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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Gradient Descent Simulator</title>
    <script src="https://cdn.tailwindcss.com"></script>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
    <link href="https://fonts.googleapis.com/css2?family=Space+Grotesk:wght@300;400;500;600;700&family=JetBrains+Mono:wght@400;500;600&display=swap" rel="stylesheet">
    <style>

        :root {

            --background: #05080a;

            --primary: #00ffff;

            --secondary: #a855f7;

            --accent: #ec4899;

            --surface: #0a1014;

            --border: #1e293b;

        }



        body {

            background-color: var(--background);

            color: #f8fafc;

            font-family: 'Space Grotesk', sans-serif;

            margin: 0;

            overflow-x: hidden;

        }



        .gradient-text {

            background: linear-gradient(135deg, var(--primary), var(--secondary));

            -webkit-background-clip: text;

            -webkit-text-fill-color: transparent;

        }



        .glass {

            background: rgba(10, 16, 20, 0.8);

            backdrop-filter: blur(12px);

            border: 1px solid rgba(30, 41, 59, 0.5);

        }



        .glow-cyan {

            box-shadow: 0 0 20px rgba(0, 255, 255, 0.3);

        }



        .canvas-container {

            width: 100%;

            height: 350px; /* Default for mobile */

            position: relative;

            background: #000;

            border-radius: 1rem;

            overflow: hidden;

            border: 1px solid var(--border);

        }



        /* Desktop override */

        @media (min-width: 768px) {

            .canvas-container {

                height: 500px;

            }

        }



        input[type=range] {

            -webkit-appearance: none;

            width: 100%;

            background: transparent;

        }



        input[type=range]::-webkit-slider-runnable-track {

            width: 100%;

            height: 6px;

            cursor: pointer;

            background: #1e293b;

            border-radius: 3px;

        }



        input[type=range]::-webkit-slider-thumb {

            height: 18px;

            width: 18px;

            border-radius: 50%;

            background: var(--primary);

            cursor: pointer;

            -webkit-appearance: none;

            margin-top: -6px;

            box-shadow: 0 0 10px rgba(0, 255, 255, 0.5);

        }



        .hidden { display: none; }

        

        @keyframes float {

            0%, 100% { transform: translateY(0px); }

            50% { transform: translateY(-10px); }

        }

        .animate-float { animation: float 3s ease-in-out infinite; }

    </style>
</head>
<body class="p-4 md:p-8">

    <div class="max-w-7xl mx-auto grid lg:grid-cols-[1fr_350px] gap-8">
        <!-- Left Side: Header & Viewport -->
        <div class="space-y-6">
            <header class="relative flex flex-col md:block">
                <h1 class="text-4xl md:text-5xl font-bold gradient-text text-center md:text-left">Gradient Descent</h1>

                <!-- Centered Button (Responsive Position) -->
                <div class="order-last md:order-none mt-4 md:mt-0 md:absolute md:left-1/2 md:-translate-x-1/2 md:top-1 flex items-center justify-center">
                    <audio id="clickSound" src="https://www.soundjay.com/buttons/sounds/button-3.mp3"></audio>
                    <a href="/gradient-descent" onclick="playSound(); return false;" class="inline-flex items-center justify-center text-center leading-none bg-blue-600 hover:bg-blue-500 text-white font-bold py-2 px-6 rounded-xl text-sm transition-all duration-150 shadow-[0_4px_0_rgb(29,78,216)] active:shadow-none active:translate-y-[4px] uppercase tracking-wider">
                        Back to Core
                    </a>
                </div>

                <p class="text-slate-400 text-sm max-w-md mt-2 text-center md:text-left mx-auto md:mx-0">
                    Optimize parameters by descending the loss landscape. Now with <b>Adaptive Learning Rate</b> logic!
                </p>
            </header>


            <div class="canvas-container" id="container">
                <div id="three-canvas"></div>
                
                <!-- Viewport Overlays -->
                <div class="absolute top-4 left-4 pointer-events-none">
                    <div class="glass px-3 py-2 rounded-lg">
                        <div class="text-[10px] text-slate-500 font-mono uppercase tracking-widest">Status</div>
                        <div id="status-text" class="text-xs font-mono text-cyan-400 mt-1 uppercase">Ready</div>
                    </div>
                </div>

