{"id":6116,"date":"2026-04-19T21:00:44","date_gmt":"2026-04-19T21:00:44","guid":{"rendered":"https:\/\/composers-inside-electronics.net\/cie-wp20\/?p=6116"},"modified":"2026-04-20T01:54:53","modified_gmt":"2026-04-20T01:54:53","slug":"ai-generate-html-to-show-the-relative-distance-to-each-speaker","status":"publish","type":"post","link":"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/","title":{"rendered":"AI Generate HTML to show the relative distance to each speaker"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a798746d0a44\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a798746d0a44\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Prompt\" >Prompt<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Response\" >Response<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#The_Mathematical_Derivation\" >The Mathematical Derivation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Interactive_Triangulation_Calculator\" >Interactive Triangulation Calculator<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Key_Considerations\" >Key Considerations<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Expected_Resolution\" >Expected Resolution<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Mathematical_Derivation\" >Mathematical Derivation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Factors_Affecting_Real-World_Resolution\" >Factors Affecting Real-World Resolution<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#MAX_And_Javascript_partial\" >MAX And Javascript (partial)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Max_MSP_Patch_Structure\" >Max MSP Patch Structure<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Expanded_JavaScript_Logic_triangulationjs\" >Expanded JavaScript Logic (triangulation.js)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generate-html-to-show-the-relative-distance-to-each-speaker\/#Implementation_Tips\" >Implementation Tips<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Prompt\"><\/span>Prompt<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">generate the html that would show the relative distance to each speaker that emits a simultaineous click received by smartphone using triangulation and time of flight. Derive the location of the phone both cartesian and polar coordinates.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Response\"><\/span>Response<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This is a classic &#8220;Acoustic GPS&#8221; problem. To solve this, we use <strong>Multilateration (MLAT)<\/strong> based on the <strong>Time Difference of Arrival (TDOA)<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Below is a self-contained HTML\/JavaScript application. It assumes three speakers at fixed coordinates and calculates the phone&#8217;s position based on the time it takes for a simultaneous &#8220;click&#8221; to reach the device.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"The_Mathematical_Derivation\"><\/span>The Mathematical Derivation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">To find the location $(x, y)$, we use the distance formula between the phone and each speaker $S_n$ at $(x_n, y_n)$:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$d_n = \\sqrt{(x &#8211; x_n)^2 + (y &#8211; y_n)^2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the clicks are simultaneous, the distance is $d_n = v \\cdot t_n$, where $v$ is the speed of sound (~343 m\/s).<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Cartesian Coordinates:<\/strong> We solve the system of quadratic equations. By subtracting the equations from one another, we linearize the problem to find $x$ and $y$.<\/li>\n\n\n\n<li><strong>Polar Coordinates:<\/strong> Once we have $(x, y)$, we convert using:\n<ul class=\"wp-block-list\">\n<li>$r = \\sqrt{x^2 + y^2}$<\/li>\n\n\n\n<li>$\\theta = \\operatorname{atan2}(y, x)$<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interactive_Triangulation_Calculator\"><\/span>Interactive Triangulation Calculator<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">HTML<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&lt;!DOCTYPE <strong>html<\/strong>&gt;\n&lt;html lang=\"en\"&gt;\n&lt;head&gt;\n    &lt;meta charset=\"UTF-8\"&gt;\n    &lt;meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\"&gt;\n    &lt;title&gt;Acoustic Triangulation Tracker&lt;\/title&gt;\n    &lt;style&gt;\n        body { font-family: sans-serif; line-height: 1.6; max-width: 800px; margin: 20px auto; padding: 0 20px; background: #f4f4f9; }\n        .card { background: white; padding: 20px; border-radius: 8px; box-shadow: 0 2px 10px rgba(0,0,0,0.1); }\n        .input-group { display: grid; grid-template-columns: 