<html>
<head><title id="pageTitle">Harmonics: 2</title></head>
<body style="display:flex;flex-direction:column;align-items:center;justify-content:center;margin:0;min-height:100vh;background:black;color:white">
<div style="margin-bottom:10px;font-family:monospace;font-size:1.1em;color:#888;text-align:left">Generated by:<br/><code>circles-sketch points examples/square.yml</code></div>
<canvas id="canvas" width="1000" height="1000" style="width:500px;height:500px"></canvas>
<div style="margin-top:10px">
<input type="range" id="slider" min="0" max="1" step="0.001" value="0" style="width:500px"/>
<span id="tval">t = 0.000</span>
</div>
<div style="margin-top:5px;display:flex;flex-wrap:wrap;gap:10px;align-items:center;justify-content:center">
<span id="loopVal">loop 0/0 — harmonics: 1</span>
<span style="color:#888">max harmonics: 500</span>
</div>
<div style="margin-top:5px;display:flex;flex-wrap:wrap;gap:10px;align-items:center;justify-content:center">
<button id="startBtn">Start</button>
<button id="stopBtn">Stop</button>
<button id="harmonicsBtn">Harmonics</button>
<label>Harmonics loop: <input type="text" id="stepsInput" value="1 1 10 3 ; 10 5 20 3 ; 20 10 100 3" style="width:400px;font-family:monospace;font-size:0.85em" title="from step to speed ; from step to speed ; ..."/></label>
</div>
<div style="margin-top:5px;display:flex;flex-wrap:wrap;gap:10px;align-items:center;justify-content:center">
<label>Contour: <select id="selContour">
<option value="always">Always</option>
<option value="never" selected>Never</option>
<option value="every">Congruence</option>
</select><input type="number" id="selContourM" min="1" value="2" style="width:45px;display:none;" title="modulo"/>/<input type="text" id="selContourR" value="0" style="width:80px;display:none;" title="congruents (comma-separated)" placeholder="0,1,..."/></label>
<label><input type="checkbox" id="chkPoint" checked/> Point</label>
<label>Trace: <select id="selTrace">
<option value="always" selected>Always</option>
<option value="never">Never</option>
<option value="every">Congruence</option>
</select><input type="number" id="selTraceM" min="1" value="2" style="width:45px;display:none;" title="modulo"/>/<input type="text" id="selTraceR" value="0" style="width:80px;display:none;" title="congruents (comma-separated)" placeholder="0,1,..."/></label>
<label><input type="checkbox" id="chkNh" checked/> NH label</label>
<label>Circles: <select id="selCircles">
<option value="always" selected>Always</option>
<option value="never">Never</option>
<option value="every">Congruence</option>
</select><input type="number" id="selCirclesM" min="1" value="2" style="width:45px;display:none;" title="modulo"/>/<input type="text" id="selCirclesR" value="0" style="width:80px;display:none;" title="congruents (comma-separated)" placeholder="0,1,..."/></label>
</div>
<div style="margin-top:5px;display:flex;flex-wrap:wrap;gap:10px;align-items:center;justify-content:center">
<label>Opacity: <input type="range" id="opacitySlider" min="0" max="1" step="0.05" value="0.5" style="width:100px"/> <span id="opacityVal">0.5</span></label>
<label>Trace length: <input type="range" id="traceLenSlider" min="0.05" max="1" step="0.05" value="0.5" style="width:100px"/> <span id="traceLenVal">0.5</span></label>
<label>Trace width: <input type="range" id="traceWidthSlider" min="0.1" max="2" step="0.1" value="1" style="width:100px"/> <span id="traceWidthVal">1</span></label>
<label>Contour width: <input type="range" id="contourWidthSlider" min="0.1" max="5" step="0.1" value="1" style="width:100px"/> <span id="contourWidthVal">1</span></label>
</div>
<div id="harmonicsDiv" style="display:none;margin-top:10px;max-height:300px;overflow:auto">
<table style="border-collapse:collapse;font-family:monospace;font-size:0.85em">
