Concatenation and convex hull

6.2.11 Concatenation and convex hull

kc_interval<T> concatenated(const kc_interval<T>& o) const; 
kc_interval<T>& concatenate(const kc_interval<T>& o); 
 
kc_interval<T> concatenated_radius(const kc_interval<T>& o) const; 
kc_interval<T>& concatenate_radius(const kc_interval<T>& o);

These functions compute the hull of the current and a further interval, $A,B∈ KC$ such that $A,B ∈X$ for the resulting interval $X ∈ KC$ . This is done in one of two ways:

By adjusting the center point to the middle of $A$ and $B$ and computing a radius that encompasses both.
By leaving the center point of $A$ in place and just expanding the radius to encompass $B$ also.

concatenated(const kc_interval<T>&): Return a new interval, that contains the hull of both the current and the argument supplied interval.
concatenate(const kc_interval<T>&): Expand the current interval such that it also contains the supplied interval. This operation will change the center point.
concatenated_radius(const kc_interval<T>&): Return a new interval with the radius expanded to encompass $B$ . The center point will be that of the current interval.
concatenate_radius(const kc_interval<T>&): Expand the radius of the current interval to encompass $B$ . The center point will remain unchanged.

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