                <div class="absolute top-4 right-4 pointer-events-none text-right">
                    <div class="glass px-3 py-2 rounded-lg">
                        <div class="text-[10px] text-slate-500 font-mono uppercase tracking-widest">Position</div>
                        <div id="pos-display" class="text-xs font-mono text-cyan-400 mt-1">X: 3.00 Y: 3.00</div>
                    </div>
                </div>

                <div class="absolute bottom-4 left-4 glass px-3 py-1 rounded-full text-[10px] text-slate-400 font-bold border border-slate-800">
                    GOAL AT <span id="goal-coords" class="text-green-400">0, 0</span>
                </div>
            </div>

            <!-- Educational Info -->
            <div class="glass rounded-xl overflow-hidden">
                <button onclick="toggleInfo()" class="w-full flex items-center justify-between p-4 hover:bg-slate-800/30 transition-colors">
                    <div class="flex items-center gap-2">
                        <svg class="w-5 h-5 text-cyan-400" fill="none" stroke="currentColor" viewBox="0 0 24 24"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M12 6.253v13m0-13C10.832 5.477 9.246 5 7.5 5S4.168 5.477 3 6.253v13C4.168 18.477 5.754 18 7.5 18s3.332.477 4.5 1.253m0-13C13.168 5.477 14.754 5 16.5 5c1.747 0 3.332.477 4.5 1.253v13C19.832 18.477 18.247 18 16.5 18c-1.746 0-3.332.477-4.5 1.253"></path></svg>
                        <span class="font-bold">Optimizer Secrets</span>
                    </div>
                    <svg id="info-arrow" class="w-5 h-5 transition-transform" fill="none" stroke="currentColor" viewBox="0 0 24 24"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M19 9l-7 7-7-7"></path></svg>
                </button>
                <div id="info-content" class="p-4 pt-0 text-sm text-slate-400 leading-relaxed grid md:grid-cols-2 gap-6 border-t border-slate-800 hidden">
                    <div class="space-y-2 pt-4">
                        <p><strong class="text-white">Momentum (β):</strong> Acts like a physical ball with weight. It keeps moving in the same direction, helping it "roll" through flat valleys and over small local pits.</p>
                    </div>
                    <div class="space-y-2 pt-4">
                        <p><strong class="text-white">The Challenge:</strong> Rosenbrock and Rastrigin are "non-convex" or have "vanishing gradients." Vanilla GD is often too weak to reach the center without help!</p>
                    </div>
                    <!-- Pro Tip Note -->
                    <div class="col-span-full pt-4 border-t border-slate-800/50 mt-2">
                        <p class="text-yellow-400 font-medium">
                            <span class="mr-2">💡</span> <b>Pro Tip:</b> If the ball gets stuck or vibrates wildly, you must <b>adjust the learning rate</b> or <b>momentum</b>. Or turn on <b>Adaptive Rate</b> to let the algorithm handle it!
                        </p>
                    </div>
                </div>
            </div>
        </div>

        <!-- Right Side: Controls -->
        <aside class="space-y-6">
            <div class="glass rounded-xl p-6 space-y-6">
                <!-- Learning Rate Slider -->
                <div class="space-y-4">
                    <div class="flex justify-between items-center">
                        <label class="text-xs font-bold text-slate-500 uppercase tracking-wider">Learning Rate (α)</label>
                        <span id="lr-value" class="text-cyan-400 font-mono bg-cyan-400/10 px-2 py-0.5 rounded border border-cyan-400/20 text-sm">0.050</span>
                    </div>
                    <input type="range" id="lr-slider" min="0.001" max="0.5" step="0.001" value="0.05">
                </div>

                <!-- Adaptive Toggle -->
                <div onclick="toggleAdaptive()" class="flex items-center justify-between p-3 rounded-lg bg-slate-800/40 border border-slate-700/50 cursor-pointer hover:bg-slate-800 transition-colors">
                    <div class="flex flex-col">
                        <span class="text-xs font-bold text-slate-300">Adaptive Rate</span>
                        <span class="text-[10px] text-slate-500">Auto-tune α during descent</span>
                    </div>
                    <div id="adaptive-toggle-bg" class="w-10 h-5 rounded-full bg-slate-700 relative transition-colors">
                        <div id="adaptive-toggle-dot" class="absolute left-1 top-1 w-3 h-3 rounded-full bg-white transition-all"></div>
                    </div>
                </div>

