On the computation of the minimal ellipse enclosing a set of planar curves

A method of finding the precise ellipse of minimal area, enclosing a finite set of regular planar curves (and points), is presented. We start with a direct approach of prescribing the problem using a set of algebraic constraints and solving them. This approach turns out to be intractable using contemporary memory support and computing power and several improvements are presented to alleviate these difficulties: the number of degrees of freedom and constraints is limited and the search domain is restricted. As a result, an alternative set of algebraic constraints is created whose solution is found in a reasonable amount of memory size and/or computing time.