<thead><tr><th style="padding:2px 8px;border-bottom:1px solid #555">#</th><th style="padding:2px 8px;border-bottom:1px solid #555">freq</th><th style="padding:2px 8px;border-bottom:1px solid #555">re</th><th style="padding:2px 8px;border-bottom:1px solid #555">im</th><th style="padding:2px 8px;border-bottom:1px solid #555">radius</th></tr></thead>
<tbody id="harmonicsTbody"></tbody>
</table>
</div>
<script>
const canvas = document.getElementById("canvas");
const ctx = canvas.getContext("2d");
const VB_X = -5;
const VB_Y = -5;
const VB_SIZE = 60;
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const fourier = 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const traceColors = ["red","lime","dodgerblue","gold","hotpink","cyan","orange"];
let traceColorIdx = 0;
const scale = VB_SIZE / 100;
const dotR = 0.42;
const sparkScale = VB_SIZE / 100;
const NUM_RAYS = 14;
const NUM_PARTICLES = 8;
let traceVisible = true;
let contourVisible = true;
let fourierVisible = true;
let dotVisible = true;
let showNh = true;
let traceOpacity = 0.5;
let traceWidth = 1;
let contourWidth = 1;
let traceHistory = [];
let firstDotX = 0, firstDotY = 0;
const dpr = window.devicePixelRatio || 1;
canvas.width = 500 * dpr;
canvas.height = 500 * dpr;
function setupTransform() {
ctx.setTransform(1,0,0,1,0,0);
ctx.scale(dpr, dpr);
const s = 500 / VB_SIZE;
ctx.translate(-VB_X * s, -VB_Y * s);
ctx.scale(s, s);
}
function getShowMode(selId) {
const sel = document.getElementById(selId);
const mode = sel.value;
if (mode === "every") {
const m = parseInt(document.getElementById(selId + "M").value) || 2;
const rs = document.getElementById(selId + "R").value.split(",").map(s => parseInt(s.trim())).filter(n => !isNaN(n));
return { modulo: m, congruents: rs.length ? rs : [0] };
}
return mode;
}
function shouldShow(mode, loopIdx) {
if (mode === "always") return true;
if (mode === "never") return false;
return mode.congruents.includes(loopIdx % mode.modulo);
}
function wireShowSelect(selId) {
const sel = document.getElementById(selId);
const mInput = document.getElementById(selId + "M");
const rInput = document.getElementById(selId + "R");
sel.addEventListener("change", function() {
const show = this.value === "every" ? "" : "none";
mInput.style.display = show;
rInput.style.display = show;
});
}
wireShowSelect("selContour");
wireShowSelect("selTrace");
wireShowSelect("selCircles");
const opacitySlider = document.getElementById("opacitySlider");
const opacityVal = document.getElementById("opacityVal");
opacitySlider.addEventListener("input", function() {
opacityVal.textContent = parseFloat(this.value).toFixed(2);
traceOpacity = parseFloat(this.value);
});
const traceLenSlider = document.getElementById("traceLenSlider");
const traceLenVal = document.getElementById("traceLenVal");
traceLenSlider.addEventListener("input", function() {
traceLenVal.textContent = parseFloat(this.value).toFixed(2);
});
const traceWidthSlider = document.getElementById("traceWidthSlider");
const traceWidthVal = document.getElementById("traceWidthVal");
traceWidthSlider.addEventListener("input", function() {
traceWidthVal.textContent = parseFloat(this.value).toFixed(1);
traceWidth = parseFloat(this.value);
});
const contourWidthSlider = document.getElementById("contourWidthSlider");
const contourWidthVal = document.getElementById("contourWidthVal");
contourWidthSlider.addEventListener("input", function() {
contourWidthVal.textContent = parseFloat(this.value).toFixed(1);
contourWidth = parseFloat(this.value);
});
document.getElementById("chkPoint").addEventListener("change", function() {
dotVisible = this.checked;
});
document.getElementById("chkNh").addEventListener("change", function() {
showNh = this.checked;
});
function evalFourier(t) {
if (!fourier) return null;
const numH = getNumHarmonics();
let cx = 0, cy = 0;
for (let k = 0; k < numH; k++) {
const c = fourier[k];
const theta = 2 * Math.PI * c.freq * t;
cx += c.re * Math.cos(theta) - c.im * Math.sin(theta);
cy += c.im * Math.cos(theta) + c.re * Math.sin(theta);
}
return [cx, cy];
}
function drawContour() {
if (!contourVisible) return;
ctx.save();
