Some trigonometry for drawing spinning squares inside other squares

spinner_trig.js

function generateStationarySquares(maxRad, squareCount) {
  const squares = [];
  for (let i = 0; i < squareCount; i++) {
    // Divide maxRad by sqrt(2) i times.
    const rad = maxRad / Math.pow(Math.sqrt(2), i);
    // We want the outermost stationary square to be rotated 90 degrees, like a
    // diamond.
    const ang = i % 2 === 0 ? Math.PI / 4 : 0;
    squares.push([rad, ang]);
  }
  squares.reverse();
  return squares;
}

function getOuterSquareAngle(outerRad, innerRad) {
  // https://www.wolframalpha.com/input/?i=L+%3D+cos(a)+%2B+sin(a);+solve+for+a
  const L = outerRad / innerRad;
  const num = 1 - Math.sqrt(2 - L * L);
  const den = L + 1;
  const ang = 2 * (Math.PI + Math.atan(num / den));
  return ang;
}

function polarToCartesian(centerX, centerY, radius, angle) {
  return {
    x: centerX + radius * Math.cos(angle),
    y: centerY + radius * Math.sin(angle),
  };
}