Calculate what 1 world unit would be in pixels at 3D point

Questions
1

I’m trying to display 3D in 2D HTML canvas making use of Three.js. I can calculate the 2D screen coordinate of a 3D point with:

function project(vector, camera, width, height){
  const v = vector.clone().project(camera);
  return new Vector2(Math.round((v.x + 1) * width / 2), Math.round((-v.y + 1) * height / 2));
}

I want to draw a circle with a radius of 1 world unit at that point and work out what it would be in pixels. I could project another point that is 1 world unit away. Another method is to use trigonometry:

function projectionScale(fieldOfView, distanceFromCameraInWorldUnits, heightInPx) {
  const focalLength = (heightInPx / 2) / Math.tan(fieldOfView / 2);
  if (distanceFromCameraInWorldUnits === 0) {
    return heightInPx / 2;
  } else {
    return (focalLength * 64) / distanceFromCameraInWorldUnits;
  }
}

I’m having to make use of an arbitrary constant 64 so it comes close to the first method so there is something wrong with it.

2

I think I figured it out:

function projectionScale(fieldOfView, distanceFromCameraInWorldUnits, heightInPx) {
  return heightInPx / (distanceFromCameraInWorldUnits * Math.tan(fieldOfView / 2) * 2);
}