                <!-- Momentum Slider -->
                <div class="space-y-4">
                    <div class="flex justify-between items-center">
                        <label class="text-xs font-bold text-slate-500 uppercase tracking-wider">Momentum (β)</label>
                        <span id="mom-value" class="text-purple-400 font-mono bg-purple-400/10 px-2 py-0.5 rounded border border-purple-400/20 text-sm">0.10</span>
                    </div>
                    <input type="range" id="mom-slider" min="0" max="0.99" step="0.01" value="0.1">
                </div>

                <!-- Playback Buttons -->
                <div class="grid grid-cols-2 gap-3">
                    <button id="btn-toggle" class="flex items-center justify-center gap-2 py-3 rounded-lg font-bold transition-all bg-cyan-400 text-black glow-cyan hover:brightness-110">
                        <span id="toggle-icon"></span> <span id="toggle-text">Start</span>
                    </button>
                    <button id="btn-step" class="flex items-center justify-center gap-2 py-3 rounded-lg border border-slate-700 hover:bg-slate-800 transition-all font-bold">
                        Step ➜
                    </button>
                </div>

                <button id="btn-reset" class="w-full flex items-center justify-center gap-2 py-2 text-slate-400 hover:text-white text-sm transition-colors font-medium">
                    Reset Position ↺
                </button>

                <!-- Stats -->
                <div class="grid grid-cols-2 gap-4 pt-4 border-t border-slate-800">
                    <div class="text-center">
                        <div id="steps-val" class="text-2xl font-mono font-bold text-cyan-400">0</div>
                        <div class="text-[10px] text-slate-500 uppercase tracking-tighter">Steps</div>
                    </div>
                    <div class="text-center">
                        <div id="loss-val" class="text-2xl font-mono font-bold text-pink-500">9.00</div>
                        <div class="text-[10px] text-slate-500 uppercase tracking-tighter">Loss</div>
                    </div>
                </div>

                <!-- Progress -->
                <div class="p-4 bg-slate-900/50 rounded-lg border border-slate-800">
                    <div class="flex justify-between text-xs mb-2">
                        <span class="text-slate-500">Distance to Target</span>
                        <span id="dist-val" class="font-mono text-slate-300">4.242</span>
                    </div>
                    <div class="h-1.5 bg-slate-800 rounded-full overflow-hidden">
                        <div id="progress-bar" class="h-full bg-cyan-400 transition-all duration-300" style="width: 10%"></div>
                    </div>
                </div>
            </div>

            <!-- Level Selector -->
            <div class="glass rounded-xl p-4 space-y-3">
                <h3 class="text-xs font-bold text-slate-500 uppercase tracking-widest px-2">Function Landscape</h3>
                <div id="level-list" class="space-y-1">
                    <!-- Levels injected here -->
                </div>
            </div>
        </aside>
    </div>

    <!-- Victory Modal -->
    <div id="victory-modal" class="fixed inset-0 z-50 flex items-center justify-center p-4 bg-black/80 backdrop-blur-sm hidden">
        <div class="glass relative max-w-sm w-full rounded-2xl p-8 text-center animate-float">
            <!-- Close Button (Cross) -->
            <button onclick="closeModal()" class="absolute top-4 right-4 text-slate-500 hover:text-white transition-colors">
                <svg class="w-6 h-6" fill="none" stroke="currentColor" viewBox="0 0 24 24"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M6 18L18 6M6 6l12 12"></path></svg>
            </button>

            <div class="w-16 h-16 bg-cyan-400/20 rounded-full flex items-center justify-center mx-auto mb-4">
                <span class="text-3xl text-cyan-400">🏆</span>
            </div>
            <h2 class="text-2xl font-bold gradient-text mb-1">Convergence!</h2>
            <p id="modal-level-name" class="text-slate-400 text-sm mb-6">Level Complete</p>
            
            <div class="bg-slate-900/80 rounded-xl p-4 mb-6">
                <div id="modal-steps" class="text-3xl font-mono text-cyan-400 font-bold">0</div>
                <div class="text-xs text-slate-500 uppercase tracking-widest">Total Steps</div>
            </div>

            <div class="flex gap-3">
                <button onclick="closeModal()" class="flex-1 py-2 rounded-lg border border-slate-700 hover:bg-slate-800 transition-colors text-sm font-semibold">Retry</button>
                <button onclick="nextLevel()" class="flex-1 py-2 rounded-lg bg-cyan-400 text-black font-bold text-sm">Next Level</button>
            </div>
        </div>
    </div>

