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| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 | import type { NumberLineState } from '../../types' import { renderRollingCircle } from './renderRollingCircle' import { renderTauConstruction, mapRange } from './renderCircleConstruction' import { numberToScreenX } from '../../numberLineTicks' const TAU = 2 * Math.PI /** * Target viewport for the tau demo. * Unit circle (r=1) rolls one turn → covers τ. Shows τ = C/r. */ export function tauDemoViewport(cssWidth: number, cssHeight: number) { const center = TAU / 2 // Fit horizontal range [-1, tau+1] = width tau+2 // Vertical: circle is 2 units tall (r=1), needs to fit above the axis const ppu = Math.min((cssWidth * 0.85) / (TAU + 2), cssHeight * 0.22) return { center, pixelsPerUnit: ppu } } // Phase boundaries within revealProgress const CONSTRUCTION_END = 0.3 const ROLLING_END = 0.92 /** * Render the tau demo overlay: constructs a unit circle (r=1) from the * number line, then rolls it one full turn along the axis from 0 to τ. * Shows π at the halfway mark. Contrasts with pi demo's smaller d=1 circle. */ export function renderTauOverlay( ctx: CanvasRenderingContext2D, state: NumberLineState, cssWidth: number, cssHeight: number, isDark: boolean, revealProgress: number, opacity: number ): void { if (opacity <= 0) return const constructionP = mapRange(revealProgress, 0, CONSTRUCTION_END) const t = mapRange(revealProgress, CONSTRUCTION_END, ROLLING_END) const labelAlpha = mapRange(revealProgress, ROLLING_END, 1.0) const circumColor = isDark ? '#2dd4bf' : '#0d9488' // teal const spokeColor = isDark ? '#f87171' : '#dc2626' const refColor = isDark ? 'rgba(255,255,255,0.25)' : 'rgba(0,0,0,0.15)' ctx.save() ctx.globalAlpha = opacity if (constructionP < 1) { // Construction phases: highlight → pivot → sweep → treads renderTauConstruction( ctx, state, cssWidth, cssHeight, { circumColor, spokeColor, refColor, }, constructionP, opacity ) } else { // Rolling phase: unit circle rolls from 0 to τ const pos = renderRollingCircle( ctx, state, cssWidth, cssHeight, { radius: 1, radiusSpoke: true, circumColor, spokeColor, refColor, accentColor: isDark ? '#fbbf24' : '#d97706', trailColor: isDark ? 'rgba(255,255,255,0.2)' : 'rgba(0,0,0,0.12)', spokeLabel: '1 to edge', }, t, 1, opacity ) const ppu = state.pixelsPerUnit const toX = (nlx: number) => numberToScreenX(nlx, state.center, ppu, cssWidth) // === Pi halfway mark (appears once rolling passes the midpoint) === const piMarkAlpha = t >= 0.5 ? Math.min(1, (t - 0.5) * 5) : 0 if (piMarkAlpha > 0) { ctx.globalAlpha = opacity * piMarkAlpha * 0.7 const piSx = toX(Math.PI) const piColor = isDark ? 'rgba(96, 165, 250, 0.8)' : 'rgba(37, 99, 235, 0.7)' // Tick mark at pi ctx.beginPath() ctx.moveTo(piSx, pos.axisY - 6) ctx.lineTo(piSx, pos.axisY + 6) ctx.strokeStyle = piColor ctx.lineWidth = 1.5 ctx.setLineDash([]) ctx.stroke() // "pi" label const piFontSize = Math.max(11, Math.min(14, ppu * 0.14)) ctx.font = `${piFontSize}px system-ui, sans-serif` ctx.fillStyle = piColor ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.fillText('\u03C0', piSx, pos.axisY + 8) // "half turn" annotation ctx.font = `${Math.max(9, piFontSize - 2)}px system-ui, sans-serif` ctx.fillText('half turn', piSx, pos.axisY + 8 + piFontSize + 2) } // === Labels (final phase) === if (labelAlpha > 0) { ctx.globalAlpha = opacity * labelAlpha // "tau" label at x = tau const tauSx = toX(TAU) const fontSize = Math.max(14, Math.min(20, ppu * 0.18)) ctx.font = `bold ${fontSize}px system-ui, sans-serif` ctx.fillStyle = circumColor ctx.textAlign = 'center' ctx.textBaseline = 'top' ctx.fillText('\u03C4', tauSx, pos.axisY + 8) // Small tick at tau ctx.beginPath() ctx.moveTo(tauSx, pos.axisY - 4) ctx.lineTo(tauSx, pos.axisY + 4) ctx.strokeStyle = circumColor ctx.lineWidth = 2 ctx.setLineDash([]) ctx.stroke() // "one full turn" annotation under tau const annoFontSize = Math.max(10, Math.min(13, ppu * 0.12)) ctx.font = `${annoFontSize}px system-ui, sans-serif` ctx.fillText('full turn', tauSx, pos.axisY + 8 + fontSize + 2) // "C = τr" formula above the circle const formulaFontSize = Math.max(13, Math.min(18, ppu * 0.16)) ctx.font = `${formulaFontSize}px system-ui, sans-serif` ctx.fillStyle = isDark ? 'rgba(255,255,255,0.9)' : 'rgba(0,0,0,0.8)' ctx.textAlign = 'center' ctx.textBaseline = 'bottom' ctx.fillText('C = \u03C4r', pos.ccx, pos.ccy - pos.screenR - 8) // "trip around ÷ center to edge" subtitle const subFontSize = Math.max(10, Math.min(13, ppu * 0.11)) ctx.font = `${subFontSize}px system-ui, sans-serif` ctx.fillStyle = isDark ? 'rgba(255,255,255,0.6)' : 'rgba(0,0,0,0.5)' ctx.fillText( 'trip around \u00F7 center to edge', pos.ccx, pos.ccy - pos.screenR - 8 - formulaFontSize - 2 ) } } ctx.globalAlpha = 1 ctx.setLineDash([]) ctx.restore() } |