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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 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | 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()
}
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