ctx.strokeStyle = "white";
ctx.lineWidth = contourWidth * scale;
ctx.stroke(contourPath2D);
ctx.restore();
}
function drawFourier(t) {
if (!fourierVisible || !fourier) return;
const numH = getNumHarmonics();
let cx = 0, cy = 0;
for (let k = 0; k < numH; k++) {
const c = fourier[k];
const theta = 2 * Math.PI * c.freq * t;
const dx = c.re * Math.cos(theta) - c.im * Math.sin(theta);
const dy = c.im * Math.cos(theta) + c.re * Math.sin(theta);
const nx = cx + dx;
const ny = cy + dy;
const color = fourierCircleColors[k % fourierCircleColors.length];
ctx.beginPath();
ctx.arc(cx, cy, c.r, 0, 2 * Math.PI);
ctx.strokeStyle = color;
ctx.lineWidth = 0.3 * scale;
ctx.setLineDash([scale, scale]);
ctx.stroke();
ctx.setLineDash([]);
ctx.beginPath();
ctx.moveTo(cx, cy);
ctx.lineTo(nx, ny);
ctx.strokeStyle = color;
ctx.lineWidth = 0.3 * scale;
ctx.stroke();
ctx.beginPath();
ctx.arc(nx, ny, 0.8 * scale, 0, 2 * Math.PI);
ctx.fillStyle = color;
ctx.fill();
if (k === 0) { firstDotX = nx; firstDotY = ny; }
cx = nx;
cy = ny;
}
}
function updateTraceData(t) {
if (!traceVisible || !fourier) return;
const pt = evalFourier(t);
if (!pt) return;
traceHistory.push(pt);
const maxLen = Math.round(parseFloat(traceLenSlider.value) * points.length);
if (traceHistory.length > maxLen) {
traceHistory = traceHistory.slice(traceHistory.length - maxLen);
}
}
function drawTrace() {
if (!traceVisible || traceHistory.length < 2) return;
ctx.save();
ctx.globalAlpha = traceOpacity;
ctx.strokeStyle = traceColors[traceColorIdx];
ctx.lineWidth = traceWidth * scale;
ctx.lineJoin = "round";
ctx.beginPath();
ctx.moveTo(traceHistory[0][0], traceHistory[0][1]);
for (let i = 1; i < traceHistory.length; i++) {
ctx.lineTo(traceHistory[i][0], traceHistory[i][1]);
}
ctx.stroke();
ctx.restore();
}
function drawSpark(px, py) {
if (!dotVisible) return;
ctx.save();
ctx.translate(px, py);
const glowR = dotR * 3;
const grad = ctx.createRadialGradient(0, 0, 0, 0, 0, glowR);
grad.addColorStop(0, "white");
grad.addColorStop(0.2, "lightyellow");
grad.addColorStop(0.5, "orange");
grad.addColorStop(0.8, "orangered");
grad.addColorStop(1, "transparent");
ctx.beginPath();
ctx.arc(0, 0, glowR, 0, 2 * Math.PI);
ctx.fillStyle = grad;
ctx.globalAlpha = 0.9;
ctx.fill();
ctx.globalAlpha = 1;
ctx.beginPath();
ctx.arc(0, 0, dotR * 0.5, 0, 2 * Math.PI);
ctx.fillStyle = "white";
ctx.fill();
ctx.lineCap = "round";
for (let i = 0; i < NUM_RAYS; i++) {
const angle = Math.random() * Math.PI * 2;
const len = (2.0 + Math.random() * 6.0) * sparkScale;
const inner = (0.2 + Math.random() * 0.5) * sparkScale;
const cos = Math.cos(angle), sin = Math.sin(angle);
ctx.beginPath();
ctx.moveTo(cos * inner, sin * inner);
ctx.lineTo(cos * len, sin * len);
ctx.strokeStyle = Math.random() > 0.4 ? "gold" : "darkorange";
ctx.lineWidth = (0.3 + Math.random() * 0.5) * sparkScale;
ctx.globalAlpha = 0.3 + Math.random() * 0.6;
ctx.stroke();
}
for (let i = 0; i < NUM_PARTICLES; i++) {
const angle = Math.random() * Math.PI * 2;
const dist = (2.0 + Math.random() * 5.0) * sparkScale;
ctx.beginPath();
ctx.arc(Math.cos(angle) * dist, Math.sin(angle) * dist, (0.1 + Math.random() * 0.3) * sparkScale, 0, 2 * Math.PI);
ctx.fillStyle = "gold";
ctx.globalAlpha = 0.3 + Math.random() * 0.5;
ctx.fill();
}
ctx.restore();
}
function drawNhLabel() {
if (!showNh || !fourier) return;
ctx.save();
ctx.fillStyle = "white";
ctx.font = (VB_SIZE * 4 / 100) + "px sans-serif";
ctx.textBaseline = "middle";
ctx.fillText(getNumHarmonics(), firstDotX + 2 * scale, firstDotY);
ctx.restore();
}
let numHarmonics = 2;
function getNumHarmonics() {
if (!fourier) return 0;
return Math.max(1, Math.min(numHarmonics, fourier.length));
}
function updateDisplay(t) {
tval.textContent = "t = " + t.toFixed(3);
slider.value = t;
ctx.setTransform(1,0,0,1,0,0);
ctx.clearRect(0, 0, canvas.width, canvas.height);
setupTransform();
drawContour();
drawFourier(t);
updateTraceData(t);
drawTrace();
const pt = evalFourier(t);
if (pt) drawSpark(pt[0], pt[1]);