1fr 1fr; gap: 10px; margin-bottom: 20px; }\n        input { padding: 8px; border: 1px solid #ccc; border-radius: 4px; }\n        button { padding: 10px 20px; background: #007bff; color: white; border: none; border-radius: 4px; cursor: pointer; }\n        button:hover { background: #0056b3; }\n        #results { margin-top: 20px; border-top: 2px solid #eee; padding-top: 20px; }\n        .coord-box { background: #e9ecef; padding: 15px; border-radius: 4px; font-family: monospace; }\n    &lt;\/style&gt;\n&lt;\/head&gt;\n&lt;body&gt;\n\n&lt;div class=\"card\"&gt;\n    &lt;h2&gt;Acoustic Localization (ToF)&lt;\/h2&gt;\n    &lt;p&gt;Enter the time (ms) it took for the click to reach the phone from each speaker.&lt;\/p&gt;\n    \n    &lt;div class=\"input-group\"&gt;\n        &lt;div&gt;\n            &lt;label&gt;Speaker A (0,0) - Time (ms):&lt;\/label&gt;&lt;br&gt;\n            &lt;input type=\"number\" id=\"t1\" value=\"10\" step=\"0.1\"&gt;\n        &lt;\/div&gt;\n        &lt;div&gt;\n            &lt;label&gt;Speaker B (10,0) - Time (ms):&lt;\/label&gt;&lt;br&gt;\n            &lt;input type=\"number\" id=\"t2\" value=\"15\" step=\"0.1\"&gt;\n        &lt;\/div&gt;\n        &lt;div&gt;\n            &lt;label&gt;Speaker C (5,10) - Time (ms):&lt;\/label&gt;&lt;br&gt;\n            &lt;input type=\"number\" id=\"t3\" value=\"12\" step=\"0.1\"&gt;\n        &lt;\/div&gt;\n    &lt;\/div&gt;\n\n    &lt;button onclick=\"calculateLocation()\"&gt;Calculate Position&lt;\/button&gt;\n\n    &lt;div id=\"results\"&gt;\n        &lt;h3&gt;Calculated Location:&lt;\/h3&gt;\n        &lt;div class=\"coord-box\" id=\"output\"&gt;\n            Click calculate to see coordinates...\n        &lt;\/div&gt;\n    &lt;\/div&gt;\n&lt;\/div&gt;\n\n&lt;script&gt;\n    const V_SOUND = 343; \/\/ Speed of sound in m\/s\n\n    \/\/ Speaker coordinates (Fixed anchors)\n    const S1 = { x: 0, y: 0 };\n    const S2 = { x: 10, y: 0 };\n    const S3 = { x: 5, y: 10 };\n\n    function calculateLocation() {\n        \/\/ Convert ms to s and calculate distances (d = v * t)\n        const d1 = (document.getElementById('t1').value \/ 1000) * V_SOUND;\n        const d2 = (document.getElementById('t2').value \/ 1000) * V_SOUND;\n        const d3 = (document.getElementById('t3').value \/ 1000) * V_SOUND;\n\n        \/* Using Trilateration formula:\n           x = (d1^2 - d2^2 + x2^2) \/ (2 * x2)\n           y = (d1^2 - d3^2 + x3^2 + y3^2 - 2*x*x3) \/ (2 * y3)\n        *\/\n        \n        const x = (Math.pow(d1, 2) - Math.pow(d2, 2) + Math.pow(S2.x, 2)) \/ (2 * S2.x);\n        const y = (Math.pow(d1, 2) - Math.pow(d3, 2) + Math.pow(S3.x, 2) + Math.pow(S3.y, 2) - (2 * x * S3.x)) \/ (2 * S3.y);\n\n        \/\/ Convert to Polar\n        const r = Math.sqrt(x*x + y*y);\n        const thetaRad = Math.atan2(y, x);\n        const thetaDeg = thetaRad * (180 \/ Math.PI);\n\n        document.getElementById('output').innerHTML = `\n            &lt;strong&gt;Relative Distances:&lt;\/strong&gt;&lt;br&gt;\n            Dist to S1: ${d1.toFixed(2)}m | S2: ${d2.toFixed(2)}m | S3: ${d3.toFixed(2)}m&lt;br&gt;&lt;br&gt;\n            \n            &lt;strong&gt;Cartesian Coordinates:&lt;\/strong&gt;&lt;br&gt;\n            X: ${x.toFixed(3)} m&lt;br&gt;\n            Y: ${y.toFixed(3)} m&lt;br&gt;&lt;br&gt;\n            \n            &lt;strong&gt;Polar Coordinates:&lt;\/strong&gt;&lt;br&gt;\n            Radius (r): ${r.toFixed(3)} m&lt;br&gt;\n            Azimuth (\u03b8): ${thetaDeg.toFixed(2)}\u00b0\n        `;\n    }\n&lt;\/script&gt;\n\n&lt;\/body&gt;\n&lt;\/html&gt;\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Key_Considerations\"><\/span>Key Considerations<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>HTTPS Requirement:<\/strong> As noted in your <a href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generated-node-js-convolution-player\/\" target=\"_blank\" rel=\"noreferrer noopener\">CIE Project Log<\/a>, if you plan to use actual smartphone hardware (IMU or Mic), modern browsers will require an <strong>HTTPS<\/strong> connection to access the <code>AudioContext<\/code> and motion sensors.<\/li>\n\n\n\n<li><strong>Clock Sync:<\/strong> This code assumes a &#8220;simultaneous&#8221; click. In practice, unless the speakers are wired to the same source, you would likely calculate <strong>TDOA<\/strong> (Time Difference of Arrival) rather than absolute Time of Flight, which requires a slightly different hyperbolic positioning algorithm.<\/li>\n\n\n\n<li><strong>Environmental Factors:<\/strong> The speed of sound varies with temperature ($v \\approx 331.3 + 0.606T$). For high precision, you should adjust the <code>V_SOUND<\/code> constant based on the room temperature.