Formula to calculate if a point is on a dash or a gap

Question

I'm looking for a formula to check if a point on a dashed line of any length either falls onto a dash or gap.

My approach is to use the following formula

/**
 * @param t The point to check
 * @param dash The length of a dash
 * @param gap The length of a gap
 */
function isOnDash(t, dash, gap) {
  const verticalOffset = 1 - gap / (dash + gap);
  const period = (2 * Math.PI) / (dash + gap);
  const phase = Math.asin(-verticalOffset) / period;

  return Math.sin(period * (t + phase)) + verticalOffset >= 0;
}

This nearly works, but it's not 100% accurate. Here is a JSFiddle that shows this approach in comparison to a drawing a dashed line on a HTML canvas element.

Answer 1

This is an arithmetic problem, not a problem with continuous numbers. As much as possible, you should avoid floating-points and functions like Math.sin or floating-point division, which will unavoidably result in approximation errors.

Instead, modulo is a simple arithmetic answer to your problem.

/**
 * @param t The point to check
 * @param dash The length of a dash
 * @param gap The length of a gap
 */
function isOnDash(t, dash, gap) {
  return (t % (dash + gap)) < dash;
}