Press n or j to go to the next uncovered block, b, p or k for the previous block.
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import { DEFAULT_TICK_THRESHOLDS } from './types'
import type { CollisionFadeMap } from '../shared/collisionDetection'
import { computeTickMarks, numberToScreenX } from './numberLineTicks'
import { renderConstantDropLines } from './constants/renderConstants'
import { primeColorRgba } from './primes/primeColors'
import type { PrimePairArc } from './primes/specialPrimes'
import { MERSENNE_PRIMES, ARC_COLORS } from './primes/specialPrimes'
import type { InterestingPrime } from './primes/interestingness'
import type { SieveTickTransform } from './primes/renderSieveOverlay'
import {
getTickHeight,
getTickLineWidth,
getTickAlpha,
getTickFontSize,
getTickFontWeight,
formatTickLabel,
LIGHT_COLORS,
DARK_COLORS,
COLLISION_FADE_MS,
SYSTEM_FONT,
} from '../shared/tickMath'
export interface RenderTarget {
value: number
emoji: string
/** Pre-computed opacity (0-1) from proximity engine */
opacity: number
}
export interface RenderIndicator {
numbers: number[]
range?: { from: number; to: number }
/** Pre-computed overall alpha (0-1) handling fade-in/hold/fade-out lifecycle */
alpha: number
}
/**
* Render the number line onto a canvas context.
* Assumes ctx.scale(dpr, dpr) has already been called.
*/
export function renderNumberLine(
ctx: CanvasRenderingContext2D,
state: NumberLineState,
cssWidth: number,
cssHeight: number,
isDark: boolean,
thresholds: TickThresholds = DEFAULT_TICK_THRESHOLDS,
zoomVelocity = 0,
zoomHue = 0,
zoomFocalX = 0.5,
target?: RenderTarget,
collisionFadeMap?: CollisionFadeMap,
constants?: RenderConstant[],
primeInfos?: Map<number, PrimeTickInfo>,
hoveredTick?: number | null,
interestingPrimes?: InterestingPrime[],
primePairArcs?: PrimePairArc[],
highlightedPrimes?: Set<number>,
highlightedArcs?: Set<string>,
sieveTransforms?: Map<number, SieveTickTransform>,
/** 0-1 blend toward uniform tick sizes during sieve (smooth ramp-in) */
sieveUniformity = 0,
indicator?: RenderIndicator,
/** Multiplier for all label font sizes (0.5–3, default 1) */
labelScale = 1,
/** Minimum opacity floor for all labels (0–1, default 0) */
labelMinOpacity = 0
): boolean {
const colors = isDark ? DARK_COLORS : LIGHT_COLORS
const centerY = cssHeight / 2
// Clear
ctx.clearRect(0, 0, cssWidth, cssHeight)
// Zoom velocity background wash — hue and focal point are pre-smoothed by caller
if (Math.abs(zoomVelocity) > 0.001) {
const intensity = Math.min(Math.abs(zoomVelocity) * 3, 0.35)
const sat = 80
const lum = isDark ? 30 : 70
const focalPx = zoomFocalX * cssWidth
const gradient = ctx.createRadialGradient(focalPx, centerY, 0, focalPx, centerY, cssWidth * 0.7)
gradient.addColorStop(0, `hsla(${zoomHue}, ${sat}%, ${lum}%, ${intensity})`)
gradient.addColorStop(1, `hsla(${zoomHue}, ${sat}%, ${lum}%, 0)`)
ctx.fillStyle = gradient
ctx.fillRect(0, 0, cssWidth, cssHeight)
}
// Draw horizontal axis line
ctx.beginPath()
ctx.moveTo(0, centerY)
ctx.lineTo(cssWidth, centerY)
ctx.strokeStyle = colors.axisLine
ctx.lineWidth = 1
ctx.stroke()
// Indicator pass: range band + point glows (drawn behind ticks)
if (indicator && indicator.alpha > 0) {