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Expected_Resolution\"><\/span>Expected Resolution<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>click here for response on prompt regarding resolution in meters at 48khz sample rate<\/summary>\n<p class=\"wp-block-paragraph\">At a sampling rate of <strong>48 kHz<\/strong>, the raw expected resolution (or &#8220;granularity&#8221;) of an acoustic time-of-flight measurement is approximately <strong>0.00715 meters (7.15 mm)<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Mathematical_Derivation\"><\/span>Mathematical Derivation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The spatial resolution is determined by how much distance sound travels in the duration of a single sample.<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Sample Period ($T_s$):<\/strong>$$T_s = \\frac{1}{\\text{Sampling Rate}} = \\frac{1}{48,000 \\text{ Hz}} \\approx 20.83 \\text{ \\mu s}$$<\/li>\n\n\n\n<li><strong>Distance per Sample ($d$):<\/strong>Using the standard speed of sound ($v \\approx 343.2 \\text{ m\/s}$ at 20\u00b0C):$$d = v \\times T_s = 343.2 \\text{ m\/s} \\times 0.00002083 \\text{ s} \\approx 0.00715 \\text{ m}$$<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Factors_Affecting_Real-World_Resolution\"><\/span>Factors Affecting Real-World Resolution<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">While <strong>7.15 mm<\/strong> is the physical limit of a single discrete sample, your actual accuracy in the <a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/composers-inside-electronics.net\/cie-wp20\/ai-generated-node-js-convolution-player\/\">triangulation script you are building<\/a> will be influenced by:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Geometric Dilution of Precision (GDOP):<\/strong> The resolution is highest when the phone is centered between speakers; as the phone moves toward the edge of the &#8220;tracking box,&#8221; the mathematical resolution degrades even if the sampling rate remains constant.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sub-sample Interpolation:<\/strong> By using cross-correlation or phase-shifting techniques, it is possible to achieve &#8220;sub-sample&#8221; resolution, potentially reaching accuracies in the <strong>1\u20132 mm<\/strong> range.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Temperature Sensitivity:<\/strong> The speed of sound changes by about <strong>0.6 m\/s<\/strong> for every <strong>1\u00b0C<\/strong> change. If your room temperature drifts by 5\u00b0C, your distance calculation could be off by more than <strong>1%<\/strong> (approx. 3 cm over a 3-meter span).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Clock Jitter &amp; Latency:<\/strong> In smartphone-based tracking, OS-level audio buffer latencies can introduce significant jitter. For the best results, you should use a low-latency API like <strong>Web Audio API<\/strong> or <strong>Oboe (Android)<\/strong> to ensure the most consistent time-stamping possible.<\/p>\n<\/details>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"MAX_And_Javascript_partial\"><\/span>MAX And Javascript (partial)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To implement the detection logic in <strong>Max MSP<\/strong>, you will need to precisely time the interval between the click emission and the arrival at the microphone.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since you are working with <strong>ADC 1<\/strong> for the microphone and <strong>DAC 1\u20134<\/strong> for the speakers, the most robust method involves using a high-priority timer triggered by the audio signal itself.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Max_MSP_Patch_Structure\"><\/span>Max MSP Patch Structure<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Emission Logic:<\/strong> Use a <code>click~<\/code> object. Send it through a <code>gate~ 4<\/code> to cycle through your speakers.<\/li>\n\n\n\n<li><strong>Timing:<\/strong> Use <code>cpuclock<\/code> or <code>timer<\/code>. Trigger the &#8220;start&#8221; when the click is sent and the &#8220;stop&#8221; when the <code>threshold~<\/code> of the microphone is breached.<\/li>\n\n\n\n<li><strong>Signal Detection:<\/strong> Use <code>abs~<\/code> followed by <code>threshold~<\/code> to detect the incoming click. You may need a small <code>gate<\/code> to prevent false triggers from room noise or echoes.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Expanded_JavaScript_Logic_triangulationjs\"><\/span>Expanded JavaScript Logic (<code>triangulation.js<\/code>)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Based on your current setup and the dimensions of your room (20ft x 12ft), this script handles the conversion of arrival times into coordinates. It incorporates the speed of sound and the speaker coordinates you specified.