Determine the radius of the minimum sized circle that encompasses all the points.
Per Smallest Sphere Paper this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.
Input: Points (eg [0 0;0 1;2 0]) Minimum of 3 points
Output: r (radius of optimally centered circle)
Example: [0 0;0 1;2 0] yields [xc,yc,r] [1 .5 1.118] Output r=1.118
Theory: Best Circumcircle may occur in two ways:
1) Center of Line connecting pair with maximum separation, or
2) A circle utilizing three points from the set
Warning: Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.