const a = indicator.alpha
const accentHue = 200 // blue accent
const accentSat = 90
const accentLumRange = isDark ? 55 : 50
const accentLumPoint = isDark ? 65 : 55
// Range band
if (indicator.range) {
const fromX = numberToScreenX(
indicator.range.from,
state.center,
state.pixelsPerUnit,
cssWidth
)
const toX = numberToScreenX(indicator.range.to, state.center, state.pixelsPerUnit, cssWidth)
const left = Math.min(fromX, toX)
const right = Math.max(fromX, toX)
ctx.fillStyle = `hsla(${accentHue}, ${accentSat}%, ${accentLumRange}%, ${a * 0.15})`
ctx.fillRect(left, 0, right - left, cssHeight)
// Brighter edge lines
ctx.strokeStyle = `hsla(${accentHue}, ${accentSat}%, ${accentLumRange}%, ${a * 0.35})`
ctx.lineWidth = 1.5
ctx.beginPath()
ctx.moveTo(left, 0)
ctx.lineTo(left, cssHeight)
ctx.moveTo(right, 0)
ctx.lineTo(right, cssHeight)
ctx.stroke()
}
// Point glows
const pulsePhase = (Date.now() % 2000) / 2000
const pulseScale = 1 + 0.15 * Math.sin(pulsePhase * Math.PI * 2)
for (const n of indicator.numbers) {
const x = numberToScreenX(n, state.center, state.pixelsPerUnit, cssWidth)
if (x < -30 || x > cssWidth + 30) continue
const radius = 20 * pulseScale
const glow = ctx.createRadialGradient(x, centerY, 0, x, centerY, radius)
glow.addColorStop(0, `hsla(${accentHue}, ${accentSat}%, ${accentLumPoint}%, ${a * 0.7})`)
glow.addColorStop(0.5, `hsla(${accentHue}, ${accentSat}%, ${accentLumPoint}%, ${a * 0.25})`)
glow.addColorStop(1, `hsla(${accentHue}, ${accentSat}%, ${accentLumPoint}%, 0)`)
ctx.fillStyle = glow
ctx.fillRect(x - radius, centerY - radius, radius * 2, radius * 2)
}
}
// Compute ticks
const ticks = computeTickMarks(state, cssWidth, thresholds)
// During sieve animation: smoothly blend integer ticks toward uniform
// prominence. The normal tick system uses magnitude-based hierarchy (powers
// of 10) which hides individual integers at low zoom. The sieve needs every
// integer visible so composites can shake/fall and primes remain standing.
// sieveUniformity (0-1) controls the blend so the transition is gradual.
// Gate on sieveUniformity alone — the transform map may still be empty
// during the intro before factor 2's sweep marks any composites.
const u = sieveUniformity
if (u > 0) {
const UNIFORM_PROMINENCE = 0.7
const halfRange = cssWidth / (2 * state.pixelsPerUnit)
const minInt = Math.max(1, Math.floor(state.center - halfRange) - 1)
const maxInt = Math.ceil(state.center + halfRange) + 1
const existingValues = new Set(ticks.map((t) => t.value))
// Inject missing integer ticks (fade in with uniformity blend)
for (let n = minInt; n <= maxInt; n++) {
if (!existingValues.has(n)) {
ticks.push({ value: n, power: 0, prominence: UNIFORM_PROMINENCE * u, opacity: u })
}
}
// Blend existing integer ticks toward uniform prominence
for (const tick of ticks) {
if (Number.isInteger(tick.value) && tick.value >= 1 && existingValues.has(tick.value)) {
tick.prominence += (UNIFORM_PROMINENCE - tick.prominence) * u
tick.opacity += (1 - tick.opacity) * u
}
}
}
// Pre-compute screen positions
const ticksWithX = ticks.map((tick) => ({
tick,
x: numberToScreenX(tick.value, state.center, state.pixelsPerUnit, cssWidth),
}))
// Compute per-power label rotation angle.
