Calculation of euler angles

Question

I need help understanding the math behind this code. x component of the returned vec2 and the y component of the returned vec2. Can somebody explain to me what they represent. I only know this function determinate the position of the vector in sphere coordinates.

glm::vec2 calcEulerAngles(const glm::vec3& vec)
{
  glm::vec3 v = glm::normalize(vec);
  glm::vec2 result(acos(v.z), atan2(v.y, v.x));
  while (result.y < 0.0)
    result.y += TwoPi;

  return glm::vec2(glm::degrees(result.x), glm::degrees(result.y));
}

Answer 1

It is calculating the spherical coordinates phi and theta for a unit vector.

The first component (phi) will be the angle between the vector and the z-axis. The second component (theta) will be the angle on the xy-plane. It assumes that the vector can be expressed as follows:

x = cos theta sin phi
y = sin theta sin phi
z =           cos phi

If you solve this, you get the calculations in your function. Adding 2 Pi to y just ensures that the angle is between 0 and 2 Pi.