    <script>

        // --- LEVEL DEFINITIONS ---

        // Added 'presets' to automatically tune parameters for each landscape

        const LEVELS = [

            { 

                id: 1, 

                name: 'The Bowl', 

                difficulty: 'easy', 

                loss: (x, y) => x*x + y*y, 

                min: {x: 0, y: 0}, 

                winRadius: 0.15,

                presets: { lr: 0.05, mom: 0.1 } // Slow & Steady

            },

            { 

                id: 2, 

                name: 'The Ellipse', 

                difficulty: 'easy', 

                loss: (x, y) => x*x + 10*y*y, 

                min: {x: 0, y: 0}, 

                winRadius: 0.2,

                presets: { lr: 0.05, mom: 0.1 } 

            },

            { 

                id: 3, 

                name: 'Rosenbrock Valley', 

                difficulty: 'medium', 

                loss: (x, y) => Math.pow(1-x, 2) + 100*Math.pow(y-x*x, 2), 

                min: {x: 1, y: 1}, 

                winRadius: 0.25,

                presets: { lr: 0.002, mom: 0.85 } // Needs momentum to traverse the valley

            },

            { 

                id: 4, 

                name: 'Beale Function', 

                difficulty: 'medium', 

                loss: (x, y) => Math.pow(1.5-x+x*y, 2) + Math.pow(2.25-x+x*y*y, 2) + Math.pow(2.625-x+x*y*y*y, 2), 

                min: {x: 3, y: 0.5}, 

                winRadius: 0.25,

                presets: { lr: 0.01, mom: 0.5 }

            },

            { 

                id: 5, 

                name: 'Rastrigin', 

                difficulty: 'hard', 

                loss: (x, y) => 20 + x*x - 10*Math.cos(2*Math.PI*x) + y*y - 10*Math.cos(2*Math.PI*y), 

                min: {x: 0, y: 0}, 

                winRadius: 0.3,

                presets: { lr: 0.005, mom: 0.95 } // HIGH MOMENTUM to escape local minima

            }

        ];



        // Constants for 3D Visuals

        const SURFACE_OFFSET = -0.5;

        const Z_SCALE = 0.8;

        const BALL_FLOAT = 0.1;



        // --- APP STATE ---

        let currentLevel = LEVELS[0];

        let pos = { x: 3, y: 3 };

        let velocity = { x: 0, y: 0 }; 

        let path = [];

        let learningRate = 0.05;

        let momentum = 0.1; // Default starting momentum

        let isAdaptive = false;

        let isRunning = false;

        let steps = 0;

        let loopId = null;

        let prevLoss = Infinity;



        // --- THREE.JS SETUP ---

        const container = document.getElementById('container');

        const scene = new THREE.Scene();

        scene.background = new THREE.Color(0x05080a);

        

        const camera = new THREE.PerspectiveCamera(45, container.clientWidth / container.clientHeight, 0.1, 1000);

        camera.position.set(8, 8, 8);

        camera.lookAt(0, 0, 0);



        const renderer = new THREE.WebGLRenderer({ antialias: true });

        renderer.setSize(container.clientWidth, container.clientHeight);

        renderer.setPixelRatio(window.devicePixelRatio);

        document.getElementById('three-canvas').appendChild(renderer.domElement);



        const ambientLight = new THREE.AmbientLight(0xffffff, 0.4);

        scene.add(ambientLight);

        const pointLight = new THREE.PointLight(0x00ffff, 1);

        pointLight.position.set(10, 10, 10);

        scene.add(pointLight);



        function calculateVizHeight(x, y) {

            let z = currentLevel.loss(x, y);

            z = Math.min(z, 50);

            return (Math.log(z + 1) * Z_SCALE) + SURFACE_OFFSET;

        }



        // Surface

        let surfaceMesh;

        function updateSurface() {

            if (surfaceMesh) scene.remove(surfaceMesh);

            

            const size = 64;

            const geo = new THREE.PlaneBufferGeometry(10, 10, size, size);

            const posAttr = geo.attributes.position;

            const colorAttr = new THREE.BufferAttribute(new Float32Array(posAttr.count * 3), 3);