// When labels fit horizontally: angle = 0. As they get more crowded the angle
// increases smoothly. At angle θ the horizontal footprint is labelWidth·cos(θ),
// so the exact no-overlap angle is acos(spacing / labelWidth).
const LABEL_PAD = 6
const MAX_LABEL_ANGLE = Math.PI / 3 // cap at 60°
const powerAngle = new Map<number, number>()
const powerSpacingPx = new Map<number, number>()
for (const { tick } of ticksWithX) {
if (!powerSpacingPx.has(tick.power)) {
const spacing = 10 ** tick.power
powerSpacingPx.set(tick.power, spacing * state.pixelsPerUnit)
}
}
// Measure a representative label for each power to compute the needed angle
const measuredPowers = new Set<number>()
for (const { tick } of ticksWithX) {
if (measuredPowers.has(tick.power)) continue
if (tick.opacity <= 0) continue
measuredPowers.add(tick.power)
const fontSize = getTickFontSize(tick.prominence)
const fontWeight = getTickFontWeight(tick.prominence)
ctx.font = `${fontWeight} ${fontSize}px -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif`
const label = formatTickLabel(tick.value, tick.power)
const labelWidth = ctx.measureText(label).width
const spacingPx = powerSpacingPx.get(tick.power) ?? Infinity
// ratio < 1 means labels overlap horizontally
const ratio = Math.max(0, spacingPx - LABEL_PAD) / labelWidth
if (ratio >= 1) {
powerAngle.set(tick.power, 0)
} else {
// acos(ratio) gives the exact angle where labels just fit
powerAngle.set(tick.power, Math.min(Math.acos(ratio), MAX_LABEL_ANGLE))
}
}
// Pre-compute label info for cross-power collision detection.
// Each label occupies a horizontal extent on the x-axis; when a lower-prominence
// label overlaps a higher-prominence one, the lower-prominence label is hidden.
interface LabelInfo {
tick: (typeof ticksWithX)[number]['tick']
x: number
label: string
fontSize: number
fontWeight: number
labelWidth: number
angle: number
height: number
/** Horizontal extent: [xMin, xMax] on the canvas */
xMin: number
xMax: number
}
const labelInfos: LabelInfo[] = []
for (const { tick, x } of ticksWithX) {
if (x < -50 || x > cssWidth + 50) continue
if (tick.opacity <= 0) continue
const label = formatTickLabel(tick.value, tick.power)
const fontSize = getTickFontSize(tick.prominence)
const fontWeight = getTickFontWeight(tick.prominence)
ctx.font = `${fontWeight} ${fontSize}px -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif`
const labelWidth = ctx.measureText(label).width
const angle = powerAngle.get(tick.power) ?? 0
const height = getTickHeight(tick.prominence, cssHeight)
// Compute horizontal footprint of the (possibly rotated) label.
// The label is drawn at (x, labelY) then rotated by angle.
// Its horizontal extent is approximately labelWidth·cos(angle) + fontSize·sin(angle).
