Smallest Enclosing Ellipses - Fast and Exact

The problem of nding the smallest enclosing ellipsoid of an n-point set P in d-space is an instance of convex programming and can be solved by general methods in time O(n) if the dimension is xed. The problem-speciic parts of these methods are encapsulated in primitive operations that deal with subproblems of constant size. We derive explicit formulae for the primitive operations of Welzl's randomized method 22] in dimension d = 2. Compared to previous ones, these formulae are simpler and faster to evaluate, and they only contain rational expressions, allowing for an exact solution.