With the advent of contemporary GPUs, it has been possible to perform volume deformation at interactive rates. In particular, it has been shown that deformation can be important for the purposes of illustration. In such cases, rather than being the result of a physically-based simulation, volume deformation is often goal-oriented and user-guided. For this purpose, it is important to provide the user with tools for directly specifying a deformation interactively and refine it based on constraints or user intention. In many cases, deformation is obtained based on a reference object or image. In this paper, we present a method for deforming volumetric objects based on user guided scattered data interpolation. A GPU-based implementation enables real-time manipulation of 2D images and volumes. We show how this approach can have applications in scientific illustration, volume exploration and visualization, generation of animations and special effects, among others.