const t = MAX_LABEL_ANGLE > 0 ? Math.min(angle / MAX_LABEL_ANGLE, 1) : 0
const xOffset = (-labelWidth / 2) * (1 - t)
const hFootprint = labelWidth * Math.cos(angle) + fontSize * Math.sin(angle)
const xMin = x + xOffset * Math.cos(angle)
const xMax = xMin + hFootprint
labelInfos.push({ tick, x, label, fontSize, fontWeight, labelWidth, angle, height, xMin, xMax })
}
// Sort by prominence descending so higher-prominence labels take priority
labelInfos.sort((a, b) => b.tick.prominence - a.tick.prominence)
// Mark which labels survive collision detection
const labelVisible = new Set<LabelInfo>()
const occupiedExtents: { xMin: number; xMax: number }[] = []
for (const info of labelInfos) {
const pad = LABEL_PAD / 2
let overlaps = false
for (const occ of occupiedExtents) {
if (info.xMin - pad < occ.xMax && info.xMax + pad > occ.xMin) {
overlaps = true
break
}
}
if (!overlaps) {
labelVisible.add(info)
occupiedExtents.push({ xMin: info.xMin, xMax: info.xMax })
}
}
// Pass 1: tick lines
let maxTickHeight = 0
for (const { tick, x } of ticksWithX) {
if (x < -50 || x > cssWidth + 50) continue
// Apply sieve transforms: skip fully hidden ticks
const sxf = sieveTransforms?.get(tick.value)
if (sxf && sxf.opacity <= 0.01) continue
let height = getTickHeight(tick.prominence, cssHeight)
if (height > maxTickHeight) maxTickHeight = height
let lineWidth = getTickLineWidth(tick.prominence)
const tickAlpha = getTickAlpha(tick.prominence)
const primeInfo = primeInfos?.get(tick.value)
const isHovered = hoveredTick != null && tick.value === hoveredTick
// Prime ticks: slightly taller + thicker
if (primeInfo?.isPrime) {
height *= 1.15
lineWidth += 0.5
}
// Apply sieve transform (shake, fall, rotation)
const hasXf = sxf && (sxf.offsetX !== 0 || sxf.offsetY !== 0 || sxf.rotation !== 0)
if (hasXf) {
ctx.save()
ctx.translate(x + sxf.offsetX, sxf.offsetY)
ctx.translate(0, centerY)
ctx.rotate(sxf.rotation)
ctx.translate(0, -centerY)
}
ctx.globalAlpha = tick.opacity * (sxf?.opacity ?? 1)
ctx.beginPath()
if (hasXf) {
// Already translated to (x + offsetX, 0), draw relative to 0
ctx.moveTo(0, centerY - height)
ctx.lineTo(0, centerY + height)
} else {
ctx.moveTo(x, centerY - height)
ctx.lineTo(x, centerY + height)
}
if (primeInfo && primeInfo.classification !== 'one') {
// Color by smallest prime factor
const alpha = isHovered ? Math.min(1, tickAlpha + 0.3) : tickAlpha
ctx.strokeStyle = primeColorRgba(primeInfo.smallestPrimeFactor, alpha, isDark)
} else {
ctx.strokeStyle = `rgba(${colors.tickRgb}, ${tickAlpha})`
}
ctx.lineWidth = lineWidth
ctx.stroke()
// Hover highlight: subtle glow ring
if (isHovered && primeInfo && primeInfo.classification !== 'one') {
const savedAlpha = ctx.globalAlpha
ctx.globalAlpha = 0.25 * tick.opacity * (sxf?.opacity ?? 1)
ctx.strokeStyle = primeColorRgba(primeInfo.smallestPrimeFactor, 1, isDark)
ctx.lineWidth = lineWidth + 3
ctx.beginPath()
if (hasXf) {
ctx.moveTo(0, centerY - height)
ctx.lineTo(0, centerY + height)
} else {
ctx.moveTo(x, centerY - height)
ctx.lineTo(x, centerY + height)
}
ctx.stroke()
ctx.globalAlpha = savedAlpha
}
if (hasXf) ctx.restore()
ctx.globalAlpha = 1
}
// Pass 2: labels with smooth collision fade.
