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Distance zero corresponds to the boundary of the ellipsoid and then it follows a path perpendicular to it. The black line is for ellipsoid a (sphere); the red lines are for ellipsoid b and the blue lines are for ellipsoid c. In ellipsoids b and c we have two lines, the upper one following a path perpendicular to the ellipsoid's axis and the lower one following a path parallel to the ellipsoid's axis.
