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<head><title id="pageTitle">Harmonics: 2</title></head>
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<g id="fourier-group"></g>
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<circle id="dot" cx="0" cy="0" r="0.7559999999999999" fill="none" stroke="red" stroke-width="1.08"/>
<text id="nh-label" fill="white" font-size="4.32" style="pointer-events:none"></text>
</svg>
<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>
</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>
<label>Speed: <input type="range" id="speedSlider" min="0.1" max="10" step="0.1" value="3" style="width:120px"/> <span id="speedVal">3x</span></label>
<label>Harmonics loop: <input type="text" id="stepsInput" value="10 1 ; 20 5 ; 100 10 ; 100" style="width:300px;font-family:monospace;font-size:0.85em" title="start step ; start step ; ... ; max_harmonic"/></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">Every N</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="remainders (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">Every N</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="remainders (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">Every N</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="remainders (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="5" 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>
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const fourier = 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const slider = document.getElementById("slider");
const dot = document.getElementById("dot");
const tval = document.getElementById("tval");
const svgNS = "http://www.w3.org/2000/svg";
const fourierCircleColors = ["blue", "green", "orange", "purple", "cyan", "magenta"];
const traceColors = ["red","lime","dodgerblue","gold","hotpink","cyan","orange"];
let traceColorIdx = 0;
const scale = 108 / 100;
const traceEl = document.getElementById("trace");
const contourPath = document.getElementById("contour-path");
const fourierGroup = document.getElementById("fourier-group");
const nhLabel = document.getElementById("nh-label");
let traceVisible = true;
let traceHistory = [];
traceEl.setAttribute("opacity", 0.5);
traceEl.setAttribute("stroke-width", 1 * scale);
contourPath.setAttribute("stroke-width", 1 * scale);
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, remainders: rs.length ? rs : [0] };
}
return mode;
}
function shouldShow(mode, loopIdx) {
if (mode === "always") return true;
if (mode === "never") return false;
return mode.remainders.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);
traceEl.setAttribute("opacity", 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);
traceEl.setAttribute("stroke-width", parseFloat(this.value) * scale);
});
const contourWidthSlider = document.getElementById("contourWidthSlider");
const contourWidthVal = document.getElementById("contourWidthVal");
contourWidthSlider.addEventListener("input", function() {
contourWidthVal.textContent = parseFloat(this.value).toFixed(1);
contourPath.setAttribute("stroke-width", parseFloat(this.value) * scale);
});
document.getElementById("chkPoint").addEventListener("change", function() {
dot.style.display = this.checked ? "" : "none";
});
document.getElementById("chkNh").addEventListener("change", function() {
nhLabel.style.display = this.checked ? "" : "none";
});
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 updateTrace(t) {
if (!traceVisible || !fourier) {
traceEl.style.display = "none";
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);
}
traceEl.setAttribute("points", traceHistory.map(p => p[0] + "," + p[1]).join(" "));
traceEl.style.display = "";
}
function initFourier() {
if (!fourier) return;
const g = fourierGroup;
for (let k = 0; k < fourier.length; k++) {
const color = fourierCircleColors[k % fourierCircleColors.length];
const circle = document.createElementNS(svgNS, "circle");
circle.id = "fourier-circle-" + k;
circle.setAttribute("fill", "none");
circle.setAttribute("stroke", color);
circle.setAttribute("stroke-width", 0.3 * scale);
circle.setAttribute("stroke-dasharray", scale + "," + scale);
circle.setAttribute("r", fourier[k].r);
g.appendChild(circle);