// All labels are rendered (not just visible ones) so that collision-hidden
// labels can fade out over COLLISION_FADE_MS instead of disappearing instantly.
const now = performance.now()
let animating = false
const seenValues = new Set<number>()
for (const info of labelInfos) {
const { tick, x, label, fontSize, fontWeight, labelWidth, angle, height } = info
// Apply sieve transforms: skip fully hidden labels
const sxf = sieveTransforms?.get(tick.value)
if (sxf && sxf.opacity <= 0.01) continue
// During sieve: skip collision detection entirely. Composites are already
// hidden by the opacity<=0.01 check above; only primes remain, and they
// should all show labels regardless of overlap at low zoom.
const sieveActive = u > 0
const hasSieveXf = sxf && (sxf.offsetX !== 0 || sxf.offsetY !== 0 || sxf.rotation !== 0)
const isVisible = sieveActive || hasSieveXf || labelVisible.has(info)
seenValues.add(tick.value)
// Compute collision opacity (1 = fully visible, 0 = collision-hidden)
let collisionOpacity = isVisible ? 1 : 0
if (collisionFadeMap && !sieveActive && !hasSieveXf) {
let entry = collisionFadeMap.get(tick.value)
if (!entry) {
// First time seeing this label — no fade, just snap to current state
entry = { visible: isVisible, startTime: now, startOpacity: isVisible ? 1 : 0 }
collisionFadeMap.set(tick.value, entry)
} else if (entry.visible !== isVisible) {
// Visibility changed — start transition from current animated position
const elapsed = now - entry.startTime
const t = Math.min(1, elapsed / COLLISION_FADE_MS)
const prevTarget = entry.visible ? 1 : 0
const currentOpacity = entry.startOpacity + (prevTarget - entry.startOpacity) * t
entry.visible = isVisible
entry.startTime = now
entry.startOpacity = currentOpacity
}
const elapsed = now - entry.startTime
const t = Math.min(1, elapsed / COLLISION_FADE_MS)
const target = entry.visible ? 1 : 0
collisionOpacity = entry.startOpacity + (target - entry.startOpacity) * t
if (t < 1) animating = true
}
// Skip fully hidden labels
if (collisionOpacity <= 0.01) continue
const labelAlpha = Math.max(getTickAlpha(tick.prominence), labelMinOpacity)
const scaledFontSize = fontSize * labelScale
ctx.font = `${fontWeight} ${scaledFontSize}px -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif`
ctx.globalAlpha = tick.opacity * collisionOpacity * (sxf?.opacity ?? 1)
const labelPrimeInfo = primeInfos?.get(tick.value)
if (labelPrimeInfo && labelPrimeInfo.classification !== 'one') {
ctx.fillStyle = primeColorRgba(labelPrimeInfo.smallestPrimeFactor, labelAlpha, isDark)
} else {
ctx.fillStyle = `rgba(${colors.labelRgb}, ${labelAlpha})`
}
const labelY = centerY + height + 4
// t: 0 = fully horizontal/centered, 1 = fully rotated/left-aligned
const tAngle = MAX_LABEL_ANGLE > 0 ? Math.min(angle / MAX_LABEL_ANGLE, 1) : 0
const xOffset = (-labelWidth / 2) * (1 - tAngle)
ctx.save()
if (hasSieveXf) {
// Apply sieve transform: translate + rotate around the label's position
ctx.translate(x + sxf.offsetX, labelY + sxf.offsetY)
ctx.rotate(sxf.rotation + angle)
} else {
ctx.translate(x, labelY)
ctx.rotate(angle)
}
ctx.textAlign = 'left'
ctx.textBaseline = 'top'
ctx.fillText(label, xOffset, 0)
ctx.restore()
ctx.globalAlpha = 1