            

            let minVal = Infinity, maxVal = -Infinity;

            const vals = [];



            for (let i = 0; i < posAttr.count; i++) {

                const x = posAttr.getX(i);

                const y = posAttr.getY(i);

                let z = currentLevel.loss(x, y);

                z = Math.min(z, 50);

                z = Math.log(z + 1) * Z_SCALE;

                vals.push(z);

                minVal = Math.min(minVal, z);

                maxVal = Math.max(maxVal, z);

            }



            for (let i = 0; i < posAttr.count; i++) {

                const z = vals[i];

                posAttr.setZ(i, z);

                const t = (z - minVal) / (maxVal - minVal || 1);

                colorAttr.setXYZ(i, 0.1 + t * 0.8, 0.8 - t * 0.6, 0.8 + t * 0.2);

            }



            geo.setAttribute('color', colorAttr);

            geo.computeVertexNormals();



            const mat = new THREE.MeshStandardMaterial({ vertexColors: true, side: THREE.DoubleSide, transparent: true, opacity: 0.8, roughness: 0.5 });

            surfaceMesh = new THREE.Mesh(geo, mat);

            surfaceMesh.rotation.x = -Math.PI / 2;

            surfaceMesh.position.y = SURFACE_OFFSET;

            scene.add(surfaceMesh);

        }



        const ball = new THREE.Mesh(

            new THREE.SphereGeometry(0.18, 24, 24),

            new THREE.MeshStandardMaterial({ color: 0xff66cc, emissive: 0xff0088, emissiveIntensity: 0.5 })

        );

        scene.add(ball);



        let pathLine;

        function updatePath() {

            if (pathLine) scene.remove(pathLine);

            if (path.length < 2) return;



            const points = path.map(p => new THREE.Vector3(p.x, calculateVizHeight(p.x, p.y) + 0.05, p.y));

            const geo = new THREE.BufferGeometry().setFromPoints(points);

            const mat = new THREE.LineBasicMaterial({ color: 0x00ffff, transparent: true, opacity: 0.8 });

            pathLine = new THREE.Line(geo, mat);

            scene.add(pathLine);

        }



        const goalMarker = new THREE.Group();

        const torus = new THREE.Mesh(new THREE.TorusGeometry(0.3, 0.02, 16, 32), new THREE.MeshBasicMaterial({ color: 0x00ff66, transparent: true, opacity: 0.5 }));

        torus.rotation.x = Math.PI/2;

        const star = new THREE.Mesh(new THREE.SphereGeometry(0.08, 8, 8), new THREE.MeshBasicMaterial({ color: 0x00ff66 }));

        goalMarker.add(torus);

        goalMarker.add(star);

        scene.add(goalMarker);



        function updateGoalMarker() {

            const gx = currentLevel.min.x;

            const gy = currentLevel.min.y;

            const gz = calculateVizHeight(gx, gy);

            goalMarker.position.set(gx, gz + 0.05, gy);

            document.getElementById('goal-coords').innerText = `[${gx}, ${gy}]`;

        }



        scene.add(new THREE.GridHelper(10, 20, 0x1a3a4a, 0x0a1a2a));



        // --- OPTIMIZER LOGIC ---

        function calculateGradient(x, y) {

            const h = 0.0001;

            const dx = (currentLevel.loss(x + h, y) - currentLevel.loss(x - h, y)) / (2 * h);

            const dy = (currentLevel.loss(x, y + h) - currentLevel.loss(x, y - h)) / (2 * h);

            

            const magnitude = Math.sqrt(dx*dx + dy*dy);

            const limit = 50;

            if (magnitude > limit) {

                return { x: (dx / magnitude) * limit, y: (dy / magnitude) * limit, magnitude: limit };

            }

            return { x: dx, y: dy, magnitude };

        }



        function step() {

            const currentLoss = currentLevel.loss(pos.x, pos.y);

            const grad = calculateGradient(pos.x, pos.y);

            

            // --- ADAPTIVE LOGIC ---

            if (isAdaptive) {

                if (currentLoss > prevLoss * 1.05) {

                    learningRate *= 0.5; 

                } 

                else if (Math.abs(currentLoss - prevLoss) < 0.00001 && grad.magnitude < 0.01) {

                    learningRate *= 1.2; 

                }

                

                learningRate = Math.max(0.001, Math.min(0.5, learningRate));

                updateLRElement();

            }



            // Momentum Logic

            velocity.x = momentum * velocity.x - learningRate * grad.x;

            velocity.y = momentum * velocity.y - learningRate * grad.y;

