Calculate positions of dots to draw a filled circle made of dots.

circleOfDots_Spiral.js

// Calling this function will return a function that gives you the position of the dot at an index.
// This version uses the golden angle to create a tightly packed spiral.
// This is made as a closure so that the array of positions is only calculated once.
//
// Usage:
// let getDotPosition = initCircleOfDots_Spiral();
// let p = getDotPosition(50);
//
// This will return a point in the format { x: 2.9227, y: 1.9894 }
// The distance between the dots is approximately 1, so you probably have to scale the positions.

function initCircleOfDots_Spiral() {
  // move the center point a little bit to the left to make it look better
  const arr = [{ x: 0.35, y: -0.05 }];
  let gAngle = Math.PI * (3 - Math.sqrt(5));
  let radius = 0.5;
  let t = -0.02;
  // scale the dots a little bit to make the distance approximately 1
  let adjustmentFactor = 1.1;

  function getDotPosition(index) {
    if (index < arr.length) {
      return arr[index];
    }

    for (let i = arr.length; i <= index; i++) {
      let theta = gAngle * i;
      let r = radius * Math.sqrt(i);
      let x = r * Math.cos(theta + t);
      let y = r * Math.sin(theta + t);
      arr.push({ x: x * adjustmentFactor, y: y * adjustmentFactor });
    }
    return arr[index];
  }

  return getDotPosition;
}