const line = document.createElementNS(svgNS, "line");
line.id = "fourier-line-" + k;
line.setAttribute("stroke", color);
line.setAttribute("stroke-width", 0.3 * scale);
g.appendChild(line);
const fdot = document.createElementNS(svgNS, "circle");
fdot.id = "fourier-dot-" + k;
fdot.setAttribute("r", 0.8 * scale);
fdot.setAttribute("fill", color);
g.appendChild(fdot);
}
}
let numHarmonics = 2;
function getNumHarmonics() {
if (!fourier) return 0;
return Math.max(1, Math.min(numHarmonics, fourier.length));
}
function updateFourier(t) {
if (!fourier) return;
const numH = getNumHarmonics();
let cx = 0, cy = 0;
let firstDotX = 0, firstDotY = 0;
for (let k = 0; k < fourier.length; k++) {
const circle = document.getElementById("fourier-circle-" + k);
const line = document.getElementById("fourier-line-" + k);
const fdot = document.getElementById("fourier-dot-" + k);
if (k >= numH) {
circle.style.display = "none";
line.style.display = "none";
fdot.style.display = "none";
continue;
}
circle.style.display = "";
line.style.display = "";
fdot.style.display = "";
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;
circle.setAttribute("cx", cx);
circle.setAttribute("cy", cy);
line.setAttribute("x1", cx);
line.setAttribute("y1", cy);
line.setAttribute("x2", nx);
line.setAttribute("y2", ny);
fdot.setAttribute("cx", nx);
fdot.setAttribute("cy", ny);
if (k === 0) { firstDotX = nx; firstDotY = ny; }
cx = nx;
cy = ny;
}
if (document.getElementById("chkNh").checked) {
nhLabel.setAttribute("x", firstDotX + 2 * scale);
nhLabel.setAttribute("y", firstDotY);
nhLabel.textContent = numH;
}
}
initFourier();
updateFourier(0);
function updateDisplay(t) {
tval.textContent = "t = " + t.toFixed(3);
slider.value = t;
updateFourier(t);
updateTrace(t);
const pt = evalFourier(t);
if (pt) {
dot.setAttribute("cx", pt[0]);
dot.setAttribute("cy", pt[1]);
}
}
slider.addEventListener("input", function() {
traceHistory = [];
updateDisplay(parseFloat(this.value));
});
let animId = null;
let lastTime = null;
let currentT = 0;
let loopIndex = 0;
const maxNh = fourier ? fourier.length : 1;
let nhSteps = [];
let totalLoops = 0;
function parseStepsStr(str) {
const groups = str.split(";").map(s => s.trim()).filter(s => s.length > 0);
if (groups.length === 0) return { thresholds: [], maxH: 1 };
const maxH = parseInt(groups[groups.length - 1]) || 1;
const thresholds = [];
for (let i = 0; i < groups.length - 1; i++) {
const parts = groups[i].split(/\s+/).map(Number);
if (parts.length === 2 && !isNaN(parts[0]) && !isNaN(parts[1])) {
thresholds.push({ start: parts[0], step: parts[1] });
}
}
return { thresholds, maxH };
}
function rebuildNhSteps(str) {
const cfg = parseStepsStr(str);
const cap = Math.min(cfg.maxH, maxNh);
if (cfg.thresholds.length === 0 || cap < 1) { nhSteps = [1]; totalLoops = 1; return; }
nhSteps = [];
let nh = cfg.thresholds[0].start || 1;
let inc = cfg.thresholds[0].step || 1;
while (nh < cap && nhSteps.length < 10000) {
nhSteps.push(nh);
for (const t of cfg.thresholds) {
if (nh >= t.start) inc = t.step || 1;
}
nh += inc;
}
nhSteps.push(cap);
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;
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;
traceEl.setAttribute("stroke", traceColors[traceColorIdx]);
const traceMode = getShowMode("selTrace");
traceVisible = shouldShow(traceMode, loopIndex);
if (!traceVisible) { traceHistory = []; traceEl.style.display = "none"; }
contourPath.style.display = shouldShow(getShowMode("selContour"), loopIndex) ? "" : "none";
fourierGroup.style.display = shouldShow(getShowMode("selCircles"), loopIndex) ? "" : "none";
}
applyLoopParams();
function animate(timestamp) {
if (lastTime === null) lastTime = timestamp;
const dt = (timestamp - lastTime) / 1000;
lastTime = timestamp;
const speed = parseFloat(document.getElementById("speedSlider").value);
currentT += dt * speed * 0.1;
if (currentT > 1) {
currentT -= 1;
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;
}
});
const speedSliderEl = document.getElementById("speedSlider");
const speedValEl = document.getElementById("speedVal");
speedSliderEl.addEventListener("input", function() {
speedValEl.textContent = parseFloat(this.value).toFixed(1) + "x";
});
// Auto-start
lastTime = null;
animId = requestAnimationFrame(animate);
</script>
</body>
</html>