            

            pos.x = Math.max(-5, Math.min(5, pos.x + velocity.x));

            pos.y = Math.max(-5, Math.min(5, pos.y + velocity.y));

            

            path.push({...pos});

            steps++;

            prevLoss = currentLoss;

            updateUI();



            const dist = Math.sqrt(Math.pow(pos.x - currentLevel.min.x, 2) + Math.pow(pos.y - currentLevel.min.y, 2));

            if (dist < currentLevel.winRadius) {

                stopDescent();

                showVictory();

            } else if (steps > 3000) { 

                stopDescent();

            }

        }



        function updateLRElement() {

            document.getElementById('lr-slider').value = learningRate;

            document.getElementById('lr-value').innerText = learningRate.toFixed(3);

        }



        function updateUI() {

            document.getElementById('pos-display').innerText = `X: ${pos.x.toFixed(2)} Y: ${pos.y.toFixed(2)}`;

            document.getElementById('steps-val').innerText = steps;

            const lossVal = currentLevel.loss(pos.x, pos.y);

            document.getElementById('loss-val').innerText = lossVal.toFixed(2);

            

            const dist = Math.sqrt(Math.pow(pos.x - currentLevel.min.x, 2) + Math.pow(pos.y - currentLevel.min.y, 2));

            document.getElementById('dist-val').innerText = dist.toFixed(3);

            document.getElementById('progress-bar').style.width = `${Math.max(5, Math.min(100, (1 - dist / 7) * 100))}%`;



            const ballZ = calculateVizHeight(pos.x, pos.y);

            ball.position.set(pos.x, ballZ + BALL_FLOAT, pos.y);

            updatePath();

        }



        function toggleAdaptive() {

            isAdaptive = !isAdaptive;

            const bg = document.getElementById('adaptive-toggle-bg');

            const dot = document.getElementById('adaptive-toggle-dot');

            if (isAdaptive) {

                bg.classList.replace('bg-slate-700', 'bg-cyan-400');

                dot.style.left = '22px';

            } else {

                bg.classList.replace('bg-cyan-400', 'bg-slate-700');

                dot.style.left = '4px';

            }

        }



        function startDescent() {

            isRunning = true;

            document.getElementById('toggle-text').innerText = 'Pause';

            document.getElementById('status-text').innerText = 'Descending...';

            document.getElementById('status-text').className = 'text-xs font-mono text-yellow-400 mt-1 uppercase';

            prevLoss = currentLevel.loss(pos.x, pos.y);

            loopId = setInterval(step, 50);

        }



        function stopDescent() {

            isRunning = false;

            document.getElementById('toggle-text').innerText = 'Start';

            document.getElementById('status-text').innerText = 'Paused';

            document.getElementById('status-text').className = 'text-xs font-mono text-cyan-400 mt-1 uppercase';

            clearInterval(loopId);

        }



        function showVictory() {

            document.getElementById('modal-level-name').innerText = currentLevel.name;

            document.getElementById('modal-steps').innerText = steps;

            document.getElementById('victory-modal').classList.remove('hidden');

        }



        function reset() {

            stopDescent();

            if(currentLevel.id === 3) pos = { x: -3, y: -3 }; 

            else if(currentLevel.id === 4) pos = { x: 1, y: 1 }; 

            else pos = { x: (Math.random() - 0.5) * 8, y: (Math.random() - 0.5) * 8 };

            

            velocity = { x: 0, y: 0 };

            path = [{...pos}];

            steps = 0;

            updateUI();

        }



        // --- EVENT HANDLERS ---

        document.getElementById('btn-toggle').onclick = () => isRunning ? stopDescent() : startDescent();

        document.getElementById('btn-step').onclick = step;

        document.getElementById('btn-reset').onclick = reset;

        document.getElementById('lr-slider').oninput = (e) => {

            learningRate = parseFloat(e.target.value);

            document.getElementById('lr-value').innerText = learningRate.toFixed(3);

        };

        document.getElementById('mom-slider').oninput = (e) => {

            momentum = parseFloat(e.target.value);

            document.getElementById('mom-value').innerText = momentum.toFixed(2);

        };



        function toggleInfo() {

            const content = document.getElementById('info-content');

            content.classList.toggle('hidden');

        }



        function closeModal() {

            document.getElementById('victory-modal').classList.add('hidden');

            reset();

