — separator only, never the loop's own line ctx.strokeStyle = border; ctx.lineWidth = 1; ctx.globalAlpha = 1; ctx.beginPath(); ctx.moveTo(cx - side / 2, cy); ctx.lineTo(cx + side / 2, cy); ctx.moveTo(cx, cy - side / 2); ctx.lineTo(cx, cy + side / 2); ctx.stroke(); const amp = envelopeAmplitude(t); const loop = buildLoop(amp); // enclosed hysteresis area — the "energy lost to saturation" — as a // very low-opacity foreground fill, never a hue ctx.beginPath(); loop.forEach((p, i) => { const x = xFor(p.h); const y = yFor(p.b); if (i === 0) ctx.moveTo(x, y); else ctx.lineTo(x, y); }); ctx.closePath(); ctx.fillStyle = fg; ctx.globalAlpha = AREA_FILL_ALPHA; ctx.fill(); // the loop stroke itself ctx.globalAlpha = 1; ctx.strokeStyle = fg; ctx.lineWidth = 1.5; ctx.beginPath(); loop.forEach((p, i) => { const x = xFor(p.h); const y = yFor(p.b); if (i === 0) ctx.moveTo(x, y); else ctx.lineTo(x, y); }); ctx.closePath(); ctx.stroke(); // marker riding the loop's edge — the one thing to follow const marker = markerPoint(t, amp); ctx.beginPath(); ctx.arc(xFor(marker.h), yFor(marker.b), MARKER_RADIUS_PX, 0, Math.PI * 2); ctx.fillStyle = fg; ctx.globalAlpha = 1; ctx.fill(); }; // -- loop ---------------------------------------------------------------- let raf = 0; let last = 0; let globalT = 0; const loop = (now: number) => { const dtMs = last ? Math.min(250, now - last) : 1000 / 60; last = now; globalT += dtMs / 1000; draw(globalT); if (!document.hidden) raf = requestAnimationFrame(loop); }; const mo = new MutationObserver(() => { readTokens(); draw(reduced ? FREEZE_T : globalT); }); mo.observe(document.documentElement, { attributes: true, attributeFilter: ["class"], }); let resizeTimer: ReturnType | null = null; const onResize = () => { if (resizeTimer) clearTimeout(resizeTimer); resizeTimer = setTimeout(() => { resizeTimer = null; readTokens(); resize(); draw(reduced ? FREEZE_T : globalT); }, 150); }; const ro = new ResizeObserver(onResize); ro.observe(canvas); const io = new IntersectionObserver( (entries) => { const visible = entries[0]?.isIntersecting; if (visible && !reduced && sized) { cancelAnimationFrame(raf); last = 0; raf = requestAnimationFrame(loop); } else if (!visible) { cancelAnimationFrame(raf); } }, { threshold: 0 } ); io.observe(canvas); const onVis = () => { cancelAnimationFrame(raf); if (!document.hidden && !reduced && sized) { last = 0; raf = requestAnimationFrame(loop); } }; document.addEventListener("visibilitychange", onVis); // no paint before the first token read readTokens(); resize(); if (reduced) { draw(FREEZE_T); } else { draw(0); raf = requestAnimationFrame(loop); } return () => { cancelAnimationFrame(raf); if (resizeTimer) clearTimeout(resizeTimer); mo.disconnect(); ro.disconnect(); io.disconnect(); document.removeEventListener("visibilitychange", onVis); }; }, [height]); return (

{label.toUpperCase()} H / B LOOP

Hc {COERCIVITY_HC.toFixed(2)} Bsat {B_SAT.toFixed(2)}

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