title: Calculate centre of sphere whose surface contains 4 points (C#)
body: <p>I am using a 3D Voronoi library called MIConvexHull, which calculates a 3D Voronoi diagram for a series of points in 3D space.  However, it does not provide high-level information about the structure of the Voronoi diagram; the reported edges are simply a list of coordinate pairs which then have to have the circumcentre calculated.</p>
  
  <p>Now the library provides an implementation of the circumcentre calculation for a series of 2D points.  As you can see here, the coordinate pairs for the start (orange) and end (green) are shown:</p>
  
  <p><img src="https://i.stack.imgur.com/0ZCrr.png" alt="Edge coordinate pairs"></p>
  
  <p>You can visually see that if you take the vertexes listed in each of the edges and you make a circle such that the circumference of that circle touches all of the edges, the centre is where the edge starts.</p>
  
  <p>The <em>problem</em> that I have is that my points are 3D and thus it won't be the centre of a circle that's returned, but the centre of a <em>sphere</em>.  Unfortunately, advanced mathematics is not something that my head can really handle that well, so I have no idea how to approach this problem.</p>
  
  <p><strong>How, given 4 points in 3D space, can I get the centre of a sphere such that all of the points lie on the surface of the sphere?</strong></p>
  
  <p><em>EDIT:</em> In 3D, there will be 4 points provided, not 3.</p>