        }



        function nextLevel() {

            const idx = LEVELS.findIndex(l => l.id === currentLevel.id);

            const next = LEVELS[(idx + 1) % LEVELS.length];

            selectLevel(next.id);

            document.getElementById('victory-modal').classList.add('hidden');

        }



        function selectLevel(id) {

            currentLevel = LEVELS.find(l => l.id === id);

            

            // Apply Presets if they exist

            if (currentLevel.presets) {

                learningRate = currentLevel.presets.lr;

                momentum = currentLevel.presets.mom;

                

                // Update UI Controls

                document.getElementById('lr-slider').value = learningRate;

                document.getElementById('lr-value').innerText = learningRate.toFixed(3);

                document.getElementById('mom-slider').value = momentum;

                document.getElementById('mom-value').innerText = momentum.toFixed(2);

            }



            renderLevels();

            updateSurface();

            updateGoalMarker();

            reset();

        }



        function renderLevels() {

            const list = document.getElementById('level-list');

            list.innerHTML = LEVELS.map(l => `

                <button onclick="selectLevel(${l.id})" class="w-full text-left p-3 rounded-lg transition-all border ${currentLevel.id === l.id ? 'bg-cyan-400/10 border-cyan-400/50' : 'border-transparent hover:bg-slate-800'}">

                    <div class="flex justify-between items-center mb-1">

                        <span class="font-bold text-sm ${currentLevel.id === l.id ? 'text-cyan-400' : ''}">${l.name}</span>

                        <span class="text-[9px] px-1.5 py-0.5 rounded border ${l.difficulty === 'easy' ? 'border-green-500/30 text-green-400' : l.difficulty === 'medium' ? 'border-yellow-500/30 text-yellow-400' : 'border-red-500/30 text-red-400'} uppercase">${l.difficulty}</span>

                    </div>

                </button>

            `).join('');

        }



        function animate() {

            requestAnimationFrame(animate);

            if (isRunning) {

                const s = 1 + Math.sin(Date.now() * 0.01) * 0.15;

                ball.scale.setScalar(s);

            }

            renderer.render(scene, camera);

        }



        window.addEventListener('resize', () => {

            camera.aspect = container.clientWidth / container.clientHeight;

            camera.updateProjectionMatrix();

            renderer.setSize(container.clientWidth, container.clientHeight);

        });



        renderLevels();

        updateSurface();

        updateGoalMarker();

        updateUI();

        animate();



        // --- MOUSE & TOUCH CONTROLS ---

        let isMouseDown = false;

        let prevMouse = { x: 0, y: 0 };



        // Mouse Events

        container.addEventListener('mousedown', (e) => { 

            isMouseDown = true; 

            prevMouse = { x: e.clientX, y: e.clientY }; 

        });

        window.addEventListener('mouseup', () => isMouseDown = false);

        window.addEventListener('mousemove', (e) => handleCameraRotate(e.clientX, e.clientY));



        // Touch Events (Mobile)

        container.addEventListener('touchstart', (e) => {

            if(e.touches.length === 1) {

                isMouseDown = true;

                prevMouse = { x: e.touches[0].clientX, y: e.touches[0].clientY };

            }

        }, { passive: false });



        window.addEventListener('touchend', () => isMouseDown = false);

        

        window.addEventListener('touchmove', (e) => {

            if(e.touches.length === 1 && isMouseDown) {

                handleCameraRotate(e.touches[0].clientX, e.touches[0].clientY);

            }

        }, { passive: false });



        // Common Rotation Logic

        function handleCameraRotate(clientX, clientY) {

            if (!isMouseDown) return;

            const dx = (clientX - prevMouse.x) * 0.005;

            const dy = (clientY - prevMouse.y) * 0.005;

            const radius = camera.position.length();

            let phi = Math.atan2(camera.position.x, camera.position.z);

            let theta = Math.acos(camera.position.y / radius);

            phi -= dx;

            theta = Math.max(0.1, Math.min(Math.PI / 2.1, theta - dy));

            camera.position.x = radius * Math.sin(theta) * Math.sin(phi);

            camera.position.y = radius * Math.cos(theta);

            camera.position.z = radius * Math.sin(theta) * Math.cos(phi);

            camera.lookAt(0, 0, 0);

            prevMouse = { x: clientX, y: clientY };

        }



    </script>
</body>
</html>