Rotational Symmetry

JuniorMathematics
Domain · Geometry

display: flex; flex-wrap: wrap; gap: .75rem; align-items: center;

Learn the methodRead guide

#symmetry-paint { max-width: 960px; margin: 0 auto; } #symmetry-paint .toolbar { display: flex; flex-wrap: wrap; gap: .75rem; align-items: center; padding: .75rem; border: 1px solid #e5e7eb; border-radius: 18px; background: linear-gradient(135deg, #fff, #fafafa); box-shadow: 0 8px 24px rgba(0,0,0,.06); margin-bottom: .75rem; } #symmetry-paint .toolbar-group { display

; align-items
; gap:.5rem; } #symmetry-paint label { font-size: .9rem; color: #374151; display
; gap:.4rem; align-items
; } #symmetry-paint select, #symmetry-paint input[type="color"], #symmetry-paint input[type="range"] { accent-color: var(--accent); } #symmetry-paint .btn { border: 1px solid #e5e7eb; border-radius: 12px; padding: .5rem .8rem; font-weight: 600; background: white; cursor: pointer; transition: transform .04s ease, box-shadow .2s ease, border-color .2s ease; } #symmetry-paint .btn
{ box-shadow: 0 4px 14px rgba(0,0,0,.08); } #symmetry-paint .btn
{ transform: translateY(1px); } #symmetry-paint .btn.primary { background: linear-gradient(135deg, var(--accent), var(--accent-2)); color: white; border: none; } #symmetry-paint .swatches { display
; gap:.4rem; align-items
; } #symmetry-paint .swatch { width: 22px; height: 22px; border-radius: 50%; border: 1px solid rgba(0,0,0,.2); cursor: pointer; }

#symmetry-paint .canvas-wrap { position: relative; width: 100%; aspect-ratio: 1 / 1; border-radius: 22px; overflow: hidden; border

solid #e5e7eb; background:#fff; box-shadow: 0 16px 36px rgba(0,0,0,.08); } #symmetry-paint canvas { width: 100%; height: 100%; display
; touch-action: none; } #symmetry-paint .overlay { position
; inset
; pointer-events
; } #symmetry-paint .tiny { font-size: .8rem; color:#6b7280; margin-top:.5rem; text-align
; }

Symmetry

23456789

Colour

Brush 6px

Guides

Clear Download PNG

Tip: Try symmetry 6 or 8 for snowflake/mandala vibes. White acts like an eraser.

(function(){ const wrap = document.getElementById('sp-wrap'); const canvas = document.getElementById('sp-canvas'); const overlay = document.getElementById('sp-overlay'); const ctx = canvas.getContext('2d'); const octx = overlay.getContext('2d');

const symmetryEl = document.getElementById('sp-symmetry'); const colorEl = document.getElementById('sp-color'); const brushEl = document.getElementById('sp-brush'); const brushValEl = document.getElementById('sp-brush-val'); const guidesEl = document.getElementById('sp-guides'); const clearBtn = document.getElementById('sp-clear'); const downloadBtn = document.getElementById('sp-download');

// State let isDrawing = false; let prev = null; // previous point in CSS pixels let dpr = Math.max(1, window.devicePixelRatio || 1);

function resizeCanvases(){ const rect = wrap.getBoundingClientRect(); dpr = Math.max(1, window.devicePixelRatio || 1);

// Main canvas canvas.width = Math.floor(rect.width * dpr); canvas.height = Math.floor(rect.height * dpr); canvas.style.width = rect.width + 'px'; canvas.style.height = rect.height + 'px'; ctx.setTransform(dpr, 0, 0, dpr, 0, 0); // scale drawing to CSS pixel space

// Overlay canvas overlay.width = Math.floor(rect.width * dpr); overlay.height = Math.floor(rect.height * dpr); overlay.style.width = rect.width + 'px'; overlay.style.height = rect.height + 'px'; octx.setTransform(dpr, 0, 0, dpr, 0, 0);

drawGuides(); }

function center(){ const rect = wrap.getBoundingClientRect(); return { x: rect.width/2, y: rect.height/2, r: Math.min(rect.width, rect.height)/2 }; }

function getSymmetry(){ return parseInt(symmetryEl.value, 10) || 4; } function angleStep(){ return (Math.PI * 2) / getSymmetry(); }

function getPos(evt){ const br = canvas.getBoundingClientRect(); return { x: evt.clientX - br.left, y: evt.clientY - br.top }; }

function rotatePoint(p, ang, c){ const dx = p.x - c.x, dy = p.y - c.y; const cos = Math.cos(ang), sin = Math.sin(ang); return { x: c.x + dxcos - dysin, y: c.y + dxsin + dycos }; }

function drawSegment(p0, p1){ const k = getSymmetry(); const step = angleStep(); const c = center(); ctx.strokeStyle = colorEl.value; ctx.lineWidth = parseFloat(brushEl.value) || 6; ctx.lineCap = 'round'; ctx.lineJoin = 'round';

for(let i=0;i{ e.preventDefault(); canvas.setPointerCapture(e.pointerId); isDrawing = true; prev = getPos(e); drawDot(prev); // so taps leave a mark }); canvas.addEventListener('pointermove', (e)=>{ if(!isDrawing) return; const cur = getPos(e); drawSegment(prev, cur); prev = cur; }); function stopDrawing(e){ if(isDrawing){ isDrawing = false; prev = null; canvas.releasePointerCapture?.(e.pointerId); } } canvas.addEventListener('pointerup', stopDrawing); canvas.addEventListener('pointercancel', stopDrawing); canvas.addEventListener('pointerleave', stopDrawing);

// Controls symmetryEl.addEventListener('change', drawGuides); guidesEl.addEventListener('change', drawGuides); brushEl.addEventListener('input', ()=> brushValEl.textContent = (parseFloat(brushEl.value)||6) + 'px');

// Swatches -> set colour input document.querySelectorAll('#symmetry-paint .swatch').forEach(btn=>{ btn.addEventListener('click', ()=>{ colorEl.value = btn.dataset.colour; }); });

clearBtn.addEventListener('click', ()=>{ const W = canvas.width / dpr, H = canvas.height / dpr; ctx.clearRect(0,0,W,H); });

downloadBtn.addEventListener('click', ()=>{ // Create a composite with guides hidden for a clean export const wasGuides = guidesEl.checked; guidesEl.checked = false; drawGuides(); try { const link = document.createElement('a'); link.download = 'symmetry-drawing.png'; link.href = canvas.toDataURL('image/png'); link.click(); } finally { guidesEl.checked = wasGuides; drawGuides(); } });

// Resize handling (responsive & HiDPI) const ro = new ResizeObserver(resizeCanvases); ro.observe(wrap); window.addEventListener('orientationchange', resizeCanvases); resizeCanvases(); })();