A special scattered data interpolation technique is introduced. The interpolation problem is converted to a higher order auxiliary PDE, typically to an iterated Laplace or Helmholtz equation. To solve this PDE, robust multilevel methods are used which are based on a quadtree/octtree subdivision algorithm. Thus, the solution of large interpolation equations are avoided. Using this interpolation method, meshless techniques are constructed which require a set of boundary points only, without any structure. Theoretical results as well as numerical examples are also presented.