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">JavaScript<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\/\/ triangulation.js\n\/\/ Designed for a 20x12ft room\nconst V_SOUND = 1125; \/\/ Speed of sound in ft\/s (approx 70\u00b0F)\n\n\/\/ Corner Speaker Coordinates (ft)\nconst S1 = { x: 0,  y: 0  }; \/\/ DAC 1\nconst S2 = { x: 20, y: 0  }; \/\/ DAC 2\nconst S3 = { x: 20, y: 12 }; \/\/ DAC 3\nconst S4 = { x: 0,  y: 12 }; \/\/ DAC 4\n\nfunction list() {\n    \/\/ Expects a list of 4 arrival times in milliseconds\n    var times = arrayfromargs(arguments);\n    if (times.length &lt; 4) {\n        error(\"Requires 4 time values (one per speaker).\");\n        return;\n    }\n\n    \/\/ 1. Convert ms to Distance (d = v * t)\n    \/\/ t is divided by 1000 to convert ms to seconds\n    var d = times.map(function(t) { \n        return (t \/ 1000) * V_SOUND; \n    });\n\n    \/\/ 2. Trilateration Calculation (Solving for X and Y)\n    \/\/ We use the first three speakers as primary anchors\n    var x = (Math.pow(d&#91;0], 2) - Math.pow(d&#91;1], 2) + Math.pow(S2.x, 2)) \/ (2 * S2.x);\n    \n    \/\/ Using S1 and S4 for the Y calculation\n    var y = (Math.pow(d&#91;0], 2) - Math.pow(d&#91;3], 2) + Math.pow(S4.y, 2)) \/ (2 * S4.y);\n\n    \/\/ 3. Polar Coordinates Calculation\n    var r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));\n    var theta = Math.atan2(y, x) * (180 \/ Math.PI);\n\n    \/\/ 4. Output to Max\n    outlet(0, \"cartesian\", x, y);\n    outlet(1, \"polar\", r, theta);\n    \n    \/\/ Optional: Validation check using the 4th speaker\n    var d4_calc = Math.sqrt(Math.pow(x - S3.x, 2) + Math.pow(y - S3.y, 2));\n    var error_margin = Math.abs(d4_calc - d&#91;2]);\n    outlet(2, \"error\", error_margin);\n}\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Implementation_Tips\"><\/span>Implementation Tips<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Calibration:<\/strong> For the most accurate results, perform a &#8220;zero-distance&#8221; test. Place the microphone directly against a speaker and measure the time. This value is your <strong>system latency<\/strong>. Subtract this constant from all future measurements before sending them to the <code>js<\/code> object.<\/li>\n\n\n\n<li><strong>Room Environment:<\/strong> If you are working in a space like the <a href=\"https:\/\/www.google.com\/search?q=https:\/\/composers-inside-electronics.net\/cie-wp20\/about-cie-2020-2026\/\" target=\"_blank\" rel=\"noreferrer noopener\">Eclipse Gallery<\/a>, remember that large flat surfaces can cause reflections. You may want to use a <strong>windowing<\/strong> function or a simple <code>gate<\/code> in Max to ensure you are only timing the <em>first<\/em> arrival of the sound, not the reverberation.<\/li>\n\n\n\n<li><strong>Coordinate Mapping:<\/strong> In the <code>js<\/code> code above, Speaker 1 is the origin $(0,0)$. If your room layout differs, simply update the <code>S1<\/code> through <code>S4<\/code> constants to match your actual physical measurements.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Do you need help setting up the <code>threshold~<\/code> subpatch to ensure the click detection is reliable against background noise?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Prompt generate the html that would show the relative distance to each speaker that emits a simultaineous click received by smartphone using triangulation and time [&#8230;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"h5ap_radio_sources":[],"footnotes":""},"categories":[5],"tags":[403,416,412,418,417],"class_list":["post-6116","post","type-post","status-publish","format-standard","hentry","category-technical","tag-ai","tag-html","tag-proxima","tag-tdoa","tag-triangulation"],"post_type":"post","author_name":"Philip Edelstein","_links":{"self":[{"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/posts\/6116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/comments?post=6116"}],"version-history":[{"count":3,"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/posts\/6116\/revisions"}],"predecessor-version":[{"id":6126,"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/posts\/6116\/revisions\/6126"}],"wp:attachment":[{"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/media?parent=6116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/categories?post=6116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/composers-inside-electronics.net\/cie-wp20\/wp-json\/wp\/v2\/tags?post=6116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}