distance Function

   pure function distance(self, point)
   !< Compute the (minimum) distance from a point to the triangulated surface.
   class(aabb_tree_object), intent(in) :: self            !< AABB tree.
   type(vector_R8P),        intent(in) :: point           !< Point coordinates.
   real(R8P)                           :: distance        !< Minimum distance from point to the triangulated surface.
   real(R8P), allocatable              :: distance_(:)    !< Minimum distance, temporary buffer.
   integer(I4P), allocatable           :: aabb_closest(:) !< Index of closest AABB.
   integer(I4P)                        :: level           !< Counter.
   integer(I4P)                        :: b, bb, bbb      !< Counter.

   associate(node=>self%node)
      allocate(distance_(0:self%refinement_levels))
      allocate(aabb_closest(0:self%refinement_levels))
      distance_ = MaxR8P
      aabb_closest = -1
      do level=0, self%refinement_levels                  ! loop over refinement levels
         b = first_node(level=level)                      ! first node at finest level
         do bb=1, nodes_number_at_level(level=level)      ! loop over nodes at level
            bbb = b + bb - 1                              ! node numeration in tree
            if (node(bbb)%is_allocated()) then
               distance = node(bbb)%distance(point=point) ! node distance
               if (distance <= distance_(level)) then
                  distance_(level) = distance             ! update minimum distance
                  aabb_closest(level) = bbb               ! store closest node
               endif
            endif
         enddo
      enddo
      distance = MaxR8P
      do level=0, self%refinement_levels
         if (aabb_closest(level) >= 0) then
            distance = min(distance, node(aabb_closest(level))%distance_from_facets(point=point))
         endif
      enddo
   endassociate
   endfunction distance