}
// Clean up stale entries no longer in the viewport
if (collisionFadeMap) {
for (const key of collisionFadeMap.keys()) {
if (!seenValues.has(key)) {
collisionFadeMap.delete(key)
}
}
}
// Pass 2.25: prime markers
// Two sources of prime dots:
// (a) Tick-based dots (above prime ticks) — visible when zoomed in enough for integer ticks
// (b) Axis-level dots from visiblePrimes — visible at any zoom level, independent of ticks
if (primeInfos) {
for (const { tick, x } of ticksWithX) {
if (x < -50 || x > cssWidth + 50) continue
const pi = primeInfos.get(tick.value)
if (!pi?.isPrime) continue
const height = getTickHeight(tick.prominence, cssHeight) * 1.15
const dotRadius = 2 + tick.prominence * 2
const dotY = centerY - height - 4
ctx.globalAlpha = tick.opacity
ctx.beginPath()
ctx.arc(x, dotY, dotRadius, 0, Math.PI * 2)
ctx.fillStyle = primeColorRgba(pi.value, 0.85, isDark)
ctx.fill()
// Mersenne prime halo
if (MERSENNE_PRIMES.has(pi.value)) {
ctx.beginPath()
ctx.arc(x, dotY, dotRadius + 3, 0, Math.PI * 2)
ctx.strokeStyle = isDark ? 'rgba(255, 158, 238, 0.6)' : 'rgba(160, 48, 142, 0.5)'
ctx.lineWidth = 1.5
ctx.stroke()
}
ctx.globalAlpha = 1
}
}
// Axis-level prime dots (visible when zoomed out) — score-based sizing
if (interestingPrimes && interestingPrimes.length > 0) {
const count = interestingPrimes.length
const baseAlpha = count < 50 ? 0.8 : count < 200 ? 0.65 : count < 800 ? 0.5 : 0.35
// Offset dots slightly above axis so they don't get hidden by the axis line
const dotY = centerY - 1
for (const ip of interestingPrimes) {
const x = numberToScreenX(ip.value, state.center, state.pixelsPerUnit, cssWidth)
if (x < -5 || x > cssWidth + 5) continue
// Skip if this prime already has a visible tick-based dot (avoid double-drawing)
const tickInfo = primeInfos?.get(ip.value)
if (tickInfo) continue
// Score-based dot radius: clamp(2 + score/20, 1.5, 6)
const dotRadius = Math.max(1.5, Math.min(6, 2 + ip.score / 20))
// Higher-scoring primes are more opaque
const alpha = Math.min(baseAlpha + ip.score / 200, 0.95)
ctx.globalAlpha = alpha
ctx.beginPath()
ctx.arc(x, dotY, dotRadius, 0, Math.PI * 2)
ctx.fillStyle = primeColorRgba(ip.value, 1, isDark)
ctx.fill()
// Mersenne prime halo (axis-level)
if (MERSENNE_PRIMES.has(ip.value)) {
ctx.globalAlpha = Math.min(alpha + 0.2, 0.9)
ctx.beginPath()
ctx.arc(x, dotY, dotRadius + 2.5, 0, Math.PI * 2)
ctx.strokeStyle = isDark ? 'rgba(255, 158, 238, 0.7)' : 'rgba(160, 48, 142, 0.6)'
ctx.lineWidth = 1.5
ctx.stroke()
}
}
ctx.globalAlpha = 1
}
// Pass 2.3: prime pair arcs (twin / cousin / sexy) — for hovered or highlighted primes
const hasExplicitArcs = highlightedArcs && highlightedArcs.size > 0
const showArcs =
hoveredTick != null || (highlightedPrimes && highlightedPrimes.size > 0) || hasExplicitArcs
if (primePairArcs && primePairArcs.length > 0 && showArcs) {
const arcOrder: Array<'sexy' | 'cousin' | 'twin'> = ['sexy', 'cousin', 'twin']
// Pulsing phase for tour arc glow
const arcPulsePhase = (Date.now() % 2000) / 2000
const arcPulseAlpha = 0.2 + 0.15 * Math.sin(arcPulsePhase * Math.PI * 2)
for (const arcType of arcOrder) {
const colorTemplate = isDark ? ARC_COLORS[arcType].dark : ARC_COLORS[arcType].light
