// Generates a bell curve SVG and writes it to _includes/bell-curve.svg
// Usage: node scripts/generate-bell-curve.js

const fs = require("fs");
const path = require("path");

const width = 600;
const height = 300;
const padding = { top: 20, right: 20, bottom: 40, left: 20 };

const plotW = width - padding.left - padding.right;
const plotH = height - padding.top - padding.bottom;

// Standard normal PDF
function gaussian(x) {
  return Math.exp(-0.5 * x * x) / Math.sqrt(2 * Math.PI);
}

// Generate points from -4 to 4
const steps = 200;
const xMin = -4, xMax = 4;
const points = [];
for (let i = 0; i <= steps; i++) {
  const x = xMin + (xMax - xMin) * (i / steps);
  points.push({ x, y: gaussian(x) });
}

const yMax = gaussian(0); // peak value

function sx(x) {
  return padding.left + ((x - xMin) / (xMax - xMin)) * plotW;
}

function sy(y) {
  return padding.top + plotH - (y / yMax) * plotH;
}

// Build the curve path
const linePath = points.map((p, i) => {
  const cmd = i === 0 ? "M" : "L";
  return `${cmd}${sx(p.x).toFixed(2)},${sy(p.y).toFixed(2)}`;
}).join(" ");

// Build the filled area path (closed along the baseline)
const areaPath = linePath
  + ` L${sx(xMax).toFixed(2)},${sy(0).toFixed(2)}`
  + ` L${sx(xMin).toFixed(2)},${sy(0).toFixed(2)} Z`;

const svg = `<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 ${width} ${height}" role="img" aria-label="Standard normal distribution (bell curve)">
  <path d="${areaPath}" fill="#d0d0d0" opacity="0.5"/>
  <path d="${linePath}" fill="none" stroke="currentColor" stroke-width="2"/>
  <line x1="${sx(xMin)}" y1="${sy(0)}" x2="${sx(xMax)}" y2="${sy(0)}" stroke="currentColor" stroke-width="1"/>
</svg>`;

const outPath = path.join(__dirname, "..", "_includes", "bell-curve.svg");
fs.writeFileSync(outPath, svg);
console.log(`Wrote ${outPath}`);