drawNhLabel();
}
slider.addEventListener("input", function() {
traceHistory = [];
updateDisplay(parseFloat(this.value));
});
let animId = null;
let lastTime = null;
let currentT = 0;
let loopIndex = 0;
const maxHarmonics = 500;
const maxNh = fourier ? Math.min(maxHarmonics, fourier.length) : 1;
let nhSteps = [];
let nhSpeeds = [];
let currentSpeed = 1;
let totalLoops = 0;
function parseStepsStr(str) {
const groups = str.split(";").map(s => s.trim()).filter(s => s.length > 0);
const ranges = [];
for (const g of groups) {
const parts = g.split(/\s+/).map(Number);
if (parts.length === 4 && parts.every(n => !isNaN(n))) {
ranges.push({ from: parts[0], step: parts[1], to: parts[2], speed: parts[3] });
}
}
return ranges;
}
function rebuildNhSteps(str) {
const ranges = parseStepsStr(str);
nhSteps = [];
nhSpeeds = [];
if (ranges.length === 0) { nhSteps = [1]; nhSpeeds = [1]; totalLoops = 1; return; }
let i = ranges[0].from;
while (nhSteps.length < 10000) {
let spd = 1;
for (const r of ranges) {
if (i >= r.from && i < r.to) { spd = r.speed; break; }
}
nhSteps.push(Math.min(i, maxNh));
nhSpeeds.push(spd);
if (i >= maxNh) break;
let found = false;
for (const r of ranges) {
if (i >= r.from && i < r.to) { i += r.step; found = true; break; }
}
if (!found) {
let jumped = false;
for (let k = 0; k < ranges.length - 1; k++) {
if (i >= ranges[k].to && i < ranges[k+1].from) { i = ranges[k+1].from; jumped = true; break; }
}
if (!jumped) break;
}
}
totalLoops = nhSteps.length;
}
rebuildNhSteps(document.getElementById("stepsInput").value);
const stepsInputEl = document.getElementById("stepsInput");
stepsInputEl.addEventListener("change", function() {
rebuildNhSteps(this.value);
loopIndex = 0;
applyLoopParams();
});
stepsInputEl.addEventListener("keydown", function(e) {
if (e.key === "Enter") {
rebuildNhSteps(this.value);
loopIndex = 0;
applyLoopParams();
}
});
function applyLoopParams() {
const h = nhSteps[loopIndex];
numHarmonics = h;
currentSpeed = nhSpeeds[loopIndex] || 1;
const titleEl = document.getElementById("pageTitle");
if (titleEl) titleEl.textContent = "Harmonics: " + h;
document.getElementById("loopVal").textContent = "loop " + loopIndex + "/" + totalLoops + " \u2014 harmonics: " + h;
traceColorIdx = loopIndex % traceColors.length;
traceVisible = shouldShow(getShowMode("selTrace"), loopIndex);
if (!traceVisible) traceHistory = [];
contourVisible = shouldShow(getShowMode("selContour"), loopIndex);
fourierVisible = shouldShow(getShowMode("selCircles"), loopIndex);
}
applyLoopParams();
function animate(timestamp) {
if (lastTime === null) lastTime = timestamp;
const dt = (timestamp - lastTime) / 1000;
lastTime = timestamp;
currentT += dt * currentSpeed * 0.1;
if (currentT > 1) {
currentT -= 1;
traceHistory = [];
loopIndex = (loopIndex + 1) % totalLoops;
applyLoopParams();
}
updateDisplay(currentT);
animId = requestAnimationFrame(animate);
}
document.getElementById("startBtn").addEventListener("click", function() {
if (animId !== null) return;
lastTime = null;
animId = requestAnimationFrame(animate);
});
document.getElementById("stopBtn").addEventListener("click", function() {
if (animId !== null) {
cancelAnimationFrame(animId);
animId = null;
lastTime = null;
}
});
// Harmonics table
if (fourier) {
const tbody = document.getElementById("harmonicsTbody");
fourier.forEach((c, i) => {
const tr = document.createElement("tr");
tr.innerHTML = "<td style=\"padding:2px 8px\">"+i+"</td><td style=\"padding:2px 8px\">"+c.freq+"</td><td style=\"padding:2px 8px\">"+c.re.toFixed(4)+"</td><td style=\"padding:2px 8px\">"+c.im.toFixed(4)+"</td><td style=\"padding:2px 8px\">"+c.r.toFixed(4)+"</td>";
tbody.appendChild(tr);
});
}
document.getElementById("harmonicsBtn").addEventListener("click", function() {
const div = document.getElementById("harmonicsDiv");
div.style.display = div.style.display === "none" ? "" : "none";
});
// Auto-start
lastTime = null;
animId = requestAnimationFrame(animate);
</script>
</body>
</html>
