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Consider the problem of finding the coordinates of a point
that lie on the surface
, is inside the
sphere centered at (-1,-1,0) of radius 1 and is the closest possible
to the center of this sphere, with the constraint that
lie in the range [-2,2]. Thus we have:

With `epsilonf`=0.0001 we find out that the point is located at
at (-0.747,-0.747,0.086059) which is well inside the sphere and that
the minimal distance is 0.13529.
We may also compute the minimal distance not to a point but to a line segment,
for example
defined by
, , . In that case the optimum
function in the
evaluation procedure may be defined as:

Sqr(x+INTERVAL(0.9,1.1))+Sqr(y+1)+Sqr(z)

and with `epsilonf`=0.0001 the algorithm will return that the
minimal distance lie in the range [0.0907,0.1925].

Jean-Pierre Merlet
2012-12-20