Calculate positions of dots to draw a filled circle made of dots. This version creates simple rings. The outer ring will be partially filled most of the time.

circleOfDots_SimpleRings.js

// Calling this function will return a function that gives you the position of the dot at an index.
// This version creates rings of dots. The outer ring will be partially filled most of the time.
// This is made as a closure so that the array of positions is only calculated once.
//
// Usage:
// let getDotPosition = initCircleOfDots_SimpleRings();
// let p = getDotPosition(50);
//
// This will return a point in the format { x: 1.4724, y: 3.7191 }
// The distance between the dots is approximately 1, so you probably have to scale the positions.

function initCircleOfDots_SimpleRings(n) {
  let arr = [{ x: 0, y: 0 }];
  let r = 1;

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

    while (arr.length <= index) {
      let dotsOnRing = Math.round(2 * Math.PI * r);
      let angle = Math.PI;
      let angleInc = (-Math.PI * 2) / dotsOnRing;
      for (let j = 0; j < dotsOnRing; j++) {
        let x = Math.sin(angle) * r;
        let y = Math.cos(angle) * r;
        arr.push({ x, y });
        angle += angleInc;
      }
      r++;
    }
    return arr[index];
  }

  return getDotPosition;
}