We have contributed an efficient, object-oriented implementation of 3D nonlinear transformations to the Visualization Toolkit that can be applied to a wide variety of data types, including images and polygonal meshes. The transformations are performed via thin-plate splines or via interpolation of a regular lattice of displacement vectors, and are part of a framework that is easily extensible to other nonlinear transformation types. In this paper we demonstrate application of these transformations in medical imaging in general and image-guided surgery in particular, and present a series of performance benchmarks.