The Atan2 Function

June 16, 2018

3 min read

The inverse tangent function, Math.atan(), is useful to calculate the angle of a provided ratio of a sides of a triangle (like a velocity vector's x and y values). This can be useful to find the angle an object should be rotated to face in the direction it's moving, Math.atan(velocity.y/velocity.x).

The normal arctangent function has a couple issues though for this use case:

• In other programming languages, dividing by zero will cause an error if the x value of the vector (when moving horizontally). In JavaScript, this division returns the Inifinity number which Math.atan() can actually handle correctly.
• The arctangent function's domain is -π/2 to π/2 radians (-90° to 90°). This means it cannot distinguish between {x: 1, y: 1} and {x: -1, y: -1}. Math.atan(y/x) both evalute to 0.785 radians (45°).

This is where the arctangent2 function comes in handy. Math.atan2(y, x) functions the same way as the Math.atan(y/x) function with a special exception. This function has a domain of -π to π radians (-180° to 180°). Revisiting the earlier example, {x: 1, y: 1} and {x: -1, y: -1} evaluate to 0.785 radians (45°) and -2.356 radians (-135°) respectively. This allows you to correctly orient an object to any velocity vector in a circle.

#examples

// Returns an angle in degrees representing the facing of an object with the given velocity
function convertVelocityToAngle(velocity) {
  const { x, y } = velocity;

  return Math.atan2(y, x) * (180 / Math.PI);
}

#sources

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/atan2 https://gamedev.stackexchange.com/questions/14602/what-are-atan-and-atan2-used-for-in-games