const baseAlpha = arcType === 'twin' ? 0.7 : arcType === 'cousin' ? 0.6 : 0.5
const baseLineWidth = arcType === 'twin' ? 1.5 : 1.2
for (const arc of primePairArcs) {
if (arc.type !== arcType) continue
const arcKey = `${arc.p1}-${arc.p2}`
const matchesHover = arc.p1 === hoveredTick || arc.p2 === hoveredTick
let matchesHighlight = false
if (hasExplicitArcs) {
// Explicit mode: only show arcs in the explicit set
matchesHighlight = highlightedArcs!.has(arcKey)
} else if (highlightedPrimes && highlightedPrimes.size > 0) {
// Legacy mode: any arc touching a highlighted prime
matchesHighlight = highlightedPrimes.has(arc.p1) || highlightedPrimes.has(arc.p2)
}
if (!matchesHover && !matchesHighlight) continue
const x1 = numberToScreenX(arc.p1, state.center, state.pixelsPerUnit, cssWidth)
const x2 = numberToScreenX(arc.p2, state.center, state.pixelsPerUnit, cssWidth)
if (x2 < -10 || x1 > cssWidth + 10) continue
const screenDist = x2 - x1
if (screenDist < 3) continue
const midX = (x1 + x2) / 2
const arcDepth = Math.min(16, Math.max(3, screenDist * 0.3))
const isTourArc = hasExplicitArcs && highlightedArcs!.has(arcKey)
if (isTourArc) {
// Tour arc glow pass: wider, pulsing, lower alpha
ctx.save()
ctx.strokeStyle = colorTemplate.replace('A', String(arcPulseAlpha))
ctx.lineWidth = baseLineWidth + 4
ctx.beginPath()
ctx.moveTo(x1, centerY + 1)
ctx.quadraticCurveTo(midX, centerY + 1 + arcDepth, x2, centerY + 1)
ctx.stroke()
ctx.restore()
// Main arc: boosted alpha + thickness
ctx.strokeStyle = colorTemplate.replace('A', String(Math.min(1, baseAlpha + 0.2)))
ctx.lineWidth = baseLineWidth + 1
} else {
ctx.strokeStyle = colorTemplate.replace('A', String(baseAlpha))
ctx.lineWidth = baseLineWidth
}
ctx.beginPath()
ctx.moveTo(x1, centerY + 1)
ctx.quadraticCurveTo(midX, centerY + 1 + arcDepth, x2, centerY + 1)
ctx.stroke()
}
}
ctx.globalAlpha = 1
}
// Pass 2.5: mathematical constants
if (constants && constants.length > 0) {
renderConstantDropLines(ctx, constants, centerY, isDark, maxTickHeight)
}
// Pass 3: target emoji (Find the Number game)
if (target && target.opacity > 0) {
const tx = numberToScreenX(target.value, state.center, state.pixelsPerUnit, cssWidth)
// Scale emoji size with opacity: 24px at low opacity, 40px at full
const emojiSize = 24 + 16 * target.opacity
// Pulsing glow when nearly found
if (target.opacity > 0.8) {
const pulsePhase = (Date.now() % 1500) / 1500
const pulseAlpha = 0.15 + 0.1 * Math.sin(pulsePhase * Math.PI * 2)
const glowRadius = emojiSize * 1.2
const glow = ctx.createRadialGradient(tx, centerY, 0, tx, centerY, glowRadius)
glow.addColorStop(0, `hsla(45, 100%, 60%, ${pulseAlpha * target.opacity})`)
glow.addColorStop(1, `hsla(45, 100%, 60%, 0)`)
ctx.globalAlpha = 1
ctx.fillStyle = glow
ctx.fillRect(tx - glowRadius, centerY - glowRadius, glowRadius * 2, glowRadius * 2)
}
ctx.globalAlpha = target.opacity
ctx.font = `${emojiSize}px -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Emoji, sans-serif`
ctx.textAlign = 'center'
ctx.textBaseline = 'middle'
ctx.fillStyle = isDark ? '#fff' : '#000'
ctx.fillText(target.emoji, tx, centerY)
ctx.globalAlpha = 1
}
return animating
}
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