def get_min_distance(self, mesh):
        """
        For each point in ``mesh`` compute the minimum distance to each
        surface element and return the smallest value.

        See :meth:`superclass method
        <.base.BaseSurface.get_min_distance>`
        for spec of input and result values.
        """
        dists = [surf.get_min_distance(mesh) for surf in self.surfaces]

        return numpy.min(dists, axis=0)