cartesianToPolar for SVG circle / inverse of polartoCartesian-CodePudding

I've seen this function floating around:

function polarToCartesian(centerX, centerY, radius, angleInDegrees) {
  var angleInRadians = (angleInDegrees-90) * Math.PI / 180.0;

  return {
    x: centerX   (radius * Math.cos(angleInRadians)),
    y: centerY   (radius * Math.sin(angleInRadians))
  };
}

It works fine for my purposes - determining the absolute X, Y coordinates for the given angle on a circle having centerX, centerY and radius. It works for 360, 0, 180 — all valid SVG values.

Geometry is not my strong suit, but I have not found, nor am I able to write, a function which takes a similar description of the circle, and X, Y coordinates on its circumference (e.g. as output by polarToCartesian), and returns an answer corresponding to angleInDegrees, with no fudging. I am looking for a pair of functions with a 1->1 correspondence.

CodePudding user response：

Math.atan2(Y-centerY, X-centerX) * 180 /  Math.PI

gives you angle of point X,Y relative to center.

Note that in your formula (angleInDegrees-90) causes X/Y exchange (like you count angles from vertical axis). If you need this, add 90 to result.

Also atan2 domain is -Pi..Pi (-180..180). If you need only positive angles, add 360 if result is negative.

Seems you need this result:

 (Math.atan2(Y-centerY, X-centerX) * 180 /  Math.PI   450) % 360