title: Computing the 3D coordinates on a unit sphere from a 2D point
body: <p>I have a square bitmap of a circle and I want to compute the normals of all the pixels in that circle as if it were a sphere of radius 1:</p>
  
  <p><img src="https://i.stack.imgur.com/TU6ie.png" alt="enter image description here"></p>
  
  <p>The sphere/circle is centered in the bitmap.</p>
  
  <p>What is the equation for this?</p>